Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Bogner, Scott; Bulgac, Aurel; Carlson, Joseph A.; Engel, Jonathan; Fann, George; Furnstahl, Richard J.; Gandolfi, Stefano; Hagen, Gaute; Horoi, Mihai; Johnson, Calvin W.; Kortelainen, Markus; Lusk, Ewing; Maris, Pieter; Nam, Hai Ah; Navratil, Petr
2013-01-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Computational nuclear quantum many-body problem: The UNEDF project
Bogner, S.; Bulgac, A.; Carlson, J.; Engel, J.; Fann, G.; Furnstahl, R. J.; Gandolfi, S.; Hagen, G.; Horoi, M.; Johnson, C.; Kortelainen, M.; Lusk, E.; Maris, P.; Nam, H.; Navratil, P.; Nazarewicz, W.; Ng, E.; Nobre, G. P. A.; Ormand, E.; Papenbrock, T.; Pei, J.; Pieper, S. C.; Quaglioni, S.; Roche, K. J.; Sarich, J.; Schunck, N.; Sosonkina, M.; Terasaki, J.; Thompson, I.; Vary, J. P.; Wild, S. M.
2013-10-01
The UNEDF project was a large-scale collaborative effort that applied high-performance computing to the nuclear quantum many-body problem. The primary focus of the project was on constructing, validating, and applying an optimized nuclear energy density functional, which entailed a wide range of pioneering developments in microscopic nuclear structure and reactions, algorithms, high-performance computing, and uncertainty quantification. UNEDF demonstrated that close associations among nuclear physicists, mathematicians, and computer scientists can lead to novel physics outcomes built on algorithmic innovations and computational developments. This review showcases a wide range of UNEDF science results to illustrate this interplay.
Semiclassical expansion of quantum characteristics for many-body potential scattering problem
International Nuclear Information System (INIS)
Krivoruchenko, M.I.; Fuchs, C.; Faessler, A.
2007-01-01
In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in ℎ. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on conservation of the phase-space volume and the Poincare theorem on conservation of 2p-forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior. (Abstract Copyright [2007], Wiley Periodicals, Inc.)
Nucleon many-body problem using quantum-mechanical few-body technique
International Nuclear Information System (INIS)
Horiuchi, Wataru
2016-01-01
A nucleus is treated as a quantum-mechanical many-body system consisting of protons and neutrons that interact with each other by nuclear force. This paper explains the variational calculation using the correlated basis function as a powerful technique for obtaining the precise solution of Schroedinger equation of many-body, and tries to understand the nucleon many-body system from the viewpoint of a few-body through the application cases of various nuclear systems. It describes the important correlation that characterizes the nucleon many-body system such as the mean field, cluster, and tensor of bound state, and shows that non-bound state is also describable. Since such precise theory is mantic, it is essential for explaining the nature of unknown unstable nuclei, and for determining the nuclear reaction rate under the environment of the stars difficult for experiment. The method is general and flexible, and can be applied to various quantum-mechanical many-body problems. For example, the multi-body calculation of atoms and molecules, hypernuclei, and hadron spectroscopy can be carried out only by changing the potential and particles. (A.O.)
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
International Nuclear Information System (INIS)
Batchelor, M T
2005-01-01
A key element of theoretical physics is the conceptualisation of physical phenomena in terms of models, which are then investigated by the tools at hand. For quantum many-body systems, some models can be exactly solved, i.e., their physical properties can be calculated in an exact fashion. There is often a deep underlying reason why this can be done-the theory of integrability-which manifests itself in many guises. In Beautiful models, Bill Sutherland looks at exactly solved models in quantum many-body systems, a well established field dating back to Bethe's 1931 exact solution of the spin-1/2 Heisenberg chain. This field is enjoying a renaissance due to the ongoing and striking experimental advances in low-dimensional quantum physics, which includes the manufacture of quasi one-dimensional quantum gases. Apart from the intrinsic beauty of the subject material, Beautiful Models is written by a pioneering master of the field. Sutherland has aimed to provide a broad textbook style introduction to the subject for graduate students and interested non-experts. An important point here is the 'language' of the book. In Sutherland's words, the subject of exactly solved models 'belongs to the realm of mathematical physics-too mathematical to be 'respectable' physics, yet not rigorous enough to be 'real' mathematics. ...there are perennial attempts to translate this body of work into either respectable physics or real mathematics; this is not that sort of book.' Rather, Sutherland discusses the models and their solutions in terms of their 'intrinisic' language, which is largely as found in the physics literature. The book begins with a helpful overview of the contents and then moves on to the foundation material, which is the chapter on integrability and non-diffraction. As is shown, these two concepts go hand in hand. The topics covered in later chapters include models with δ-function potentials, the Heisenberg spin chain, the Hubbard model, exchange models, the Calogero
Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems
Energy Technology Data Exchange (ETDEWEB)
Batchelor, M T [Department of Theoretical Physics, RSPSE and Department of Mathematics, MSI, Australian National University, Canberra ACT 0200 (Australia)
2005-04-08
A key element of theoretical physics is the conceptualisation of physical phenomena in terms of models, which are then investigated by the tools at hand. For quantum many-body systems, some models can be exactly solved, i.e., their physical properties can be calculated in an exact fashion. There is often a deep underlying reason why this can be done-the theory of integrability-which manifests itself in many guises. In Beautiful models, Bill Sutherland looks at exactly solved models in quantum many-body systems, a well established field dating back to Bethe's 1931 exact solution of the spin-1/2 Heisenberg chain. This field is enjoying a renaissance due to the ongoing and striking experimental advances in low-dimensional quantum physics, which includes the manufacture of quasi one-dimensional quantum gases. Apart from the intrinsic beauty of the subject material, Beautiful Models is written by a pioneering master of the field. Sutherland has aimed to provide a broad textbook style introduction to the subject for graduate students and interested non-experts. An important point here is the 'language' of the book. In Sutherland's words, the subject of exactly solved models 'belongs to the realm of mathematical physics-too mathematical to be 'respectable' physics, yet not rigorous enough to be 'real' mathematics. ...there are perennial attempts to translate this body of work into either respectable physics or real mathematics; this is not that sort of book.' Rather, Sutherland discusses the models and their solutions in terms of their 'intrinisic' language, which is largely as found in the physics literature. The book begins with a helpful overview of the contents and then moves on to the foundation material, which is the chapter on integrability and non-diffraction. As is shown, these two concepts go hand in hand. The topics covered in later chapters include models with {delta}-function potentials, the
Pion propagator in relativistic quantum field theories of the nuclear many-body problem
International Nuclear Information System (INIS)
Matsui, T.; Serot, B.D.
1982-01-01
Pion interactions in the nuclear medium are studied using renormalizable relativistic quantum field theories. Previous studies using pseudoscalar πN coupling encountered difficulties due to the large strength of the πNN vertex. We therefore formulate renormalizable field theories with pseudovector πN coupling using techniques introduced by Weinberg and Schwinger. Calculations are performed for two specific models; the scalar-vector theory of Walecka, extended to include π and rho mesons in a non-chiral fashion, and the linear sigma-model with an additional neutral vector meson. Both models qualitatively reproduce low-energy πN phenomenology and lead to nuclear matter saturation in the relativistic Hartree formalism, which includes baryon vacuum fluctuations. The pions propagator is evaluated in the one-nucleon-loop approximation, which corresponds to a relativistic random-phase approximation built on the Hartree ground state. Virtual NN-bar loops are included, and suitable renormalization techniques are illustrated. The local-density approximation is used to compare the threshold pion self-energy to the s-wave pion-nucleus optical potential. In the non-chiral model, s-wave pion-nucleus scattering is too large in both pseudoscalar and pseudovector calculations, indicating that additional constraints must be imposed on the Lagrangian. In the chiral model, the threshold self-energy vanishes automatically in the pseudovector case, but does so for pseudoscalar coupling only if the baryon effective mass is chosen self-consistently Since extrapolation from free space to nuclear density can lead to large effects, pion propagation in the medium can determine which πN coupling is more suitable for the relativistic nuclear many-body problem. Conversely, pion interactions constrain the model Lagrangian and the nuclear matter equation of state. An approximately chiral model with pseudovector coupling is favored
Many-body problem in quantum mechanics and quantum statistical mechanics
International Nuclear Information System (INIS)
Lee, T.D.; Yang, C.N.
1983-01-01
This is a progress report on some work concerning the quantum mechanical calculation of the fugacity coefficients b/sub l/ (which correspond to the classical cluster integrals) of a Bose, a Fermi, and a Boltzmann gas at low temperatures. A binary collision expansion method is developed which allows for the systematic calculation of b/sub l/ as expansions in powers of a/λ, where a represents the parameters of the dimensions of length that characterize the low-energy two-body collision and λ is the thermal wavelength. To any power of (a/λ) the calculation of any specific b/sub l/ is reduced to a finite number of quadratures. The method, therefore, is the low-temperature counterpart of the high-temperature expansion of b/sub l/
CIME School on Quantum Many Body Systems
Rivasseau, Vincent; Solovej, Jan Philip; Spencer, Thomas
2012-01-01
The book is based on the lectures given at the CIME school "Quantum many body systems" held in the summer of 2010. It provides a tutorial introduction to recent advances in the mathematics of interacting systems, written by four leading experts in the field: V. Rivasseau illustrates the applications of constructive Quantum Field Theory to 2D interacting electrons and their relation to quantum gravity; R. Seiringer describes a proof of Bose-Einstein condensation in the Gross-Pitaevski limit and explains the effects of rotating traps and the emergence of lattices of quantized vortices; J.-P. Solovej gives an introduction to the theory of quantum Coulomb systems and to the functional analytic methods used to prove their thermodynamic stability; finally, T. Spencer explains the supersymmetric approach to Anderson localization and its relation to the theory of random matrices. All the lectures are characterized by their mathematical rigor combined with physical insights.
The relativistic atomic many-body problem
International Nuclear Information System (INIS)
Brown, G.E.
1987-01-01
Problems connected with the infinite negative energy sea of electrons in the atomic many-body problem are discussed. It is shown that as long as one works in mean-field approximations, wave functions do not need to suffer from continuum dissociation. Various effects from virtual pairs in the wave functions are discussed. (orig.)
Seniority in quantum many-body systems
International Nuclear Information System (INIS)
Van Isacker, P.
2010-01-01
The use of the seniority quantum number in many-body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah's original idea are discussed: seniority for identical nucleons in a single-j shell, its extension to the case of many, non-degenerate j shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose-Einstein condensates of atoms with spin.
The quantum mechanics of many-body systems
Thouless, David James; Brueckner, Keith A
1961-01-01
The Quantum Mechanics of Many-Body Systems provides an introduction to that field of theoretical physics known as """"many-body theory."""" It is concerned with problems that are common to nuclear physics, atomic physics, the electron theory of metals, and to the theories of liquid helium three and four, and it describes the methods which have recently been developed to solve such problems. The aim has been to produce a unified account of the field, rather than to describe all the parallel methods that have been developed; as a result, a number of important papers are not mentioned. The main
Nuclear many-body correlation dynamics--a nonperturbative approach in quantum many-body theory
International Nuclear Information System (INIS)
Wang Shunjin
1996-01-01
Based on the experimental results and theoretical experience in nuclear physics, the article has explored the basic physical ideas and theoretical methods in nuclear and quantum many-body correlation dynamics. The main theoretical results and important applications are introduced briefly. The paper addresses the fundamental ingredients and physical interpretation of theoretical results in a comprehensive way. Recent new results about correlation dynamics in quantum field theories are also presented. The perspectives of further application are viewed. (91 refs.)
Classical and quantum simulations of many-body systems
Energy Technology Data Exchange (ETDEWEB)
Murg, Valentin
2008-04-07
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new 'analog' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
Classical and quantum simulations of many-body systems
International Nuclear Information System (INIS)
Murg, Valentin
2008-01-01
This thesis is devoted to recent developments in the fields of classical and quantum simulations of many-body systems. We describe new classical algorithms that overcome problems apparent in conventional renormalization group and Monte Carlo methods. These algorithms make possible the detailed study of finite temperature properties of 2-D classical and 1-D quantum systems, the investigation of ground states of 2-D frustrated or fermionic systems and the analysis of time evolutions of 2-D quantum systems. Furthermore, we propose new ''analog'' quantum simulators that are able to realize interesting models such as a Tonks-Girardeau gas or a frustrated spin-1/2 XY model on a trigonal lattice. These quantum simulators make use of optical lattices and trapped ions and are technically feasible. In fact, the Tonks-Girardeau gas has been realized experimentally and we provide a detailed comparison between the experimental data and the theoretical predictions. (orig.)
From few- to many-body quantum systems
Schiulaz, Mauro; Távora, Marco; Santos, Lea F.
2018-01-01
How many particles are necessary to make a many-body quantum system? To answer this question, we take as reference for the many-body limit a quantum system at half-filling and compare its properties with those of a system with $N$ particles, gradually increasing $N$ from 1. We show that the convergence of the static properties of the system with few particles to the many-body limit is fast. For $N \\gtrsim 4$, the density of states is already very close to Gaussian and signatures of many-body ...
The mean field in many body quantum physics
International Nuclear Information System (INIS)
Llano, M. de
1984-01-01
As an introduction to the quantum problem of many bodies we present a panoramic view of the most elementary theories called mean field theories. They comprise: i) the fermions ideal gas theory which implies, in a simple manner, the stability of white dwarf stars and of neutron stars, ii) the Hartree-Fock approximation for thermodynamical systems which is presented here in the context of a liquid-crystal phase transition, and iii) the Thomas-Fermi theory which is applied to the total binding energy of neutral atoms. (author)
EDITORIAL: Focus on Quantum Information and Many-Body Theory
Eisert, Jens; Plenio, Martin B.
2010-02-01
Quantum many-body models describing natural systems or materials and physical systems assembled piece by piece in the laboratory for the purpose of realizing quantum information processing share an important feature: intricate correlations that originate from the coherent interaction between a large number of constituents. In recent years it has become manifest that the cross-fertilization between research devoted to quantum information science and to quantum many-body physics leads to new ideas, methods, tools, and insights in both fields. Issues of criticality, quantum phase transitions, quantum order and magnetism that play a role in one field find relations to the classical simulation of quantum systems, to error correction and fault tolerance thresholds, to channel capacities and to topological quantum computation, to name but a few. The structural similarities of typical problems in both fields and the potential for pooling of ideas then become manifest. Notably, methods and ideas from quantum information have provided fresh approaches to long-standing problems in strongly correlated systems in the condensed matter context, including both numerical methods and conceptual insights. Focus on quantum information and many-body theory Contents TENSOR NETWORKS Homogeneous multiscale entanglement renormalization ansatz tensor networks for quantum critical systems M Rizzi, S Montangero, P Silvi, V Giovannetti and Rosario Fazio Concatenated tensor network states R Hübener, V Nebendahl and W Dür Entanglement renormalization in free bosonic systems: real-space versus momentum-space renormalization group transforms G Evenbly and G Vidal Finite-size geometric entanglement from tensor network algorithms Qian-Qian Shi, Román Orús, John Ove Fjærestad and Huan-Qiang Zhou Characterizing symmetries in a projected entangled pair state D Pérez-García, M Sanz, C E González-Guillén, M M Wolf and J I Cirac Matrix product operator representations B Pirvu, V Murg, J I Cirac
Quantum theory of many-body systems techniques and applications
Zagoskin, Alexandre
2014-01-01
This text presents a self-contained treatment of the physics of many-body systems from the point of view of condensed matter. The approach, quite traditionally, uses the mathematical formalism of quasiparticles and Green’s functions. In particular, it covers all the important diagram techniques for normal and superconducting systems, including the zero-temperature perturbation theory and the Matsubara, Keldysh and Nambu-Gor'kov formalism, as well as an introduction to Feynman path integrals. This new edition contains an introduction to the methods of theory of one-dimensional systems (bosonization and conformal field theory) and their applications to many-body problems. Intended for graduate students in physics and related fields, the aim is not to be exhaustive, but to present enough detail to enable the student to follow the current research literature, or to apply the techniques to new problems. Many of the examples are drawn from mesoscopic physics, which deals with systems small enough that quantum...
Mathematical methods of many-body quantum field theory
Lehmann, Detlef
2004-01-01
Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theory, functional integral methods, bosonic and fermionic, and estimation and summation techniques for Feynman diagrams. Among the physical effects discussed in this context are BCS superconductivity, s-wave and higher l-wave, and the fractional quantum Hall effect. While the presentation is mathematically rigorous, the author does not focus solely on precise definitions and proofs, but also shows how to actually perform the computations.Presenting many recent advances and clarifying difficult concepts, this book provides the background, results, and detail needed to further explore the issue of when the standard approximation schemes in this field actually work and wh...
Detecting a many-body mobility edge with quantum quenches
Directory of Open Access Journals (Sweden)
Piero Naldesi, Elisa Ercolessi, Tommaso Roscilde
2016-10-01
Full Text Available The many-body localization (MBL transition is a quantum phase transition involving highly excited eigenstates of a disordered quantum many-body Hamiltonian, which evolve from "extended/ergodic" (exhibiting extensive entanglement entropies and fluctuations to "localized" (exhibiting area-law scaling of entanglement and fluctuations. The MBL transition can be driven by the strength of disorder in a given spectral range, or by the energy density at fixed disorder - if the system possesses a many-body mobility edge. Here we propose to explore the latter mechanism by using "quantum-quench spectroscopy", namely via quantum quenches of variable width which prepare the state of the system in a superposition of eigenstates of the Hamiltonian within a controllable spectral region. Studying numerically a chain of interacting spinless fermions in a quasi-periodic potential, we argue that this system has a many-body mobility edge; and we show that its existence translates into a clear dynamical transition in the time evolution immediately following a quench in the strength of the quasi-periodic potential, as well as a transition in the scaling properties of the quasi-stationary state at long times. Our results suggest a practical scheme for the experimental observation of many-body mobility edges using cold-atom setups.
Quantum Markov processes and applications in many-body systems
International Nuclear Information System (INIS)
Temme, P. K.
2010-01-01
This thesis is concerned with the investigation of quantum as well as classical Markov processes and their application in the field of strongly correlated many-body systems. A Markov process is a special kind of stochastic process, which is determined by an evolution that is independent of its history and only depends on the current state of the system. The application of Markov processes has a long history in the field of statistical mechanics and classical many-body theory. Not only are Markov processes used to describe the dynamics of stochastic systems, but they predominantly also serve as a practical method that allows for the computation of fundamental properties of complex many-body systems by means of probabilistic algorithms. The aim of this thesis is to investigate the properties of quantum Markov processes, i.e. Markov processes taking place in a quantum mechanical state space, and to gain a better insight into complex many-body systems by means thereof. Moreover, we formulate a novel quantum algorithm which allows for the computation of the thermal and ground states of quantum many-body systems. After a brief introduction to quantum Markov processes we turn to an investigation of their convergence properties. We find bounds on the convergence rate of the quantum process by generalizing geometric bounds found for classical processes. We generalize a distance measure that serves as the basis for our investigations, the chi-square divergence, to non-commuting probability spaces. This divergence allows for a convenient generalization of the detailed balance condition to quantum processes. We then devise the quantum algorithm that can be seen as the natural generalization of the ubiquitous Metropolis algorithm to simulate quantum many-body Hamiltonians. By this we intend to provide further evidence, that a quantum computer can serve as a fully-fledged quantum simulator, which is not only capable of describing the dynamical evolution of quantum systems, but
General many-body formalism for composite quantum particles.
Combescot, M; Betbeder-Matibet, O
2010-05-21
This Letter provides a formalism capable of exactly treating Pauli blocking between n-fermion particles. This formalism is based on an operator algebra made of commutators and anticommutators which contrasts with the usual scalar formalism of Green functions developed half a century ago for elementary quantum particles. We also provide the diagrams which visualize the very specific many-body physics induced by fermion exchanges between composite quantum particles.
Efficient tomography of a quantum many-body system
Lanyon, B. P.; Maier, C.; Holzäpfel, M.; Baumgratz, T.; Hempel, C.; Jurcevic, P.; Dhand, I.; Buyskikh, A. S.; Daley, A. J.; Cramer, M.; Plenio, M. B.; Blatt, R.; Roos, C. F.
2017-12-01
Quantum state tomography is the standard technique for estimating the quantum state of small systems. But its application to larger systems soon becomes impractical as the required resources scale exponentially with the size. Therefore, considerable effort is dedicated to the development of new characterization tools for quantum many-body states. Here we demonstrate matrix product state tomography, which is theoretically proven to allow for the efficient and accurate estimation of a broad class of quantum states. We use this technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled and individually controlled spins: a size far beyond the practical limits of quantum state tomography. Our results reveal the dynamical growth of entanglement and describe its complexity as correlations spread out during a quench: a necessary condition for future demonstrations of better-than-classical performance. Matrix product state tomography should therefore find widespread use in the study of large quantum many-body systems and the benchmarking and verification of quantum simulators and computers.
Experimental statistical signature of many-body quantum interference
Giordani, Taira; Flamini, Fulvio; Pompili, Matteo; Viggianiello, Niko; Spagnolo, Nicolò; Crespi, Andrea; Osellame, Roberto; Wiebe, Nathan; Walschaers, Mattia; Buchleitner, Andreas; Sciarrino, Fabio
2018-03-01
Multi-particle interference is an essential ingredient for fundamental quantum mechanics phenomena and for quantum information processing to provide a computational advantage, as recently emphasized by boson sampling experiments. Hence, developing a reliable and efficient technique to witness its presence is pivotal in achieving the practical implementation of quantum technologies. Here, we experimentally identify genuine many-body quantum interference via a recent efficient protocol, which exploits statistical signatures at the output of a multimode quantum device. We successfully apply the test to validate three-photon experiments in an integrated photonic circuit, providing an extensive analysis on the resources required to perform it. Moreover, drawing upon established techniques of machine learning, we show how such tools help to identify the—a priori unknown—optimal features to witness these signatures. Our results provide evidence on the efficacy and feasibility of the method, paving the way for its adoption in large-scale implementations.
International Nuclear Information System (INIS)
Levin, F.S.; Krueger, H.
1977-01-01
We propose in this article that the non-Hermitian equations typical of some many-body scattering theories be used to help solve many-body bound-state problems. The basic idea is to exploit the channel nature of many-body bound states that must exist because bound states are obvious negative-energy extensions of scattering states. Since atomic, molecular, and nuclear systems all display multichannel effects for E > 0, at least through Pauli-principle effects if not through mass-transfer reactions, this use of positive-energy methods for solving bound-state problems could have wide applicability. The development used here is based on the channel-component-state method of the channel-coupling-array theory, recently described in detail for the E > 0 case, and various aspects of the formalism are discussed. Detailed calculations using simple approximations are discussed for H 2 + , one of the simplest systems displaying channel structure. Comparison with the exact, Born-Oppenheimer results of Wind show that the non-Hermitian-equation, channel-component values of the equilibrium separation and total binding energy are accurate to within 2%, while the dissociation energy is accurate to 10%. The resulting wave function is identical to that arising from the simplest MO calculation, for which these numbers are less accurate than the preceding by at least a factor of 3. We also show that identical particle symmetry for the H 2 + case reduces the pair of coupled (two-channel) equations to a single equation with an exchange term. Similar reductions will occur for larger numbers of identical particles, thus suggesting application of the formalism to atomic structure problems. A detailed analysis of the present numerical results, their general implications, and possible applications is also given
Nonlinear Quantum Metrology of Many-Body Open Systems
Beau, M.; del Campo, A.
2017-07-01
We introduce general bounds for the parameter estimation error in nonlinear quantum metrology of many-body open systems in the Markovian limit. Given a k -body Hamiltonian and p -body Lindblad operators, the estimation error of a Hamiltonian parameter using a Greenberger-Horne-Zeilinger state as a probe is shown to scale as N-[k -(p /2 )], surpassing the shot-noise limit for 2 k >p +1 . Metrology equivalence between initial product states and maximally entangled states is established for p ≥1 . We further show that one can estimate the system-environment coupling parameter with precision N-(p /2 ), while many-body decoherence enhances the precision to N-k in the noise-amplitude estimation of a fluctuating k -body Hamiltonian. For the long-range Ising model, we show that the precision of this parameter beats the shot-noise limit when the range of interactions is below a threshold value.
Many-body quantum simulation with Rydberg atoms and ions
International Nuclear Information System (INIS)
Mueller, M.
2010-01-01
This thesis presents my work that is located at the interface between the fields of atomic physics, quantum optics and quantum information. The work was performed at the Institute of Theoretical Physics of the University of Innsbruck and the Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences under the supervision of Prof. Peter Zoller. The main topic of this thesis is the investigation of new schemes for quantum simulation of interacting many-body systems. The thesis is divided into three parts, which cover my work on i) chains of trapped Rydberg ions ii) quantum information processing and simulation with Rydberg atoms and iii) quantum simulation with ground state ions. The first part of this thesis is concerned with the study of Rydberg ions trapped in a linear Paul trap. The properties of ionic Rydberg states in the presence of the static and time-dependent electric trapping fields are investigated. First it is analyzed under which conditions laser-excited Rydberg ions can be trapped in a stable configuration. Furthermore, it is shown that strong dipole-dipole interactions among the ions can be achieved by microwave dressing fields. These interactions can give rise to dynamics of Rydberg excitations through the ion crystal, which take place on a nanosecond timescale and can be described by effective spin-models. In addition, it is discussed how to achieve fast two-qubit entangling gates between pairs of Rydberg ions. In the second part of this thesis, novel possibilities of using neutral Rydberg atoms for quantum-information processing and quantum simulation are investigated. A new scheme for a multi-atom quantum gate is proposed and theoretically analyzed. This parallelized gate allows one to entangle a mesoscopic ensemble of atoms with a single control atom in a single step, with high fidelity and on a microsecond time scale. The operation relies on strong and long-ranged interactions between Rydberg atoms triggering a
Short history of nuclear many-body problem
International Nuclear Information System (INIS)
Köhler, H.S.
2014-01-01
This is a very short presentation regarding developments in the theory of nuclear many-body problems, as seen and experienced by the author during the past 60 years with particular emphasis on the contributions of Gerry Brown and his research-group. Much of his work was based on Brueckner's formulation of the nuclear many-body problem. It is reviewed briefly together with the Moszkowski–Scott separation method that was an important part of his early work. The core polarisation and his work related to effective interactions in general are also addressed
Many body quantum physics at the condensed matter
International Nuclear Information System (INIS)
Llano, M. de
1981-01-01
The non-relativistic, continuous (as opposed to spin) many-body problem as it relates to condensed matter at absolute zero temperature is reviewed in simple, non-technical terms, mainly from the standpoint of infinite order perturbation theory, for physical systems where all the particles have the same mass but which otherwise interact with arbitrary short- or long-ranged two-body forces. (author)
Quantum simulations and many-body physics with light.
Noh, Changsuk; Angelakis, Dimitris G
2017-01-01
In this review we discuss the works in the area of quantum simulation and many-body physics with light, from the early proposals on equilibrium models to the more recent works in driven dissipative platforms. We start by describing the founding works on Jaynes-Cummings-Hubbard model and the corresponding photon-blockade induced Mott transitions and continue by discussing the proposals to simulate effective spin models and fractional quantum Hall states in coupled resonator arrays (CRAs). We also analyse the recent efforts to study out-of-equilibrium many-body effects using driven CRAs, including the predictions for photon fermionisation and crystallisation in driven rings of CRAs as well as other dynamical and transient phenomena. We try to summarise some of the relatively recent results predicting exotic phases such as super-solidity and Majorana like modes and then shift our attention to developments involving 1D nonlinear slow light setups. There the simulation of strongly correlated phases characterising Tonks-Girardeau gases, Luttinger liquids, and interacting relativistic fermionic models is described. We review the major theory results and also briefly outline recent developments in ongoing experimental efforts involving different platforms in circuit QED, photonic crystals and nanophotonic fibres interfaced with cold atoms.
Universality in driven-dissipative quantum many-body systems
International Nuclear Information System (INIS)
Sieberer, L.M.
2015-01-01
Recent experimental investigations of condensation phenomena in driven-dissipative quantum many-body systems raise the question of what kind of novel universal behavior can emerge under non-equilibrium conditions. We explore various aspects of universality in this context. Our results are of relevance for a variety of open quantum systems on the interface of quantum optics and condensed matter physics, ranging from exciton-polariton condensates to cold atomic gases. In Part I we characterize the dynamical critical behavior at the Bose-Einstein condensation phase transition in driven open quantum systems in three spatial dimensions. Although thermodynamic equilibrium conditions are emergent at low frequencies, the approach to this thermalized low-frequency regime is described by a critical exponent which is specific to the non-equilibrium transition, and places the latter beyond the standard classification of equilibrium dynamical critical behavior. Our theoretical approach is based on the functional renormalization group within the framework of Keldysh non-equilibrium field theory, which is equivalent to a microscopic description of the open system dynamics in terms of a many-body quantum master equation. Universal behavior in the coherence properties of driven-dissipative condensates in reduced dimensions is investigated in Part II. We show that driven two-dimensional Bose systems cannot exhibit algebraic order as in thermodynamic equilibrium, unless they are sufficiently anisotropic. However, we find evidence that even isotropic systems may have a finite superfluidity fraction. In one-dimensional systems, non-equilibrium conditions are traceable in the behavior of the autocorrelation function. We obtain these results by mapping the long-wavelength condensate dynamics onto the Kardar-Parisi-Zhang equation. In Part III we show that systems in thermodynamic equilibrium have a specific symmetry, which makes them distinct from generic driven open systems. The novel
Quantum many-body physics in a nutshell
Shuryak, Edward
2018-01-01
This book provides an essential introduction to the physics of quantum many-body systems, which are at the heart of atomic and nuclear physics, condensed matter, and particle physics. Unlike other textbooks on the subject, it covers topics across a broad range of physical fields―phenomena as well as theoretical tools―and does so in a simple and accessible way. Edward Shuryak begins with Feynman diagrams of the quantum and statistical mechanics of a particle―in these applications, the diagrams are easy to calculate and there are no divergencies. He discusses the renormalization group and illustrates its uses and covers systems such as weakly and strongly coupled Bose and Fermi gases, electron gas, nuclear matter, and quark-gluon plasmas. Phenomena include Bose condensation and superfluidity. Shuryak also looks at Cooper pairing and superconductivity for electrons in metals, liquid 3He, nuclear matter, and quark-gluon plasma. A recurring topic throughout is topological matter, ranging from ensembles of q...
Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet
Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.
2018-06-01
We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.
Quantum phase transition in strongly correlated many-body system
You, Wenlong
The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions (QPTs), driven by experimental advance on the cuprate superconductors, the heavy fermion materials, organic conductors, Quantum Hall effect, Fe-As based superconductors and other related compounds. It is clear that strong electronic interactions play a crucial role in the systems of current interest, and simple paradigms for the behavior of such systems near quantum critical points remain unclear. Furthermore, the rapid progress in Feshbach resonance and optical lattice provides a flexible platform to study QPT. Quantum Phase Transition (QPT) describes the non-analytic behaviors of the ground-state properties in a many-body system by varying a physical parameter at absolute zero temperature - such as magnetic field or pressure, driven by quantum fluctuations. Such quantum phase transitions can be first-order phase transition or continuous. The phase transition is usually accompanied by a qualitative change in the nature of the correlations in the ground state, and describing this change shall clearly be one of our major interests. We address this issue from three prospects in a few strong correlated many-body systems in this thesis, i.e., identifying the ordered phases, studying the properties of different phases, characterizing the QPT points. In chapter 1, we give an introduction to QPT, and take one-dimensional XXZ model as an example to illustrate the QPT therein. Through this simple example, we would show that when the tunable parameter is varied, the system evolves into different phases, across two quantum QPT points. The distinct phases exhibit very different behaviors. Also a schematic phase diagram is appended. In chapter 2, we are engaged in research on ordered phases. Originating in the work of Landau and Ginzburg on second-order phase transition, the spontaneous symmetry breaking induces nonzero expectation of field operator, e.g., magnetization M
Resonating-group method for nuclear many-body problems
International Nuclear Information System (INIS)
Tang, Y.C.; LeMere, M.; Thompson, D.R.
1977-01-01
The resonating-group method is a microscopic method which uses fully antisymmetric wave functions, treats correctly the motion of the total center of mass, and takes cluster correlation into consideration. In this review, the formulation of this method is discussed for various nuclear many-body problems, and a complex-generator-coordinate technique which has been employed to evaluate matrix elements required in resonating-group calculations is described. Several illustrative examples of bound-state, scattering, and reaction calculations, which serve to demonstrate the usefulness of this method, are presented. Finally, by utilization of the results of these calculations, the role played by the Pauli principle in nuclear scattering and reaction processes is discussed. 21 figures, 2 tables, 185 references
Genuine quantum correlations in quantum many-body systems: a review of recent progress.
De Chiara, Gabriele; Sanpera, Anna
2018-04-19
Quantum information theory has considerably helped in the understanding of quantum many-body systems. The role of quantum correlations and in particular, bipartite entanglement, has become crucial to characterise, classify and simulate quantum many body systems. Furthermore, the scaling of entanglement has inspired modifications to numerical techniques for the simulation of many-body systems leading to the, now established, area of tensor networks. However, the notions and methods brought by quantum information do not end with bipartite entanglement. There are other forms of correlations embedded in the ground, excited and thermal states of quantum many-body systems that also need to be explored and might be utilised as potential resources for quantum technologies. The aim of this work is to review the most recent developments regarding correlations in quantum many-body systems focussing on multipartite entanglement, quantum nonlocality, quantum discord, mutual information but also other non classical measures of correlations based on quantum coherence. Moreover, we also discuss applications of quantum metrology in quantum many-body systems. © 2018 IOP Publishing Ltd.
Nuclear many-body problem with repulsive hard core interactions
Energy Technology Data Exchange (ETDEWEB)
Haddad, L M
1965-07-01
The nuclear many-body problem is considered using the perturbation-theoretic approach of Brueckner and collaborators. This approach is outlined with particular attention paid to the graphical representation of the terms in the perturbation expansion. The problem is transformed to centre-of-mass coordinates in configuration space and difficulties involved in ordinary methods of solution of the resulting equation are discussed. A new technique, the 'reference spectrum method', devised by Bethe, Brandow and Petschek in an attempt to simplify the numerical work in presented. The basic equations are derived in this approximation and considering the repulsive hard core part of the interaction only, the effective mass is calculated at high momentum (using the same energy spectrum for both 'particle' and 'hole' states). The result of 0.87m is in agreement with that of Bethe et al. A more complete treatment using the reference spectrum method in introduced and a self-consistent set of equations is established for the reference spectrum parameters again for the case of hard core repulsions. (author)
Many-body physics with circuit quantum electrodynamics
International Nuclear Information System (INIS)
Leib, Martin H.
2015-01-01
We present proposals to simulate many-body physics with superconducting circuits. The ''body'' to work with for superconducting circuits is the microwave photon and interaction is induced by the nonlinearity of the Josephson effect. We present two different approaches to simulate Bose-Hubbard physics, one based on a polariton scheme and another with nonlinear resonators. We also present a Dicke-model like simulator for ultrastrongly coupled Josephson junctions to a resonator and show a scheme for implementing long range interactions.
Characterizing and quantifying frustration in quantum many-body systems.
Giampaolo, S M; Gualdi, G; Monras, A; Illuminati, F
2011-12-23
We present a general scheme for the study of frustration in quantum systems. We introduce a universal measure of frustration for arbitrary quantum systems and we relate it to a class of entanglement monotones via an exact inequality. If all the (pure) ground states of a given Hamiltonian saturate the inequality, then the system is said to be inequality saturating. We introduce sufficient conditions for a quantum spin system to be inequality saturating and confirm them with extensive numerical tests. These conditions provide a generalization to the quantum domain of the Toulouse criteria for classical frustration-free systems. The models satisfying these conditions can be reasonably identified as geometrically unfrustrated and subject to frustration of purely quantum origin. Our results therefore establish a unified framework for studying the intertwining of geometric and quantum contributions to frustration.
Introduction to modern methods of quantum many-body theory and their applications
Fantoni, Stefano; Krotscheck, Eckhard S
2002-01-01
This invaluable book contains pedagogical articles on the dominant nonstochastic methods of microscopic many-body theories - the methods of density functional theory, coupled cluster theory, and correlated basis functions - in their widest sense. Other articles introduce students to applications of these methods in front-line research, such as Bose-Einstein condensates, the nuclear many-body problem, and the dynamics of quantum liquids. These keynote articles are supplemented by experimental reviews on intimately connected topics that are of current relevance. The book addresses the striking l
Many-body problems in high temperature superconductivity
International Nuclear Information System (INIS)
Yu Lu.
1991-10-01
In this brief review the basic experimental facts about high T c superconductors are outlined. The superconducting properties of these superconductors are not very different from those of the ordinary superconductors. However, their normal state properties cannot be described by the standard Fermi liquid (FL) theory. Our current understanding of the strongly correlated models is summarized. In one dimension these systems behave like a ''Luttinger liquid'', very much distinct from the FL. In spite of the enormous efforts made in two-dimensional studies, the question of FL vs non-FL behaviour is still open. The numerical results as well as various approximation schemes are discussed. Both the single hole problem in a quantum antiferromagnet and finite doping regime are considered. (author). 104 refs, 9 figs
Ruelle resonances in quantum many-body dynamics
International Nuclear Information System (INIS)
Prosen, Tomaz
2002-01-01
We define a quantum Perron-Frobenius master operator over a suitable normed space of translationally invariant states adjoint to the quasi-local C* algebra of quantum lattice gasses (e.g. spin chains), whose spectrum determines the exponents of decay of time correlation functions. The theoretical ideas are applied to a generic example of kicked Ising spin 1/2 chains. We show that the 'chaotic eigenmodes' corresponding to leading eigenvalue resonances have fractal structure in the basis of local operators. (letter to the editor)
Quantum Many-Body Virial Theorem And Matsubara Green's Function
International Nuclear Information System (INIS)
Anma, D.; Fukuda, T.; Fujita, M.; Toyoda, T.; Takiuchi, K.
2004-01-01
We discuss the quantum field theoretical formulation of the virial theorem on the basis of the canonical field theory of the generalized coordinate transformation and show the equation of motion of a charged Fermion system coupled to an electromagnetic field. Possible application to Fermion-Boson mixtures is also discussed
Applications of quantum measurement in single and many body systems
International Nuclear Information System (INIS)
Steixner, V.
2010-01-01
This thesis contains a study about the influence of the back action of a signal emitted by a trapped ion onto itself. The continuous measurement signal is used to alter the motional state of the ion, corresponding to classical friction, in order to cool the ion. The quantum mechanical evolution of the ion with the help of stochastic Schroedinger- and master equations is explored, as well as experimental results. A second method of feedback to obtain the momentum necessary for cooling by means of electromagnetically induced transparency is discussed next. This method allows for a theoretical cooling down to the motional ground state. In a second part of the thesis, the measurement of particle currents in optical lattices is discussed. The usual method of measuring spatial correlations in a cold gas, the time-of-flight method, disadvantageously destroys the measured sample. Here a measurement scheme for atoms with an internal Lambda level structure, coupled with lasers as a Raman transition, is used instead. The measured photons are transformed with the help of homodyne detection into a continuous photon current proportional to the particle current. This thesis contains numerical and analytical calculations for this measurement process and the back action on the measured system. As an application example, the measurement of superfluid currents in a ring optical lattice is described, as well as the entanglement of two of these macroscopic quantum objects. (author) [de
International Nuclear Information System (INIS)
Kushnirenko, A.N.
1989-01-01
An attempt was made to substantiate statistical physics from the viewpoint of many-body quantum mechanics in the representation of occupation numbers. This approach enabled to develop the variation method for solution of stationary and nonstationary nonequilibrium problems
Collective motion in quantum many-body systems
Energy Technology Data Exchange (ETDEWEB)
Haemmerling, Jens
2011-06-07
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics. This allows us to derive the spreading for the collective coordinate from first principles. After that we study the interplay between collective and incoherent single-particle motion in a model of two chains of particles whose interaction comprises a non-integrable part. In the perturbative regime, but for a general form of the interaction, we calculate the Fourier transform of the time correlation for the collective coordinate. We obtain the remarkable result that it always has a unique semi-classical interpretation. We show this by a proper renormalization procedure which also allows us to map the non-integrable system to the integrable model of Caldeira-Leggett-type considered previously in which the bath is part of the system.
Many-body problem in one-dimension
International Nuclear Information System (INIS)
Emery, V.J.
1979-11-01
This work attempts to give a qualitative feeling for the more important physical ideas involved with the study of many-body systems in one dimension, and considers a particular strong-coupling model. This model provides an excellent description of the chains of mercury ions in Hg/sub 3-delta/AsF 6 ; some of the predictions of the theory can be checked by x-ray and neutron diffraction. Much of the physics of nearly one-dimensional materials is concerned with understanding the possible types of phase transition that may take place, and establishing the conditions in which one or another will be predominant. The most significant feature of purely one-dimensional systems is the dominant effect of fluctuations. The paper is organized as follows: introduction; qualitative aspects of one-dimensional systems (general survey, mathematical model, qualitative discussion of strong coupling - strong attractive U, strong repulsive U, large V); strong coupling between parallel spins (independent spin systems, coupling between opposite spins); mercury chains; electrons with arbitrary coupling; boson representations of operators; and classical Coulomb gas
Nonlocality in many-body quantum systems detected with two-body correlators
Energy Technology Data Exchange (ETDEWEB)
Tura, J., E-mail: jordi.tura@icfo.es [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Augusiak, R.; Sainz, A.B. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); Lücke, B.; Klempt, C. [Institut für Quantenoptik, Leibniz Universität Hannover, Welfengarten 1, D-30167 Hannover (Germany); Lewenstein, M.; Acín, A. [ICFO—Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona) (Spain); ICREA—Institució Catalana de Recerca i Estudis Avançats, Lluis Campanys 3, 08010 Barcelona (Spain)
2015-11-15
Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, “theorist- and experimentalist-friendly” many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Tura et al., Science 344 (2014) 1256]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states—ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures.
A New Class of Solvable Many-Body Problems
Directory of Open Access Journals (Sweden)
Francesco Calogero
2012-10-01
Full Text Available A new class of solvable N-body problems is identified. They describe N unit-mass point particles whose time-evolution, generally taking place in the complex plane, is characterized by Newtonian equations of motion ''of goldfish type'' (acceleration equal force, with specific velocity-dependent one-body and two-body forces featuring several arbitrary coupling constants. The corresponding initial-value problems are solved by finding the eigenvalues of a time-dependent N×N matrix U(t explicitly defined in terms of the initial positions and velocities of the N particles. Some of these models are asymptotically isochronous, i.e. in the remote future they become completely periodic with a period T independent of the initial data (up to exponentially vanishing corrections. Alternative formulations of these models, obtained by changing the dependent variables from the N zeros of a monic polynomial of degree N to its N coefficients, are also exhibited.
Quantum Simulation with Circuit-QED Lattices: from Elementary Building Blocks to Many-Body Theory
Zhu, Guanyu
Recent experimental and theoretical progress in superconducting circuits and circuit QED (quantum electrodynamics) has helped to develop high-precision techniques to control, manipulate, and detect individual mesoscopic quantum systems. A promising direction is hence to scale up from individual building blocks to form larger-scale quantum many-body systems. Although realizing a scalable fault-tolerant quantum computer still faces major barriers of decoherence and quantum error correction, it is feasible to realize scalable quantum simulators with state-of-the-art technology. From the technological point of view, this could serve as an intermediate stage towards the final goal of a large-scale quantum computer, and could help accumulating experience with the control of quantum systems with a large number of degrees of freedom. From the physical point of view, this opens up a new regime where condensed matter systems can be simulated and studied, here in the context of strongly correlated photons and two-level systems. In this thesis, we mainly focus on two aspects of circuit-QED based quantum simulation. First, we discuss the elementary building blocks of the quantum simulator, in particular a fluxonium circuit coupled to a superconducting resonator. We show the interesting properties of the fluxonium circuit as a qubit, including the unusual structure of its charge matrix elements. We also employ perturbation theory to derive the effective Hamiltonian of the coupled system in the dispersive regime, where qubit and the photon frequencies are detuned. The observables predicted with our theory, including dispersive shifts and Kerr nonlinearity, are compared with data from experiments, such as homodyne transmission and two-tone spectroscopy. These studies also relate to the problem of detection in a circuit-QED quantum simulator. Second, we study many-body physics of circuit-QED lattices, serving as quantum simulators. In particular, we focus on two different
Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory
Kos, Pavel; Ljubotina, Marko; Prosen, Tomaž
2018-04-01
A key goal of quantum chaos is to establish a relationship between widely observed universal spectral fluctuations of clean quantum systems and random matrix theory (RMT). Most prominent features of such RMT behavior with respect to a random spectrum, both encompassed in the spectral pair correlation function, are statistical suppression of small level spacings (correlation hole) and enhanced stiffness of the spectrum at large spectral ranges. For single-particle systems with fully chaotic classical counterparts, the problem has been partly solved by Berry [Proc. R. Soc. A 400, 229 (1985), 10.1098/rspa.1985.0078] within the so-called diagonal approximation of semiclassical periodic-orbit sums, while the derivation of the full RMT spectral form factor K (t ) (Fourier transform of the spectral pair correlation function) from semiclassics has been completed by Müller et al. [Phys. Rev. Lett. 93, 014103 (2004), 10.1103/PhysRevLett.93.014103]. In recent years, the questions of long-time dynamics at high energies, for which the full many-body energy spectrum becomes relevant, are coming to the forefront even for simple many-body quantum systems, such as locally interacting spin chains. Such systems display two universal types of behaviour which are termed the "many-body localized phase" and "ergodic phase." In the ergodic phase, the spectral fluctuations are excellently described by RMT, even for very simple interactions and in the absence of any external source of disorder. Here we provide a clear theoretical explanation for these observations. We compute K (t ) in the leading two orders in t and show its agreement with RMT for nonintegrable, time-reversal invariant many-body systems without classical counterparts, a generic example of which are Ising spin-1 /2 models in a periodically kicking transverse field. In particular, we relate K (t ) to partition functions of a class of twisted classical Ising models on a ring of size t ; hence, the leading-order RMT behavior
Probing quantum and thermal noise in an interacting many-body system
DEFF Research Database (Denmark)
Hofferberth, S.; Lesanovsky, Igor; Schumm, Thorsten
2008-01-01
of the shot-to-shot variations of interference-fringe contrast for pairs of independently created one-dimensional Bose condensates. Analysing different system sizes, we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from poissonian......The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum-mechanical noise reveals non-local correlations of the underlying many-body states. Here, we provide a complete experimental analysis....... Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system....
A quantum information perspective of fermionic quantum many-body systems
Energy Technology Data Exchange (ETDEWEB)
Kraus, Christina V.
2009-11-02
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS
A quantum information perspective of fermionic quantum many-body systems
International Nuclear Information System (INIS)
Kraus, Christina V.
2009-01-01
In this Thesis fermionic quantum many-body system are theoretically investigated from a quantum information perspective. Quantum correlations in fermionic many-body systems, though central to many of the most fascinating effects of condensed matter physics, are poorly understood from a theoretical perspective. Even the notion of ''paired'' fermions which is widely used in the theory of superconductivity and has a clear physical meaning there, is not a concept of a systematic and mathematical theory so far. Applying concepts and tools from entanglement theory, we close this gap, developing a pairing theory allowing to unambiguously characterize paired states. We develop methods for the detection and quantification of pairing according to our definition which are applicable to current experimental setups. Pairing is shown to be a quantum correlation distinct from any notion of entanglement proposed for fermionic systems, giving further understanding of the structure of highly correlated quantum states. In addition, we show the resource character of paired states for precision metrology, proving that BCS-states allow phase measurements at the Heisenberg limit. Next, the power of fermionic systems is considered in the context of quantum simulations, where we study the possibility to simulate Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range interactions we determine time evolutions which can and those which can not be simulated. Bosonic and finite-dimensional quantum systems (''spins'') are included in our investigations. Furthermore, we develop new techniques for the classical simulation of fermionic many-body systems. First, we introduce a new family of states, the fermionic Projected Entangled Pair States (fPEPS) on lattices in arbitrary spatial dimension. These are the natural generalization of the PEPS known for spin systems, and they
Determinant method and quantum simulations of many-body effects in a single impurity Anderson model
International Nuclear Information System (INIS)
Gubernatis, J.E.; Olson, T.; Scalapino, D.J.; Sugar, R.L.
1985-01-01
A short description is presented of a quantum Monte Carlo technique, often referred to as the determinant method, that has proved useful for simulating many-body effects in systems of interacting fermions at finite temperatures. Preliminary results using this technique on a single impurity Anderson model are reported. Examples of such many-body effects as local moment formation, Kondo behavior, and mixed valence phenomena found in the simulations are shown. 10 refs., 3 figs
Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
Imbrie, John Z
2016-01-01
We consider a weakly interacting quantum spin chain with random local interactions. We prove that many-body localization follows from a physically reasonable assumption that limits the extent of level attraction in the statistics of eigenvalues. In a KAM-style construction, a sequence of local unitary transformations is used to diagonalize the Hamiltonian by deforming the initial tensor product basis into a complete set of exact many-body eigenfunctions.
The many-body content of quantum gauge theories and its connection to mass generation mechanisms
International Nuclear Information System (INIS)
Natoli, C.R.; Palumbo, F.
1985-01-01
The aim of the paper is to get more knowledge about many-body systems and their properties, about many-body content of quantum gauge theories and its connection with mass generation mechanisms. The way to achieve this is to perform the galilean limit of the relativistic theory by sending the speed of light c to infinity. This limiting process exposes the low energy behaviour of the relativistic theory
Rotation of quantum impurities in the presence of a many-body environment
Lemeshko, Mikhail; Schmidt, Richard
2015-05-01
Pioneered by the seminal works of Wigner and Racah, the quantum theory of angular momentum evolved into a powerful machinery, commonly used to classify the states of isolated quantum systems and perturbations to their structure due to electromagnetic or crystalline fields. In ``realistic'' experiments, however, quantum systems are almost inevitably coupled to a many-particle environment and a field of elementary excitations associated with it, which is capable of fundamentally altering the physics of the system. We present the first systematic treatment of quantum rotation coupled to a many-particle environment. By using a series of canonical transformations on a generic microscopic Hamiltonian, we single out the conserved quantities of the problem. Using a variational ansatz accounting for an infinite number of many-body excitations, we characterize the spectrum of angular momentum eigenstates and identify the regions of instability, accompanied by emission of angular Cerenkov radiation. The developed technique can be applied to a wide range of systems described by the angular momentum algebra, from Rydberg atoms immersed into BEC's, to cold molecules solvated in helium droplets, to ultracold molecular ions.
Ultracold atoms in optical lattices simulating quantum many-body systems
Lewenstein, Maciej; Ahufinger, Verònica
2012-01-01
Quantum computers, though not yet available on the market, will revolutionize the future of information processing. Quantum computers for special purposes like quantum simulators are already within reach. The physics of ultracold atoms, ions and molecules offer unprecedented possibilities of control of quantum many body systems and novel possibilities of applications to quantum information processing and quantum metrology. Particularly fascinating is the possibility of usingultracold atoms in lattices to simulate condensed matter or even high energy physics.This book provides a complete and co
Effective linear two-body method for many-body problems in atomic and nuclear physics
International Nuclear Information System (INIS)
Kim, Y.E.; Zubarev, A.L.
2000-01-01
We present an equivalent linear two-body method for the many body problem, which is based on an approximate reduction of the many-body Schroedinger equation by the use of a variational principle. The method is applied to several problems in atomic and nuclear physics. (author)
Quantum scaling in many-body systems an approach to quantum phase transitions
Continentino, Mucio
2017-01-01
Quantum phase transitions are strongly relevant in a number of fields, ranging from condensed matter to cold atom physics and quantum field theory. This book, now in its second edition, approaches the problem of quantum phase transitions from a new and unifying perspective. Topics addressed include the concepts of scale and time invariance and their significance for quantum criticality, as well as brand new chapters on superfluid and superconductor quantum critical points, and quantum first order transitions. The renormalisation group in real and momentum space is also established as the proper language to describe the behaviour of systems close to a quantum phase transition. These phenomena introduce a number of theoretical challenges which are of major importance for driving new experiments. Being strongly motivated and oriented towards understanding experimental results, this is an excellent text for graduates, as well as theorists, experimentalists and those with an interest in quantum criticality.
Physics in one dimension: theoretical concepts for quantum many-body systems.
Schönhammer, K
2013-01-09
Various sophisticated approximation methods exist for the description of quantum many-body systems. It was realized early on that the theoretical description can simplify considerably in one-dimensional systems and various exact solutions exist. The focus in this introductory paper is on fermionic systems and the emergence of the Luttinger liquid concept.
Quantum Many-Body System in Presence of Time-Dependent Potential and Electric Field
Energy Technology Data Exchange (ETDEWEB)
Sobhani, Hadi; Hassanabadi, Hassan [Shahrood University of Technology, Shahrood (Iran, Islamic Republic of)
2017-07-15
In this article, a quantum many-body system is considered. Then two time-dependent interactions have been added to the system. Changing of them is assumed in general form. After that, by using algebraic method, time evolution of this many-body system has been investigated. In order to study the time evolution, Lewis-Riesenfeld dynamical invariant and time evolution operator method have been used. Appropriate dynamical invariants are constructed and their Eigenvalues are derived as well as appropriate time evolution operators are constructed. These calculations have been done in general form so there are no limiting assumptions on changing of time-dependent functions.
Moments of generalized Husimi distributions and complexity of many-body quantum states
International Nuclear Information System (INIS)
Sugita, Ayumu
2003-01-01
We consider generalized Husimi distributions for many-body systems, and show that their moments are good measures of complexity of many-body quantum states. Our construction of the Husimi distribution is based on the coherent state of the single-particle transformation group. Then the coherent states are independent-particle states, and, at the same time, the most localized states in the Husimi representation. Therefore delocalization of the Husimi distribution, which can be measured by the moments, is a sign of many-body correlation (entanglement). Since the delocalization of the Husimi distribution is also related to chaoticity of the dynamics, it suggests a relation between entanglement and chaos. Our definition of the Husimi distribution can be applied not only to systems of distinguishable particles, but also to those of identical particles, i.e., fermions and bosons. We derive an algebraic formula to evaluate the moments of the Husimi distribution
Many-body quantum chaos: Recent developments and applications to nuclei
International Nuclear Information System (INIS)
Gomez, J.M.G.; Kar, K.; Kota, V.K.B.; Molina, R.A.; Relano, A.; Retamosa, J.
2011-01-01
In the last decade, there has been an increasing interest in the analysis of energy level spectra and wave functions of nuclei, particles, atoms and other quantum many-body systems by means of statistical methods and random matrix ensembles. The concept of quantum chaos plays a central role for understanding the universal properties of the energy spectrum of quantum systems. Since these properties concern the whole spectrum, statistical methods become an essential tool. Besides random matrix theory, new theoretical developments making use of information theory, time series analysis, and the merging of thermodynamics and the semiclassical approximation are emphasized. Applications of these methods to quantum systems, especially to atomic nuclei, are reviewed. We focus on recent developments like the study of 'imperfect spectra' to estimate the degree of symmetry breaking or the fraction of missing levels, the existence of chaos remnants in nuclear masses, the onset of chaos in nuclei, and advances in the comprehension of the Hamiltonian structure in many-body systems. Finally, some applications of statistical spectroscopy methods generated by many-body chaos and two-body random matrix ensembles are described, with emphasis on Gamow-Teller strength sums and beta decay rates for stellar evolution and supernovae.
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space
Directory of Open Access Journals (Sweden)
J. Schachenmayer
2015-02-01
Full Text Available Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.
Quasiparticle engineering and entanglement propagation in a quantum many-body system.
Jurcevic, P; Lanyon, B P; Hauke, P; Hempel, C; Zoller, P; Blatt, R; Roos, C F
2014-07-10
The key to explaining and controlling a range of quantum phenomena is to study how information propagates around many-body systems. Quantum dynamics can be described by particle-like carriers of information that emerge in the collective behaviour of the underlying system, the so-called quasiparticles. These elementary excitations are predicted to distribute quantum information in a fashion determined by the system's interactions. Here we report quasiparticle dynamics observed in a quantum many-body system of trapped atomic ions. First, we observe the entanglement distributed by quasiparticles as they trace out light-cone-like wavefronts. Second, using the ability to tune the interaction range in our system, we observe information propagation in an experimental regime where the effective-light-cone picture does not apply. Our results will enable experimental studies of a range of quantum phenomena, including transport, thermalization, localization and entanglement growth, and represent a first step towards a new quantum-optic regime of engineered quasiparticles with tunable nonlinear interactions.
Many-body physics and the capacity of quantum channels with memory
International Nuclear Information System (INIS)
Plenio, M B; Virmani, S
2008-01-01
In most studies of the capacity of quantum channels, it is assumed that the errors in the use of each channel are independent. However, recent work has begun to investigate the effects of memory or correlations in the error, and has led to suggestions that there can be interesting non-analytic behaviour in the capacity of such channels. In a previous paper, we pursued this issue by connecting the study of channel capacities under correlated error to the study of critical behaviour in many-body physics. This connection enables the use of techniques from many-body physics to either completely solve or understand qualitatively a number of interesting models of correlated error with analogous behaviour to associated many-body systems. However, in order for this approach to work rigorously, there are a number of technical properties that need to be established for the lattice systems being considered. In this paper, we discuss these properties in detail, and establish them for some classes of many-body system
Many-body localization-delocalization transition in the quantum Sherrington-Kirkpatrick model
Mukherjee, Sudip; Nag, Sabyasachi; Garg, Arti
2018-04-01
We analyze the many-body localization- (MBL) to-delocalization transition in the Sherrington-Kirkpatrick (SK) model of Ising spin glass in the presence of a transverse field Γ . Based on energy-resolved analysis, which is of relevance for a closed quantum system, we show that the quantum SK model has many-body mobility edges separating the MBL phase, which is nonergodic and nonthermal, from the delocalized phase, which is ergodic and thermal. The range of the delocalized regime increases with an increase in the strength of Γ , and eventually for Γ larger than ΓCP the entire many-body spectrum is delocalized. We show that the Renyi entropy is almost independent of the system size in the MBL phase while the delocalized phase shows extensive Renyi entropy. We further obtain the spin-glass transition curve in the energy density ɛ -Γ plane from the collapse of the eigenstate spin susceptibility. We demonstrate that in most of the parameter regime, the spin-glass transition occurs close to the MBL transition, indicating that the spin-glass phase is nonergodic and nonthermal while the paramagnetic phase is delocalized and thermal.
Enhancement and sign change of magnetic correlations in a driven quantum many-body system
Görg, Frederik; Messer, Michael; Sandholzer, Kilian; Jotzu, Gregor; Desbuquois, Rémi; Esslinger, Tilman
2018-01-01
Periodic driving can be used to control the properties of a many-body state coherently and to realize phases that are not accessible in static systems. For example, exposing materials to intense laser pulses makes it possible to induce metal-insulator transitions, to control magnetic order and to generate transient superconducting behaviour well above the static transition temperature. However, pinning down the mechanisms underlying these phenomena is often difficult because the response of a material to irradiation is governed by complex, many-body dynamics. For static systems, extensive calculations have been performed to explain phenomena such as high-temperature superconductivity. Theoretical analyses of driven many-body Hamiltonians are more challenging, but approaches have now been developed, motivated by recent observations. Here we report an experimental quantum simulation in a periodically modulated hexagonal lattice and show that antiferromagnetic correlations in a fermionic many-body system can be reduced, enhanced or even switched to ferromagnetic correlations (sign reversal). We demonstrate that the description of the many-body system using an effective Floquet-Hamiltonian with a renormalized tunnelling energy remains valid in the high-frequency regime by comparing the results to measurements in an equivalent static lattice. For near-resonant driving, the enhancement and sign reversal of correlations is explained by a microscopic model of the system in which the particle tunnelling and magnetic exchange energies can be controlled independently. In combination with the observed sufficiently long lifetimes of the correlations in this system, periodic driving thus provides an alternative way of investigating unconventional pairing in strongly correlated systems experimentally.
Experimental quantum simulations of many-body physics with trapped ions.
Schneider, Ch; Porras, Diego; Schaetz, Tobias
2012-02-01
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
Paradeisos: A perfect hashing algorithm for many-body eigenvalue problems
Jia, C. J.; Wang, Y.; Mendl, C. B.; Moritz, B.; Devereaux, T. P.
2018-03-01
We describe an essentially perfect hashing algorithm for calculating the position of an element in an ordered list, appropriate for the construction and manipulation of many-body Hamiltonian, sparse matrices. Each element of the list corresponds to an integer value whose binary representation reflects the occupation of single-particle basis states for each element in the many-body Hilbert space. The algorithm replaces conventional methods, such as binary search, for locating the elements of the ordered list, eliminating the need to store the integer representation for each element, without increasing the computational complexity. Combined with the "checkerboard" decomposition of the Hamiltonian matrix for distribution over parallel computing environments, this leads to a substantial savings in aggregate memory. While the algorithm can be applied broadly to many-body, correlated problems, we demonstrate its utility in reducing total memory consumption for a series of fermionic single-band Hubbard model calculations on small clusters with progressively larger Hilbert space dimension.
Simulating local measurements on a quantum many-body system with stochastic matrix product states
DEFF Research Database (Denmark)
Gammelmark, Søren; Mølmer, Klaus
2010-01-01
We demonstrate how to simulate both discrete and continuous stochastic evolutions of a quantum many-body system subject to measurements using matrix product states. A particular, but generally applicable, measurement model is analyzed and a simple representation in terms of matrix product operators...... is found. The technique is exemplified by numerical simulations of the antiferromagnetic Heisenberg spin-chain model subject to various instances of the measurement model. In particular, we focus on local measurements with small support and nonlocal measurements, which induce long-range correlations....
Real-space decoupling transformation for quantum many-body systems.
Evenbly, G; Vidal, G
2014-06-06
We propose a real-space renormalization group method to explicitly decouple into independent components a many-body system that, as in the phenomenon of spin-charge separation, exhibits separation of degrees of freedom at low energies. Our approach produces a branching holographic description of such systems that opens the path to the efficient simulation of the most entangled phases of quantum matter, such as those whose ground state violates a boundary law for entanglement entropy. As in the coarse-graining transformation of Vidal [Phys. Rev. Lett. 99, 220405 (2007).
Nuclear quantum many-body dynamics: from collective vibrations to heavy-ion collisions
International Nuclear Information System (INIS)
Simenel, Cedric
2012-01-01
This report gives a summary of my research on nuclear dynamics during the past ten years. The choice of this field has been motivated by the desire to understand the physics of complex systems obeying quantum mechanics. In particular, the interplay between collective motion and single-particle degrees of freedom is a source of complex and fascinating behaviours. For instance, giant resonances are characterised by a collective vibration of many nucleons, but their decay may occur by the emission of a single nucleon. Another example could be taken from the collision of nuclei where the transfer of few nucleons may have a strong impact on the formation of a compound system is non trivial. To describe these complex systems, one needs to solve the quantum many-body problem. The description of the dynamics of composite systems can be very challenging, especially when two such systems interact. An important goal of nuclear physics is to find a unified way to describe the dynamics of nuclear systems. Ultimately, the same theoretical model should be able to describe vibrations, rotations, fission, all the possible outcomes of heavy-ion collisions (elastic and inelastic scattering, particle transfer, fusion, and multifragmentation), and even the dynamics of neutron star crust. This desire for a global approach to nuclear dynamics has strongly influenced my research activities. In particular, all the numerical applications presented in this report have been obtained from few numerical codes solving equations derived from the same variational principle. Beside the quest for a unified model of nuclear dynamics, possible applications of heavy-ion collisions such as the formation of new nuclei is also a strong motivation for the experimental and theoretical studies of reaction mechanisms. This report is not a review article, but should be considered as a reading guide of the main papers my collaborators and myself have published. It also gives the opportunity to detail some
Identifying the closeness of eigenstates in quantum many-body systems
International Nuclear Information System (INIS)
Li Hai-bin; Yang Yang; Wang Pei; Wang Xiao-guang
2017-01-01
We propose a quantity called modulus fidelity to measure the closeness of two quantum pure states. We use it to investigate the closeness of eigenstates in one-dimensional hard-core bosons. When the system is integrable, eigenstates close to their neighbor or not, which leads to a large fluctuation in the distribution of modulus fidelity. When the system becomes chaos, the fluctuation is reduced dramatically, which indicates all eigenstates become close to each other. It is also found that two kind of closeness, i.e., closeness of eigenstates and closeness of eigenvalues, are not correlated at integrability but correlated at chaos. We also propose that the closeness of eigenstates is the underlying mechanism of eigenstate thermalization hypothesis (ETH) which explains the thermalization in quantum many-body systems. (paper)
Many-body Tunneling and Nonequilibrium Dynamics of Doublons in Strongly Correlated Quantum Dots.
Hou, WenJie; Wang, YuanDong; Wei, JianHua; Zhu, ZhenGang; Yan, YiJing
2017-05-30
Quantum tunneling dominates coherent transport at low temperatures in many systems of great interest. In this work we report a many-body tunneling (MBT), by nonperturbatively solving the Anderson multi-impurity model, and identify it a fundamental tunneling process on top of the well-acknowledged sequential tunneling and cotunneling. We show that the MBT involves the dynamics of doublons in strongly correlated systems. Proportional to the numbers of dynamical doublons, the MBT can dominate the off-resonant transport in the strongly correlated regime. A T 3/2 -dependence of the MBT current on temperature is uncovered and can be identified as a fingerprint of the MBT in experiments. We also prove that the MBT can support the coherent long-range tunneling of doublons, which is well consistent with recent experiments on ultracold atoms. As a fundamental physical process, the MBT is expected to play important roles in general quantum systems.
Many-body effects in transport through a quantum-dot cavity system
Dinu, I. V.; Moldoveanu, V.; Gartner, P.
2018-05-01
We theoretically describe electric transport through an optically active quantum dot embedded in a single-mode cavity, and coupled to source-drain particle reservoirs. The populations of various many-body configurations (e.g., excitons, trions, biexciton) and the photon-number occupancies are calculated from a master equation which is derived in the basis of dressed states. These take into account both the Coulomb and the light-matter interaction. The former is essential in the description of the transport, while for the latter we identify situations in which it can be neglected in the expression of tunneling rates. The fermionic nature of the particle reservoirs plays an important role in the argument. The master equation is numerically solved for the s -shell many-body configurations of disk-shaped quantum dots. If the cavity is tuned to the biexciton-exciton transition, the most efficient optical processes take place in a three-level Λ system. The alternative exciton-ground-state route is inhibited as nonresonant due to the biexciton binding energy. The steady-state current is analyzed as a function of the photon frequency and the coupling to the leads. An unexpected feature appears in its dependence on the cavity loss rate, which turns out to be nonmonotonic.
Many-Body Quantum Theory in Condensed Matter Physics-An Introduction
International Nuclear Information System (INIS)
Logan, D E
2005-01-01
This is undoubtedly an ambitious book. It aims to provide a wide ranging, yet self-contained and pedagogical introduction to techniques of quantum many-body theory in condensed matter physics, without losing mathematical 'rigor' (which I hope means rigour), and with an eye on physical insight, motivation and application. The authors certainly bring plenty of experience to the task, the book having grown out of their graduate lectures at the Niels Bohr Institute in Copenhagen over a five year period, with the feedback and refinement this presumably brings. The book is also of course ambitious in another sense, for it competes in the tight market of general graduate/advanced undergraduate texts on many-particle physics. Prospective punters will thus want reasons to prefer it to, or at least give it space beside, well established texts in the field. Subject-wise, the book is a good mix of the ancient and modern, the standard and less so. Obligatory chapters deal with the formal cornerstones of many-body theory, from second quantization, time-dependence in quantum mechanics and linear response theory, to Green's function and Feynman diagrams. Traditional topics are well covered, including two chapters on the electron gas, chapters on phonons and electron-phonon coupling, and a concise account of superconductivity (confined, no doubt judiciously, to the conventional BCS case). Less mandatory, albeit conceptually vital, subjects are also aired. These include a chapter on Fermi liquid theory, from both semi-classical and microscopic perspectives, and a freestanding account of one-dimensional electron gases and Luttinger liquids which, given the enormity of the topic, is about as concise as it could be without sacrificing clarity. Quite naturally, the authors' own interests also influence the choice of material covered. A persistent theme, which brings a healthy topicality to the book, is the area of transport in mesoscopic systems or nanostructures. Two chapters, some
BOOK REVIEW: Many-Body Quantum Theory in Condensed Matter Physics—An Introduction
Logan, D. E.
2005-02-01
This is undoubtedly an ambitious book. It aims to provide a wide ranging, yet self-contained and pedagogical introduction to techniques of quantum many-body theory in condensed matter physics, without losing mathematical `rigor' (which I hope means rigour), and with an eye on physical insight, motivation and application. The authors certainly bring plenty of experience to the task, the book having grown out of their graduate lectures at the Niels Bohr Institute in Copenhagen over a five year period, with the feedback and refinement this presumably brings. The book is also of course ambitious in another sense, for it competes in the tight market of general graduate/advanced undergraduate texts on many-particle physics. Prospective punters will thus want reasons to prefer it to, or at least give it space beside, well established texts in the field. Subject-wise, the book is a good mix of the ancient and modern, the standard and less so. Obligatory chapters deal with the formal cornerstones of many-body theory, from second quantization, time-dependence in quantum mechanics and linear response theory, to Green's function and Feynman diagrams. Traditional topics are well covered, including two chapters on the electron gas, chapters on phonons and electron phonon coupling, and a concise account of superconductivity (confined, no doubt judiciously, to the conventional BCS case). Less mandatory, albeit conceptually vital, subjects are also aired. These include a chapter on Fermi liquid theory, from both semi-classical and microscopic perspectives, and a freestanding account of one-dimensional electron gases and Luttinger liquids which, given the enormity of the topic, is about as concise as it could be without sacrificing clarity. Quite naturally, the authors' own interests also influence the choice of material covered. A persistent theme, which brings a healthy topicality to the book, is the area of transport in mesoscopic systems or nanostructures. Two chapters, some
Directory of Open Access Journals (Sweden)
L. Fusco
2014-08-01
Full Text Available We analyze the nature of the statistics of the work done on or by a quantum many-body system brought out of equilibrium. We show that, for the sudden quench and for an initial state that commutes with the initial Hamiltonian, it is possible to retrieve the whole nonequilibrium thermodynamics via single projective measurements of observables. We highlight, in a physically clear way, the qualitative implications for the statistics of work coming from considering processes described by operators that either commute or do not commute with the unperturbed Hamiltonian of a given system. We consider a quantum many-body system and derive an expression that allows us to give a physical interpretation, for a thermal initial state, to all of the cumulants of the work in the case of quenched operators commuting with the unperturbed Hamiltonian. In the commuting case, the observables that we need to measure have an intuitive physical meaning. Conversely, in the noncommuting case, we show that, although it is possible to operate fully within the single-measurement framework irrespectively of the size of the quench, some difficulties are faced in providing a clear-cut physical interpretation to the cumulants. This circumstance makes the study of the physics of the system nontrivial and highlights the nonintuitive phenomenology of the emergence of thermodynamics from the fully quantum microscopic description. We illustrate our ideas with the example of the Ising model in a transverse field showing the interesting behavior of the high-order statistical moments of the work distribution for a generic thermal state and linking them to the critical nature of the model itself.
Simulation of Quantum Many-Body Dynamics for Generic Strongly-Interacting Systems
Meyer, Gregory; Machado, Francisco; Yao, Norman
2017-04-01
Recent experimental advances have enabled the bottom-up assembly of complex, strongly interacting quantum many-body systems from individual atoms, ions, molecules and photons. These advances open the door to studying dynamics in isolated quantum systems as well as the possibility of realizing novel out-of-equilibrium phases of matter. Numerical studies provide insight into these systems; however, computational time and memory usage limit common numerical methods such as exact diagonalization to relatively small Hilbert spaces of dimension 215 . Here we present progress toward a new software package for dynamical time evolution of large generic quantum systems on massively parallel computing architectures. By projecting large sparse Hamiltonians into a much smaller Krylov subspace, we are able to compute the evolution of strongly interacting systems with Hilbert space dimension nearing 230. We discuss and benchmark different design implementations, such as matrix-free methods and GPU based calculations, using both pre-thermal time crystals and the Sachdev-Ye-Kitaev model as examples. We also include a simple symbolic language to describe generic Hamiltonians, allowing simulation of diverse quantum systems without any modification of the underlying C and Fortran code.
Local Convertibility and the Quantum Simulation of Edge States in Many-Body Systems
Directory of Open Access Journals (Sweden)
Fabio Franchini
2014-11-01
Full Text Available In some many-body systems, certain ground-state entanglement (Rényi entropies increase even as the correlation length decreases. This entanglement nonmonotonicity is a potential indicator of nonclassicality. In this work, we demonstrate that such a phenomenon, known as lack of local convertibility, is due to the edge-state (deconstruction occurring in the system. To this end, we employ the example of the Ising chain, displaying an order-disorder quantum phase transition. Employing both analytical and numerical methods, we compute entanglement entropies for various system bipartitions (A|B and consider ground states with and without Majorana edge states. We find that the thermal ground states, enjoying the Hamiltonian symmetries, show lack of local convertibility if either A or B is smaller than, or of the order of, the correlation length. In contrast, the ordered (symmetry-breaking ground state is always locally convertible. The edge-state behavior explains all these results and could disclose a paradigm to understand local convertibility in other quantum phases of matter. The connection we establish between convertibility and nonlocal, quantum correlations provides a clear criterion of which features a universal quantum simulator should possess to outperform a classical machine.
Polylogs, thermodynamics and scaling functions of one-dimensional quantum many-body systems
International Nuclear Information System (INIS)
Guan, X-W; Batchelor, M T
2011-01-01
We demonstrate that the thermodynamics of one-dimensional Lieb-Liniger bosons can be accurately calculated in analytic fashion using the polylog function in the framework of the thermodynamic Bethe ansatz. The approach does away with the need to numerically solve the thermodynamic Bethe ansatz (Yang-Yang) equation. The expression for the equation of state allows the exploration of Tomonaga-Luttinger liquid physics and quantum criticality in an archetypical quantum system. In particular, the low-temperature phase diagram is obtained, along with the scaling functions for the density and compressibility. It has been shown recently by Guan and Ho (arXiv:1010.1301) that such scaling can be used to map out the criticality of ultracold fermionic atoms in experiments. We show here how to map out quantum criticality for Lieb-Liniger bosons. More generally, the polylog function formalism can be applied to a wide range of Bethe ansatz integrable quantum many-body systems which are currently of theoretical and experimental interest, such as strongly interacting multi-component fermions, spinor bosons and mixtures of bosons and fermions. (fast track communication)
Many-body strategies for multiqubit gates: Quantum control through Krawtchouk-chain dynamics
Groenland, Koen; Schoutens, Kareljan
2018-04-01
We propose a strategy for engineering multiqubit quantum gates. As a first step, it employs an eigengate to map states in the computational basis to eigenstates of a suitable many-body Hamiltonian. The second step employs resonant driving to enforce a transition between a single pair of eigenstates, leaving all others unchanged. The procedure is completed by mapping back to the computational basis. We demonstrate the strategy for the case of a linear array with an even number N of qubits, with specific X X +Y Y couplings between nearest neighbors. For this so-called Krawtchouk chain, a two-body driving term leads to the iSWAPN gate, which we numerically test for N =4 and 6.
Seniority in quantum many-body systems. I. Identical particles in a single shell
Energy Technology Data Exchange (ETDEWEB)
Van Isacker, P., E-mail: isacker@ganil.fr [Grand Accélérateur National d’Ions Lourds, CEA/DSM–CNRS/IN2P3, BP 55027, F-14076 Caen Cedex 5 (France); Heinze, S. [Institut für Kernphysik der Universität zu Köln, 50937 Köln (Germany)
2014-10-15
A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of partial conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions. - Highlights: • Unified derivation of conditions for the total and partial conservation of seniority. • General analysis of the partial conservation of seniority in boson systems. • Why partial conservation of seniority is crucial for seniority isomers in nuclei. • The effect of partial conservation of seniority on one-nucleon transfer intensities.
Seniority in quantum many-body systems. I. Identical particles in a single shell
International Nuclear Information System (INIS)
Van Isacker, P.; Heinze, S.
2014-01-01
A discussion of the seniority quantum number in many-body systems is presented. The analysis is carried out for bosons and fermions simultaneously but is restricted to identical particles occupying a single shell. The emphasis of the paper is on the possibility of partial conservation of seniority which turns out to be a peculiar property of spin-9/2 fermions but prevalent in systems of interacting bosons of any spin. Partial conservation of seniority is at the basis of the existence of seniority isomers, frequently observed in semi-magic nuclei, and also gives rise to peculiar selection rules in one-nucleon transfer reactions. - Highlights: • Unified derivation of conditions for the total and partial conservation of seniority. • General analysis of the partial conservation of seniority in boson systems. • Why partial conservation of seniority is crucial for seniority isomers in nuclei. • The effect of partial conservation of seniority on one-nucleon transfer intensities
In-Medium Similarity Renormalization Group Approach to the Nuclear Many-Body Problem
Hergert, Heiko; Bogner, Scott K.; Lietz, Justin G.; Morris, Titus D.; Novario, Samuel J.; Parzuchowski, Nathan M.; Yuan, Fei
We present a pedagogical discussion of Similarity Renormalization Group (SRG) methods, in particular the In-Medium SRG (IMSRG) approach for solving the nuclear many-body problem. These methods use continuous unitary transformations to evolve the nuclear Hamiltonian to a desired shape. The IMSRG, in particular, is used to decouple the ground state from all excitations and solve the many-body Schrödinger equation. We discuss the IMSRG formalism as well as its numerical implementation, and use the method to study the pairing model and infinite neutron matter. We compare our results with those of Coupled cluster theory (Chap. 8), Configuration-Interaction Monte Carlo (Chap. 9), and the Self-Consistent Green's Function approach discussed in Chap. 11 The chapter concludes with an expanded overview of current research directions, and a look ahead at upcoming developments.
Many-body effects in the mesoscopic x-ray edge problem
International Nuclear Information System (INIS)
Hentschel, Martina; Roeder, Georg; Ullmo, Denis
2007-01-01
Many-body phenomena, a key interest in the investigation of bulk solid state systems, are studied here in the context of the x-ray edge problem for mesoscopic systems. We investigate the many-body effects associated with the sudden perturbation following the x-ray exciton of a core electron into the conduction band. For small systems with dimensions at the nanoscale we find considerable deviations from the well-understood metallic case where Anderson orthogonality catastrophe and the Mahan-Nozieres-DeDominicis response cause characteristic deviations of the photoabsorption cross section from the naive expectation. Whereas the K-edge is typically rounded in metallic systems, we find a slightly peaked K-edge in generic mesoscopic systems with chaotic-coherent electron dynamics. Thus the behavior of the photoabsorption cross section at threshold depends on the system size and is different for the metallic and the mesoscopic case. (author)
International Nuclear Information System (INIS)
Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji
2016-01-01
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.
Energy Technology Data Exchange (ETDEWEB)
Kuwahara, Tomotaka, E-mail: tomotaka.phys@gmail.com [Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); WPI, Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577 (Japan); Mori, Takashi [Department of Physics, Graduate School of Science, University of Tokyo, Bunkyo-ku, Tokyo 113-0033 (Japan); Saito, Keiji [Department of Physics, Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522 (Japan)
2016-04-15
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet–Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems. -- Highlights: •A general framework to describe transient dynamics for periodically driven systems. •The theory is applicable to generic quantum many-body systems including long-range interacting systems. •Physical meaning of the truncation of the Floquet–Magnus expansion is rigorously established. •New mechanism of the prethermalization is proposed. •Revealing an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed.
Quantum Many-Body Dynamics with Driven Bose Condensates: Kibble-Zurek Mechanism and Bose Fireworks
Clark, Logan William
In recent years there has been an explosion of interest in the field of quantum many-body physics. Understanding the complex and often unintuitive behavior of systems containing interacting quantum constituents is not only fascinating but also crucial for developing the next generation of quantum technology, including better materials, sensors, and computers. Yet understanding such systems remains a challenge, particularly when considering the dynamics which occur when they are excited far from equilibrium. Ultracold atomic gases provide an ideal system with which to study dynamics by enabling clean, well-controlled experiments at length- and time-scales which allow us to observe the dynamics directly. This thesis describes experiments on the many-body dynamics of ultracold, bosonic cesium atoms. Our apparatus epitomizes the versatility of ultracold atoms by providing extensive control over the quantum gas. In particular, we will discuss our use of a digital micromirror device to project arbitrary, dynamic external potentials onto the gas; our development of a powerful new scheme for optically controlling Feshbach resonances to enable spatiotemporal control of the interactions between atoms; and our use of near-resonant shaking lattices to modify the kinetic energy of atoms. Taking advantage of this flexible apparatus, we have been able to test a longstanding conjecture based on the Kibble-Zurek mechanism, which says that the dynamics of a system crossing a quantum phase transition should obey a universal scaling symmetry of space and time. After accounting for this scaling symmetry, critical dynamics would be essentially independent of the rate at which a system crossed a phase transition. We tested the universal scaling of critical dynamics by using near-resonant shaking to drive Bose-Einstein condensates across an effectively ferromagnetic quantum phase transition. After crossing the phase transition, condensates divide themselves spatially into domains with
Mazziotti, David A.; Erdahl, Robert M.
2001-04-01
For the description of ground-state correlation phenomena an accurate mapping of many-body quantum mechanics onto four particles is developed. The energy for a quantum system with no more than two-particle interactions may be expressed in terms of a two-particle reduced density matrix (2-RDM), but variational optimization of the 2-RDM requires that it corresponds to an N-particle wave function. We derive N-representability conditions on the 2-RDM that guarantee the validity of the uncertainty relations for all operators with two-particle interactions. One of these conditions is shown to be necessary and sufficient to make the RDM solutions of the dispersion condition equivalent to those from the contracted Schrödinger equation (CSE) [Mazziotti, Phys. Rev. A 57, 4219 (1998)]. In general, the CSE is a stronger N-representability condition than the dispersion condition because the CSE implies the dispersion condition as well as additional N-representability constraints from the Hellmann-Feynman theorem. Energy minimization subject to the representability constraints is performed for a boson model with 10, 30, and 75 particles. Even when traditional wave-function methods fail at large perturbations, the present method yields correlation energies within 2%.
Probing correlated quantum many-body systems at the single-particle level
International Nuclear Information System (INIS)
Endres, Manuel
2013-01-01
The detection of correlation and response functions plays a crucial role in the experimental characterization of quantum many-body systems. In this thesis, we present novel techniques for the measurement of such functions at the single-particle level. Specifically, we show the single-atom- and single-site-resolved detection of an ultracold quantum gas in an optical lattice. The quantum gas is described by the Bose-Hubbard model, which features a zero temperature phase transition from a superfluid to a Mott-insulating state, a paradigm example of a quantum phase transition. We used the aforementioned detection techniques to study correlation and response properties across the superfluid-Mott-insulator transition. The single-atom sensitivity of our method is achieved by fluorescence detection of individual atoms with a high signal-to-noise ratio. A high-resolution objective collects the fluorescence light and yields in situ 'snapshots' of the quantum gas that allow for a single-site-resolved reconstruction of the atomic distribution. This allowed us to measure two-site and non-local correlation-functions across the superfluid-Mott-insulator transition. Non-local correlation functions are based on the information of an extended region of the system and play an important role for the characterization of low-dimensional quantum phases. While non-local correlation functions were so far only theoretical tools, our results show that they are actually experimentally accessible. Furthermore, we used a new thermometry scheme, based on the counting of individual thermal excitations, to measure the response of the system to lattice modulation. Using this method, we studied the excitation spectrum of the system across the two-dimensional superfluid-Mott-insulator transition. In particular, we detected a 'Higgs' amplitude mode in the strongly-interacting superfluid close to the transition point where the system is described by an effectively Lorentz-invariant low-energy theory
Probing correlated quantum many-body systems at the single-particle level
Energy Technology Data Exchange (ETDEWEB)
Endres, Manuel
2013-02-27
The detection of correlation and response functions plays a crucial role in the experimental characterization of quantum many-body systems. In this thesis, we present novel techniques for the measurement of such functions at the single-particle level. Specifically, we show the single-atom- and single-site-resolved detection of an ultracold quantum gas in an optical lattice. The quantum gas is described by the Bose-Hubbard model, which features a zero temperature phase transition from a superfluid to a Mott-insulating state, a paradigm example of a quantum phase transition. We used the aforementioned detection techniques to study correlation and response properties across the superfluid-Mott-insulator transition. The single-atom sensitivity of our method is achieved by fluorescence detection of individual atoms with a high signal-to-noise ratio. A high-resolution objective collects the fluorescence light and yields in situ 'snapshots' of the quantum gas that allow for a single-site-resolved reconstruction of the atomic distribution. This allowed us to measure two-site and non-local correlation-functions across the superfluid-Mott-insulator transition. Non-local correlation functions are based on the information of an extended region of the system and play an important role for the characterization of low-dimensional quantum phases. While non-local correlation functions were so far only theoretical tools, our results show that they are actually experimentally accessible. Furthermore, we used a new thermometry scheme, based on the counting of individual thermal excitations, to measure the response of the system to lattice modulation. Using this method, we studied the excitation spectrum of the system across the two-dimensional superfluid-Mott-insulator transition. In particular, we detected a 'Higgs' amplitude mode in the strongly-interacting superfluid close to the transition point where the system is described by an effectively Lorentz
Two novel classes of solvable many-body problems of goldfish type with constraints
Energy Technology Data Exchange (ETDEWEB)
Calogero, F [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , 00185 Rome (Italy); Gomez-Ullate, D [Departamento de Fisica Teorica II, Universidad Complutense, 28040 Madrid (Spain)
2007-05-18
Two novel classes of many-body models with nonlinear interactions 'of goldfish type' are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints), i.e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited, i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.
Spectrum of quantum transfer matrices via classical many-body systems
Energy Technology Data Exchange (ETDEWEB)
Gorsky, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Zabrodin, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Institute of Biochemical Physics,Kosygina str. 4, 119991, Moscow (Russian Federation); National Research University Higher School of Economics,Myasnitskaya str. 20, 101000, Moscow (Russian Federation); Zotov, A. [ITEP,Bolshaya Cheremushkinskaya str. 25, 117218, Moscow (Russian Federation); MIPT,Inststitutskii per. 9, 141700, Dolgoprudny, Moscow region (Russian Federation); Steklov Mathematical Institute, RAS,Gubkina str. 8, 119991, Moscow (Russian Federation)
2014-01-15
In this paper we clarify the relationship between inhomogeneous quantum spin chains and classical integrable many-body systems. It provides an alternative (to the nested Bethe ansatz) method for computation of spectra of the spin chains. Namely, the spectrum of the quantum transfer matrix for the inhomogeneous gl{sub n}-invariant XXX spin chain on N sites with twisted boundary conditions can be found in terms of velocities of particles in the rational N-body Ruijsenaars-Schneider model. The possible values of the velocities are to be found from intersection points of two Lagrangian submanifolds in the phase space of the classical model. One of them is the Lagrangian hyperplane corresponding to fixed coordinates of all N particles and the other one is an N-dimensional Lagrangian submanifold obtained by fixing levels of N classical Hamiltonians in involution. The latter are determined by eigenvalues of the twist matrix. To support this picture, we give a direct proof that the eigenvalues of the Lax matrix for the classical Ruijsenaars-Schneider model, where velocities of particles are substituted by eigenvalues of the spin chain Hamiltonians, calculated through the Bethe equations, coincide with eigenvalues of the twist matrix, with certain multiplicities. We also prove a similar statement for the gl{sub n} Gaudin model with N marked points (on the quantum side) and the Calogero-Moser system with N particles (on the classical side). The realization of the results obtained in terms of branes and supersymmetric gauge theories is also discussed.
Quantum optics meets quantum many-body theory: coupled cluster studies of the Rabi Hamiltonian
International Nuclear Information System (INIS)
Davidson, N.J.; Quick, R.M.; Bishop, R.F.; Van der Walt, D.M.
1998-01-01
The Rabi Hamiltonian, which describes the interaction of a single mode of electromagnetic radiation with a two level system, is one of the fundamental models of quantum optics. It is also of wider interest as it provides a generic model for the interaction of bosons and fermions. To allow for a systematic analysis of the strong-coupling behaviour, we have applied the coupled cluster method (CCM) to the Rabi Hamiltonian to calculate its spectrum. We find strong evidence for the existence of a somewhat subtle quantum phase transition. (Copyright (1998) World Scientific Publishing Co. Pte. Ltd)
Quantum gases. Observation of many-body dynamics in long-range tunneling after a quantum quench.
Meinert, Florian; Mark, Manfred J; Kirilov, Emil; Lauber, Katharina; Weinmann, Philipp; Gröbner, Michael; Daley, Andrew J; Nägerl, Hanns-Christoph
2014-06-13
Quantum tunneling is at the heart of many low-temperature phenomena. In strongly correlated lattice systems, tunneling is responsible for inducing effective interactions, and long-range tunneling substantially alters many-body properties in and out of equilibrium. We observe resonantly enhanced long-range quantum tunneling in one-dimensional Mott-insulating Hubbard chains that are suddenly quenched into a tilted configuration. Higher-order tunneling processes over up to five lattice sites are observed as resonances in the number of doubly occupied sites when the tilt per site is tuned to integer fractions of the Mott gap. This forms a basis for a controlled study of many-body dynamics driven by higher-order tunneling and demonstrates that when some degrees of freedom are frozen out, phenomena that are driven by small-amplitude tunneling terms can still be observed. Copyright © 2014, American Association for the Advancement of Science.
Algorithm for simulation of quantum many-body dynamics using dynamical coarse-graining
International Nuclear Information System (INIS)
Khasin, M.; Kosloff, R.
2010-01-01
An algorithm for simulation of quantum many-body dynamics having su(2) spectrum-generating algebra is developed. The algorithm is based on the idea of dynamical coarse-graining. The original unitary dynamics of the target observables--the elements of the spectrum-generating algebra--is simulated by a surrogate open-system dynamics, which can be interpreted as weak measurement of the target observables, performed on the evolving system. The open-system state can be represented by a mixture of pure states, localized in the phase space. The localization reduces the scaling of the computational resources with the Hilbert-space dimension n by factor n 3/2 (ln n) -1 compared to conventional sparse-matrix methods. The guidelines for the choice of parameters for the simulation are presented and the scaling of the computational resources with the Hilbert-space dimension of the system is estimated. The algorithm is applied to the simulation of the dynamics of systems of 2x10 4 and 2x10 6 cold atoms in a double-well trap, described by the two-site Bose-Hubbard model.
Kuwahara, Tomotaka; Mori, Takashi; Saito, Keiji
2016-04-01
This work explores a fundamental dynamical structure for a wide range of many-body quantum systems under periodic driving. Generically, in the thermodynamic limit, such systems are known to heat up to infinite temperature states in the long-time limit irrespective of dynamical details, which kills all the specific properties of the system. In the present study, instead of considering infinitely long-time scale, we aim to provide a general framework to understand the long but finite time behavior, namely the transient dynamics. In our analysis, we focus on the Floquet-Magnus (FM) expansion that gives a formal expression of the effective Hamiltonian on the system. Although in general the full series expansion is not convergent in the thermodynamics limit, we give a clear relationship between the FM expansion and the transient dynamics. More precisely, we rigorously show that a truncated version of the FM expansion accurately describes the exact dynamics for a certain time-scale. Our theory reveals an experimental time-scale for which non-trivial dynamical phenomena can be reliably observed. We discuss several dynamical phenomena, such as the effect of small integrability breaking, efficient numerical simulation of periodically driven systems, dynamical localization and thermalization. Especially on thermalization, we discuss a generic scenario on the prethermalization phenomenon in periodically driven systems.
Quantum many-body dynamics of ultracold atoms in optical lattices
Energy Technology Data Exchange (ETDEWEB)
Kessler, Stefan
2014-04-15
Ultracold atoms can be trapped in periodic intensity patterns of light created by counterpropagating laser beams, so-called optical lattices. In contrast to its natural counterpart, electrons in a solid state crystal, this man-made setup is very clean and highly isolated from environmental degrees of freedom. Moreover, to a large extent, the experimenter has dynamical control over the relevant system parameters: the interaction between atoms, the tunneling amplitude between lattice sites, and even the dimensionality of the lattice. These advantages render this system a unique platform for the simulation of quantum many-body dynamics for various lattice Hamiltonians as has been demonstrated in several experiments by now. The most significant step in recent times has arguably been the introduction of single-site detection of individual atoms in optical lattices. This technique, based on fluorescence microscopy, opens a new doorway for the study of quantum many-body states: the detection of the microscopic atom configuration. In this thesis, we theoretically explore the dynamics of ultracold atoms in optical lattices for various setups realized in present-day experiments. Our main focus lies on aspects that become experimentally accessible by (realistic extensions of) the novel single-site measurement technique. The first part deals with the expansion of initially confined atoms in a homogeneous lattice, which is one way to create atomic motion in experiments. We analyze the buildup of spatial correlations during the expansion of a finitely extended band insulating state in one dimension. The numerical simulation reveals the creation of remote spin-entangled fermions in the strongly interacting regime. We discuss the experimental observation of such spin-entangled pairs by means of a single-site measurement. Furthermore, we suggest studying the impact of observations on the expansion dynamics for the extreme case of a projective measurement in the spatial occupation
Quantum many-body dynamics of ultracold atoms in optical lattices
International Nuclear Information System (INIS)
Kessler, Stefan
2014-01-01
Ultracold atoms can be trapped in periodic intensity patterns of light created by counterpropagating laser beams, so-called optical lattices. In contrast to its natural counterpart, electrons in a solid state crystal, this man-made setup is very clean and highly isolated from environmental degrees of freedom. Moreover, to a large extent, the experimenter has dynamical control over the relevant system parameters: the interaction between atoms, the tunneling amplitude between lattice sites, and even the dimensionality of the lattice. These advantages render this system a unique platform for the simulation of quantum many-body dynamics for various lattice Hamiltonians as has been demonstrated in several experiments by now. The most significant step in recent times has arguably been the introduction of single-site detection of individual atoms in optical lattices. This technique, based on fluorescence microscopy, opens a new doorway for the study of quantum many-body states: the detection of the microscopic atom configuration. In this thesis, we theoretically explore the dynamics of ultracold atoms in optical lattices for various setups realized in present-day experiments. Our main focus lies on aspects that become experimentally accessible by (realistic extensions of) the novel single-site measurement technique. The first part deals with the expansion of initially confined atoms in a homogeneous lattice, which is one way to create atomic motion in experiments. We analyze the buildup of spatial correlations during the expansion of a finitely extended band insulating state in one dimension. The numerical simulation reveals the creation of remote spin-entangled fermions in the strongly interacting regime. We discuss the experimental observation of such spin-entangled pairs by means of a single-site measurement. Furthermore, we suggest studying the impact of observations on the expansion dynamics for the extreme case of a projective measurement in the spatial occupation
DEFF Research Database (Denmark)
Houmark-Nielsen, Jakob; Nielsen, Torben Roland; Mørk, Jesper
2009-01-01
an important impact on the slow light properties. In the case of the Lambda and V schemes, the minimum required coupling power to achieve slow light is significantly reduced by many-body interactions. V type schemes are found to be generally preferable due to a favorable redistribution of carriers in energy......We investigate the impact of many-body interactions on group-velocity slowdown achieved via electromagnetically induced transparency in quantum dots using three different coupling-probe schemes (ladder, V, and Lambda, respectively). We find that for all schemes many-body interactions have...
Determinantal and worldline quantum Monte Carlo methods for many-body systems
International Nuclear Information System (INIS)
Vekic, M.; White, S.R.
1993-01-01
We examine three different quantum Monte Carlo methods for studying systems of interacting particles. The determinantal quantum Monte Carlo method is compared to two different worldline simulations. The first worldline method consists of a simulation carried out in the real-space basis, while the second method is implemented using as basis the eigenstates of the Hamiltonian on blocks of the two-dimensional lattice. We look, in particular, at the Hubbard model on a 4x4 lattice with periodic boundary conditions. The block method is superior to the real-space method in terms of the computational cost of the simulation, but shows a much worse negative sign problem. For larger values of U and away from half-filling it is found that the real-space method can provide results at lower temperatures than the determinantal method. We show that the sign problem in the block method can be slightly improved by an appropriate choice of basis
International Nuclear Information System (INIS)
Appel, H.
2007-05-01
In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f xc from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the propagation
Energy Technology Data Exchange (ETDEWEB)
Appel, H.
2007-05-15
In part I of this work we present a double-pole approximation (DPA) to the response equations of time-dependent density functional theory (TDDFT). The double-pole approximation provides an exact description of systems with two strongly coupled excitations which are isolated from the rest of the spectrum. In contrast to the traditional single-pole approximation of TDDFT the DPA also yields corrections to the Kohn-Sham oscillator strengths. We also demonstrate how to invert the double-pole solution which allows us to predict matrix elements of the exchange-correlation kernel f{sub xc} from experimental input. We attempt some first steps towards a time-dependent generalization of reduced density matrix functional theory (RDMFT). In part II we derive equations of motion for natural orbitals and occupation numbers. Using the equation of motion for the occupation numbers we show that an adiabatic extension of presently known ground-state functionals of static RDMFT always leads to occupation numbers which are constant in time. From the stationary conditions of the equations of motion for the N-body correlations (correlated parts of the N-body matrices) we derive a new class of ground-state functionals which can be used in static RDMFT. Applications are presented for a one-dimensional model system where the time-dependent many-body Schroedinger equation can be propagated numerically. We use optimal control theory to find optimized laser pulses for transitions in a model for atomic Helium. From the numerically exact correlated wavefunction we extract the exact time evolution of natural orbitals and occupation numbers for (i) laser-driven Helium and (ii) electron-ion scattering. Part III of this work considers time-dependent quantum transport within TDDFT. We present an algorithm for the calculation of extended eigenstates of single-particle Hamiltonians which is especially tailored to a finite-difference discretization of the Schroedinger equation. We consider the
Exact self-energy of the many-body problem from conserving approximations
International Nuclear Information System (INIS)
Takada, Y.
1995-01-01
A procedure is proposed to obtain the exact self-energy in the many-body problem. This algorithm is based on the formal analysis to reach the exact theory by repeated applications of an operator F to an arbitrarily chosen input self-energy represented as a functional of the dressed Green's function. The operator F is so defined that the microscopic conservation law for particle number is satisfied. The rigorous self-energy is obtained by the solution of an eigenfunction of F. Particular attention is paid to the relation between the present procedure and the Baym-Kadanoff framework of conserving approximations. By simplifying the procedure in F with use of the generalized Ward identity, we suggest a practical method to implement this algorithm rather easily in actual systems. In order to suggest future directions to improve on this practical method, the recently developed mean-field theory for the Hubbard model in the limit of high spatial dimensions is also discussed in the context of our theory
Stochastic many-body problems in ecology, evolution, neuroscience, and systems biology
Butler, Thomas C.
Using the tools of many-body theory, I analyze problems in four different areas of biology dominated by strong fluctuations: The evolutionary history of the genetic code, spatiotemporal pattern formation in ecology, spatiotemporal pattern formation in neuroscience and the robustness of a model circadian rhythm circuit in systems biology. In the first two research chapters, I demonstrate that the genetic code is extremely optimal (in the sense that it manages the effects of point mutations or mistranslations efficiently), more than an order of magnitude beyond what was previously thought. I further show that the structure of the genetic code implies that early proteins were probably only loosely defined. Both the nature of early proteins and the extreme optimality of the genetic code are interpreted in light of recent theory [1] as evidence that the evolution of the genetic code was driven by evolutionary dynamics that were dominated by horizontal gene transfer. I then explore the optimality of a proposed precursor to the genetic code. The results show that the precursor code has only limited optimality, which is interpreted as evidence that the precursor emerged prior to translation, or else never existed. In the next part of the dissertation, I introduce a many-body formalism for reaction-diffusion systems described at the mesoscopic scale with master equations. I first apply this formalism to spatially-extended predator-prey ecosystems, resulting in the prediction that many-body correlations and fluctuations drive population cycles in time, called quasicycles. Most of these results were previously known, but were derived using the system size expansion [2, 3]. I next apply the analytical techniques developed in the study of quasi-cycles to a simple model of Turing patterns in a predator-prey ecosystem. This analysis shows that fluctuations drive the formation of a new kind of spatiotemporal pattern formation that I name "quasi-patterns." These quasi
Fröhlich, Jürg; Knowles, Antti; Schlein, Benjamin; Sohinger, Vedran
2017-12-01
We prove that Gibbs measures of nonlinear Schrödinger equations arise as high-temperature limits of thermal states in many-body quantum mechanics. Our results hold for defocusing interactions in dimensions {d =1,2,3}. The many-body quantum thermal states that we consider are the grand canonical ensemble for d = 1 and an appropriate modification of the grand canonical ensemble for {d =2,3}. In dimensions d = 2, 3, the Gibbs measures are supported on singular distributions, and a renormalization of the chemical potential is necessary. On the many-body quantum side, the need for renormalization is manifested by a rapid growth of the number of particles. We relate the original many-body quantum problem to a renormalized version obtained by solving a counterterm problem. Our proof is based on ideas from field theory, using a perturbative expansion in the interaction, organized by using a diagrammatic representation, and on Borel resummation of the resulting series.
Rispoli, Matthew; Lukin, Alexander; Ma, Ruichao; Preiss, Philipp; Tai, M. Eric; Islam, Rajibul; Greiner, Markus
2015-05-01
Ultracold atoms in optical lattices provide a versatile tool box for observing the emergence of strongly correlated physics in quantum systems. Dynamic control of optical potentials on the single-site level allows us to prepare and probe many-body quantum states through local Hamiltonian engineering. We achieve these high precision levels of optical control through spatial light modulation with a DMD (digital micro-mirror device). This allows for both arbitrary beam shaping and aberration compensation in our imaging system to produce high fidelity optical potentials. We use these techniques to control state initialization, Hamiltonian dynamics, and measurement in experiments investigating low-dimensional many-body physics - from one-dimensional correlated quantum walks to characterizing entanglement.
Many-body effects in the gain spectra of highly excited quantum-dot lasers
International Nuclear Information System (INIS)
Schneider, H. C.; Chow, W. W.; Koch, S. W.
2001-01-01
Optical gain spectra are computed for quantum dots under high excitation conditions, where there is a non-negligible two-dimensional carrier density surrounding the dots. Using a screened Hartree-Fock theory to describe the influence of the Coulomb interaction, we find different self-energy shifts for the dot and quantum-well transitions. Furthermore, in contrast to the result for quantum-well and bulk systems, the peak gain at the quantum-dot transition computed including Coulomb effects is reduced from its free carrier value
Lattice Methods and the Nuclear Few- and Many-Body Problem
Lee, Dean
This chapter builds upon the review of lattice methods and effective field theory of the previous chapter. We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal, explaining the theory and algorithms relevant to lattice simulations of nuclear few- and many-body systems. We discuss the exact equivalence of four different lattice formalisms, the Grassmann path integral, transfer matrix operator, Grassmann path integral with auxiliary fields, and transfer matrix operator with auxiliary fields. Along with our analysis we include several coding examples and a number of exercises for the calculations of few- and many-body systems at leading order in chiral effective field theory.
Mazzucchi, Gabriel; Kozlowski, Wojciech; Caballero-Benitez, Santiago F.; Elliott, Thomas J.; Mekhov, Igor B.
2016-02-01
Trapping ultracold atoms in optical lattices enabled numerous breakthroughs uniting several disciplines. Coupling these systems to quantized light leads to a plethora of new phenomena and has opened up a new field of study. Here we introduce an unusual additional source of competition in a many-body strongly correlated system: We prove that quantum backaction of global measurement is able to efficiently compete with intrinsic short-range dynamics of an atomic system. The competition becomes possible due to the ability to change the spatial profile of a global measurement at a microscopic scale comparable to the lattice period without the need of single site addressing. In coherence with a general physical concept, where new competitions typically lead to new phenomena, we demonstrate nontrivial dynamical effects such as large-scale multimode oscillations, long-range entanglement, and correlated tunneling, as well as selective suppression and enhancement of dynamical processes beyond the projective limit of the quantum Zeno effect. We demonstrate both the breakup and protection of strongly interacting fermion pairs by measurement. Such a quantum optical approach introduces into many-body physics novel processes, objects, and methods of quantum engineering, including the design of many-body entangled environments for open systems.
Landau-Zener tunneling with many-body quantum effects in crystals of molecular magnets
Fu, Li-Bin; Chen, Shi-Gang; Hu, Bambi
2004-01-01
We present a quantum interpretation of the heights in hysteresis of $Fe_{8}$ molecule at lower temperatures by treating the crystal as an Ising spin system with the dipolar interaction between spins. Then we apply it to two limit cases : rapid and adiabatic regions. Our theoretical analysis is in agreement with the experimental observation in these regions, which indicates that the steps in hysteresis loops of magnetization of Fe$_{8}$ at lower temperatures show a pure quantum process.
Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System.
Jurcevic, P; Shen, H; Hauke, P; Maier, C; Brydges, T; Hempel, C; Lanyon, B P; Heyl, M; Blatt, R; Roos, C F
2017-08-25
The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
Direct Observation of Dynamical Quantum Phase Transitions in an Interacting Many-Body System
Jurcevic, P.; Shen, H.; Hauke, P.; Maier, C.; Brydges, T.; Hempel, C.; Lanyon, B. P.; Heyl, M.; Blatt, R.; Roos, C. F.
2017-08-01
The theory of phase transitions represents a central concept for the characterization of equilibrium matter. In this work we study experimentally an extension of this theory to the nonequilibrium dynamical regime termed dynamical quantum phase transitions (DQPTs). We investigate and measure DQPTs in a string of ions simulating interacting transverse-field Ising models. During the nonequilibrium dynamics induced by a quantum quench we show for strings of up to 10 ions the direct detection of DQPTs by revealing nonanalytic behavior in time. Moreover, we provide a link between DQPTs and the dynamics of other quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
Quantum physics. Vol. 2. From time-dependent dynamics to many-body physics and quantum chaos
International Nuclear Information System (INIS)
Zelevinsky, Vladimir
2011-01-01
This two-volume set can be naturally divided into two semester courses, and contains a full modern graduate course in quantum physics. The idea is to teach graduate students how to practically use quantum physics and theory, presenting the fundamental knowledge, and gradually moving on to applications, including atomic, nuclear and solid state physics, as well as modern subfields, such as quantum chaos and quantum entanglement. The book starts with basic quantum problems, which do not require full quantum formalism but allow the student to gain the necessary experience and elements of quantum thinking. Only then does the fundamental Schrodinger equation appear. The author has included topics that are not usually covered in standard textbooks and has written the book in such a way that every topic contains varying layers of difficulty, so that the instructor can decide where to stop. Although supplementary sources are not required, ''Further reading'' is given for each chapter, including references to scientific journals and publications, and a glossary is also provided. Problems and solutions are integrated throughout the text. (orig.)
Quantum physics. Vol. 2. From time-dependent dynamics to many-body physics and quantum chaos
Energy Technology Data Exchange (ETDEWEB)
Zelevinsky, Vladimir [NSCL Michigan State Univ., East Lansing, MI (United States). Dept. of Physics and Astronomy
2011-07-01
This two-volume set can be naturally divided into two semester courses, and contains a full modern graduate course in quantum physics. The idea is to teach graduate students how to practically use quantum physics and theory, presenting the fundamental knowledge, and gradually moving on to applications, including atomic, nuclear and solid state physics, as well as modern subfields, such as quantum chaos and quantum entanglement. The book starts with basic quantum problems, which do not require full quantum formalism but allow the student to gain the necessary experience and elements of quantum thinking. Only then does the fundamental Schrodinger equation appear. The author has included topics that are not usually covered in standard textbooks and has written the book in such a way that every topic contains varying layers of difficulty, so that the instructor can decide where to stop. Although supplementary sources are not required, ''Further reading'' is given for each chapter, including references to scientific journals and publications, and a glossary is also provided. Problems and solutions are integrated throughout the text. (orig.)
Many-body spin related phenomena in ultra-low-disorder quantum wires
International Nuclear Information System (INIS)
Reilly, D.J.; Facer, G.R.; Dzurak, A.S.; Kane, B.E.; Clark, R.G.; Stiles, P.J.; O'Brien, J.L.; Lumpkin, N.E.
2000-01-01
Full text: Zero length quantum wires (or point contacts) exhibit unexplained conductance structure close to 0.7 x 2e 2 /h in the absence of an applied magnetic field. We have studied the density- and temperature-dependent conductance of ultra-low-disorder GaAs AlGaAs quantum wires with nominal lengths l=0 and 2μm, fabricated from structures free of the disorder associated with modulation doping. In a direct comparison we observe structure near 0.7 x 2e 2 /h for l=0 whereas the l = 2μm wires show structure evolving with increasing density to 0.5 x 2e 2 /h in zero magnetic field, the value expected for an ideal spin split sub-band. Our results suggest the dominant mechanism through which electrons interact can be strongly affected by the length of the 1D region
Dominant role of many-body effects on the carrier distribution function of quantum dot lasers
Peyvast, Negin; Zhou, Kejia; Hogg, Richard A.; Childs, David T. D.
2016-03-01
The effects of free-carrier-induced shift and broadening on the carrier distribution function are studied considering different extreme cases for carrier statistics (Fermi-Dirac and random carrier distributions) as well as quantum dot (QD) ensemble inhomogeneity and state separation using a Monte Carlo model. Using this model, we show that the dominant factor determining the carrier distribution function is the free carrier effects and not the choice of carrier statistics. By using empirical values of the free-carrier-induced shift and broadening, good agreement is obtained with experimental data of QD materials obtained under electrical injection for both extreme cases of carrier statistics.
A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems
Abanin, Dmitry; De Roeck, Wojciech; Ho, Wen Wei; Huveneers, François
2017-09-01
Prethermalization refers to the transient phenomenon where a system thermalizes according to a Hamiltonian that is not the generator of its evolution. We provide here a rigorous framework for quantum spin systems where prethermalization is exhibited for very long times. First, we consider quantum spin systems under periodic driving at high frequency {ν}. We prove that up to a quasi-exponential time {τ_* ˜ e^{c ν/log^3 ν}}, the system barely absorbs energy. Instead, there is an effective local Hamiltonian {\\widehat D} that governs the time evolution up to {τ_*}, and hence this effective Hamiltonian is a conserved quantity up to {τ_*}. Next, we consider systems without driving, but with a separation of energy scales in the Hamiltonian. A prime example is the Fermi-Hubbard model where the interaction U is much larger than the hopping J. Also here we prove the emergence of an effective conserved quantity, different from the Hamiltonian, up to a time {τ_*} that is (almost) exponential in {U/J}.
Efficient Implementation of Many-body Quantum Chemical Methods on the Intel Xeon Phi Coprocessor
Energy Technology Data Exchange (ETDEWEB)
Apra, Edoardo; Klemm, Michael; Kowalski, Karol
2014-12-01
This paper presents the implementation and performance of the highly accurate CCSD(T) quantum chemistry method on the Intel Xeon Phi coprocessor within the context of the NWChem computational chemistry package. The widespread use of highly correlated methods in electronic structure calculations is contingent upon the interplay between advances in theory and the possibility of utilizing the ever-growing computer power of emerging heterogeneous architectures. We discuss the design decisions of our implementation as well as the optimizations applied to the compute kernels and data transfers between host and coprocessor. We show the feasibility of adopting the Intel Many Integrated Core Architecture and the Intel Xeon Phi coprocessor for developing efficient computational chemistry modeling tools. Remarkable scalability is demonstrated by benchmarks. Our solution scales up to a total of 62560 cores with the concurrent utilization of Intel Xeon processors and Intel Xeon Phi coprocessors.
Adiabatic approximation with exponential accuracy for many-body systems and quantum computation
International Nuclear Information System (INIS)
Lidar, Daniel A.; Rezakhani, Ali T.; Hamma, Alioscia
2009-01-01
We derive a version of the adiabatic theorem that is especially suited for applications in adiabatic quantum computation, where it is reasonable to assume that the adiabatic interpolation between the initial and final Hamiltonians is controllable. Assuming that the Hamiltonian is analytic in a finite strip around the real-time axis, that some number of its time derivatives vanish at the initial and final times, and that the target adiabatic eigenstate is nondegenerate and separated by a gap from the rest of the spectrum, we show that one can obtain an error between the final adiabatic eigenstate and the actual time-evolved state which is exponentially small in the evolution time, where this time itself scales as the square of the norm of the time derivative of the Hamiltonian divided by the cube of the minimal gap.
Tensor Renormalization of Quantum Many-Body Systems Using Projected Entangled Simplex States
Directory of Open Access Journals (Sweden)
Z. Y. Xie
2014-02-01
Full Text Available We propose a new class of tensor-network states, which we name projected entangled simplex states (PESS, for studying the ground-state properties of quantum lattice models. These states extend the pair-correlation basis of projected entangled pair states to a simplex. PESS are exact representations of the simplex solid states, and they provide an efficient trial wave function that satisfies the area law of entanglement entropy. We introduce a simple update method for evaluating the PESS wave function based on imaginary-time evolution and the higher-order singular-value decomposition of tensors. By applying this method to the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice, we obtain accurate and systematic results for the ground-state energy, which approach the lowest upper bounds yet estimated for this quantity.
Thermalization and out-of-equilibrium dynamics in open quantum many-body systems
Energy Technology Data Exchange (ETDEWEB)
Buchhold, Michael
2015-06-30
In this thesis, we address both the question whether or not a quantum system driven away from equilibrium is able to relax to a thermal state, which fulfills detailed balance, and if one can identify universal behavior in the non-equilibrium relaxation dynamics. As a first realization of driven quantum systems out of equilibrium, we investigate a system of Ising spins, interacting with the quantized radiation field in an optical cavity. For multiple cavity modes, this system forms a highly entangled and frustrated state with infinite correlation times, known as a quantum spin glass. In the thermalized system, the features of the spin glass are mirrored onto the photon degrees of freedom, leading to an emergent photon glass phase. Exploiting the inherent photon loss of the cavity, we make predictions of possible measurements on the escaping photons, which contain detailed information of the state inside the cavity and allow for a precise, non-destructive measurement of the glass state. As a further set of non-equilibrium systems, we consider one-dimensional quantum fluids driven out of equilibrium, whose universal low energy theory is formed by the so-called Luttinger Liquid description. In this thesis, we derive for the first time a kinetic equation for interacting Luttinger Liquids, which describes the time evolution of the excitation densities for arbitrary initial states. The resonant character of the interaction makes a straightforward derivation of the kinetic equation, using Fermis golden rule, impossible and we have to develop non-perturbative techniques in the Keldysh framework. We derive a closed expression for the time evolution of the excitation densities in terms of self-energies and vertex corrections. Close to equilibrium, the kinetic equation describes the exponential decay of excitations, with a decay rate σ{sup R}=ImΣ{sup R}, determined by the self-energy at equilibrium. However, for long times τ, it also reveals the presence of dynamical slow
International Nuclear Information System (INIS)
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations such as minimization of cache misses and utilization of multimedia vector instructions are discussed. A library for efficient index permutation of multi-dimensional tensors is described and experimental performance data is provided that demonstrates its effectiveness.
International Nuclear Information System (INIS)
Krishnamoorthy, Sriram; Bernholdt, David E.; Pitzer, R.M.; Sadayappan, Ponnuswamy
2009-01-01
Complex tensor contraction expressions arise in accurate electronic structure models in quantum chemistry, such as the coupled cluster method. This paper addresses two complementary aspects of performance optimization of such tensor contraction expressions. Transformations using algebraic properties of commutativity and associativity can be used to significantly decrease the number of arithmetic operations required for evaluation of these expressions. The identification of common subexpressions among a set of tensor contraction expressions can result in a reduction of the total number of operations required to evaluate the tensor contractions. The first part of the paper describes an effective algorithm for operation minimization with common subexpression identification and demonstrates its effectiveness on tensor contraction expressions for coupled cluster equations. The second part of the paper highlights the importance of data layout transformation in the optimization of tensor contraction computations on modern processors. A number of considerations, such as minimization of cache misses and utilization of multimedia vector instructions, are discussed. A library for efficient index permutation of multidimensional tensors is described, and experimental performance data is provided that demonstrates its effectiveness.
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems
Directory of Open Access Journals (Sweden)
Jutho Haegeman
2015-02-01
Full Text Available We present an operational procedure to transform global symmetries into local symmetries at the level of individual quantum states, as opposed to typical gauging prescriptions for Hamiltonians or Lagrangians. We then construct a compatible gauging map for operators, which preserves locality and reproduces the minimal coupling scheme for simple operators. By combining this construction with the formalism of projected entangled-pair states (PEPS, we can show that an injective PEPS for the matter fields is gauged into a G-injective PEPS for the combined gauge-matter system, which potentially has topological order. We derive the corresponding parent Hamiltonian, which is a frustration-free gauge-theory Hamiltonian closely related to the Kogut-Susskind Hamiltonian at zero coupling constant. We can then introduce gauge dynamics at finite values of the coupling constant by applying a local filtering operation. This scheme results in a low-parameter family of gauge-invariant states of which we can accurately probe the phase diagram, as we illustrate by studying a Z_{2} gauge theory with Higgs matter.
The many-body level density; Densite de niveaux du probleme a n-corps
Energy Technology Data Exchange (ETDEWEB)
Roccia, J
2007-09-15
We investigate the many-body level density {rho}{sub MB} for fermion and boson gases. We establish its behavior as a function of the temperature and the number of particles. We deal with correction terms due to finite number of particles effects for {rho}{sub MB}: for fermions, it seems that it exists only one behavior. We propose a semiclassical expression of {rho}{sub MB} for two types of particles with an angular momentum. It is decomposed into a smooth part coming from the saddle point method plus corrective terms due to the expansion of the number of partitions for two types of particles and an oscillating part coming from the fluctuations of the single-particle level density. Our model is validated by a numerical study. For the case of the atomic nucleus, the oscillating part of {rho}{sub MB} is controlled by a temperature factor which depends on the chaotic or integrable nature of the system and on the fluctuation of the ground state energy. This leads to consider in more detail this last quantity. For an isolated system, we give the general expression of the mean value for fixed potentials. We treat the self-bound system case through the example of the three dimensional harmonic oscillator (3DHO). Furthermore we study the oscillating part of {rho}{sub MB} for bosons in the low temperature regime for billiards and for isotropic 3DHO. We note the oscillations disappear leading to a power law correction. In the case of the isotropic 3DHO, these corrections have the same order of magnitude as the smooth part. In the same way, for the high temperature regime we show the oscillating part of {rho}{sub MB} is exponentially negligible compared to the smooth part. (author)
Directory of Open Access Journals (Sweden)
C. Eichler
2015-12-01
Full Text Available Improving the understanding of strongly correlated quantum many-body systems such as gases of interacting atoms or electrons is one of the most important challenges in modern condensed matter physics, materials research, and chemistry. Enormous progress has been made in the past decades in developing both classical and quantum approaches to calculate, simulate, and experimentally probe the properties of such systems. In this work, we use a combination of classical and quantum methods to experimentally explore the properties of an interacting quantum gas by creating experimental realizations of continuous matrix product states—a class of states that has proven extremely powerful as a variational ansatz for numerical simulations. By systematically preparing and probing these states using a circuit quantum electrodynamics system, we experimentally determine a good approximation to the ground-state wave function of the Lieb-Liniger Hamiltonian, which describes an interacting Bose gas in one dimension. Since the simulated Hamiltonian is encoded in the measurement observable rather than the controlled quantum system, this approach has the potential to apply to a variety of models including those involving multicomponent interacting fields. Our findings also hint at the possibility of experimentally exploring general properties of matrix product states and entanglement theory. The scheme presented here is applicable to a broad range of systems exploiting strong and tunable light-matter interactions.
Non-extensive statistical effects in nuclear many-body problems
International Nuclear Information System (INIS)
Lavagno, A.; Quarati, P.
2007-01-01
Density and temperature conditions in many stellar core and in the first stage of relativistic heavy-ion collisions imply the presence of non-ideal plasma effects with memory and long-range interactions between particles. Recent progress in statistical mechanics indicates that Tsallis non-extensive thermostatistics could be the natural generalization of the standard classical and quantum statistics, when memory effects and long range forces are not negligible. In this framework, we show that in weakly non-ideal plasma non-extensive effects should be taken into account to derive the equilibrium distribution functions, the quantum fluctuations and correlations between the particles. The strong influence of these effects is discussed in the context of the solar plasma physics and in the high-energy nuclear-nuclear collision experiments. Although the deviation from Boltzmann-Gibbs statistics, in both cases, is very small, the stellar plasma and the hadronic gas are strongly influenced by the non-extensive feature and the discrepancies between experimental data and theoretical previsions are sensibly reduced. (authors)
Directory of Open Access Journals (Sweden)
Phillip Weinberg, Marin Bukov
2017-02-01
Full Text Available We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon chains, called QuSpin, supporting the use of various symmetries in 1-dimension and (imaginary time evolution for chains up to 32 sites in length. The package is well-suited to study, among others, quantum quenches at finite and infinite times, the Eigenstate Thermalisation hypothesis, many-body localisation and other dynamical phase transitions, periodically-driven (Floquet systems, adiabatic and counter-diabatic ramps, and spin-photon interactions. Moreover, QuSpin's user-friendly interface can easily be used in combination with other Python packages which makes it amenable to a high-level customisation. We explain how to use QuSpin using four detailed examples: (i Standard exact diagonalisation of XXZ chain (ii adiabatic ramping of parameters in the many-body localised XXZ model, (iii heating in the periodically-driven transverse-field Ising model in a parallel field, and (iv quantised light-atom interactions: recovering the periodically-driven atom in the semi-classical limit of a static Hamiltonian.
Huang, Danhong; Iurov, Andrii; Gao, Fei; Gumbs, Godfrey; Cardimona, D. A.
2018-02-01
The effects of point defects on the loss of either energies of ballistic electron beams or incident photons are studied by using a many-body theory in a multi-quantum-well system. This theory includes the defect-induced vertex correction to a bare polarization function of electrons within the ladder approximation, and the intralayer and interlayer screening of defect-electron interactions is also taken into account in the random-phase approximation. The numerical results of defect effects on both energy-loss and optical-absorption spectra are presented and analyzed for various defect densities, numbers of quantum wells, and wave vectors. The diffusion-reaction equation is employed for calculating distributions of point defects in a layered structure. For completeness, the production rate for Frenkel-pair defects and their initial concentration are obtained based on atomic-level molecular-dynamics simulations. By combining the defect-effect, diffusion-reaction, and molecular-dynamics models with an available space-weather-forecast model, it will be possible in the future to enable specific designing for electronic and optoelectronic quantum devices that will be operated in space with radiation-hardening protection and, therefore, effectively extend the lifetime of these satellite onboard electronic and optoelectronic devices. Specifically, this theory can lead to a better characterization of quantum-well photodetectors not only for high quantum efficiency and low dark current density but also for radiation tolerance or mitigating the effects of the radiation.
Meson dynamics and the nuclear many-body problem. II. Finite density Hartree-Fock
International Nuclear Information System (INIS)
Wilets, L.; Puff, R.D.; Chiang, D.; Nutt, W.T.
1976-01-01
The field-theoretic many-nucleon problem is formulated, and an analysis which sums all ''uncrossed meson line'' diagrams is investigated in detail. The calculation of energy per nucleon, after proper identification of infinite mass renormalization terms, exhibits effects of nuclear recoil, relativistic kinematics, and retardation. Numerical results are presented for π and ω mesons, and the nucleon interaction energies obtained are compared with the traditional static limit of infinite nucleon mass
Energy Technology Data Exchange (ETDEWEB)
Canetta, G.; Maino, G.; Magnani, M.; Visparelli, D. [ENEA, Centro Ricerche Ezio Clementel, Bologna (Italy). Dipt. Innovazione
1999-07-01
The interacting boson model (IBM) is a realistic model of nuclear structure, since it allows to cut off in a suitable way the complete space of the shell model states. In such a way, it offers a great simplicity of the numerical computation of the eigenvalue problem for a many-body non-relativistic quantum system, like a nucleus. In particular, the analytical solutions obtained in the case of dynamical symmetries correspond, in the classical limit, to completely integrable systems showing a regular dynamic behaviour. In this report, a detailed analysis is performed of the IBM version 2 (IBM-2), which explicitly introduces the isospin degree of freedom. The different forms of the IBM-2 Hamiltonian usually considered in the literature, are discussed, and the explicit relations existing between them are deduced. Moreover, the semiclassical limit of the most general IBM-2 Hamiltonian is studied in the details. Finally, the expectation of chaotic dynamic behaviour near to regular dynamics, in the IBM, and, in particular, the fact that the latter ones persist more than expected a priori, is shown. Maybe, this behaviour is to adduce to the existence of partial dynamic symmetries. [Italian] Il modello a bosoni interagenti (IBM) rappresenta un modello realistico della struttura nucleare, premettendo di troncare opportunamente lo spazio completo degli stati di modello a shell, e percio' offre una notevole semplicita' computazionale nella risoluzione numerica del problema degli autovalori per un sistema quantico non relativistico a molti corpi, quale e' un nucleo. In particolare, le soluzioni analitiche ottenute nel caso di simmetrie dinamiche corrispondono, nel limite classico, a sistemi completamente integrabili che mostrano un comportamento dinamico regolare. In questo rapporto viene condotta un'analisi dettagliata del modello IBM nella versione (IBM-2), il quale introduce esplicitamente il grado di liberta' di isospin. In particolare, sono
Energy Technology Data Exchange (ETDEWEB)
Babichenko, V.S. [RRC Kurchatov Institute, Kurchatov Sq., 1, 123182 Moscow (Russian Federation); Polishchuk, I.Ya., E-mail: iyppolishchuk@gmail.com [RRC Kurchatov Institute, Kurchatov Sq., 1, 123182 Moscow (Russian Federation); Moscow Institute of Physics and Technology, 141700, 9, Institutskii per., Dolgoprudny, Moscow Region (Russian Federation)
2014-11-15
The many-body correlation effects in the spatially separated electron and hole layers in the coupled quantum wells are investigated. A special case of the many-component electron–hole system is considered. It is shown that if the hole mass is much greater than the electron mass, the negative correlation energy is mainly determined by the holes. The ground state of the system is found to be the 2D electron–hole liquid with the energy smaller than the exciton phase. It is shown that the system decays into the spatially separated neutral electron–hole drops if the initially created charge density in the layers is smaller than the certain critical value n{sub eq}.
International Nuclear Information System (INIS)
Tanaka, Toshiaki
2007-01-01
We propose an elegant formulation of parafermionic algebra and parasupersymmetry of arbitrary order in quantum many-body systems without recourse to any specific matrix representation of parafermionic operators and any kind of deformed algebra. Within our formulation, we show generically that every parasupersymmetric quantum system of order p consists of N-fold supersymmetric pairs with N≤p and thus has weak quasi-solvability and isospectral property. We also propose a new type of non-linear supersymmetries, called quasi-parasupersymmetry, which is less restrictive than parasupersymmetry and is different from N-fold supersymmetry even in one-body systems though the conserved charges are represented by higher-order linear differential operators. To illustrate how our formulation works, we construct second-order parafermionic algebra and three simple examples of parasupersymmetric quantum systems of order 2, one is essentially equivalent to the one-body Rubakov-Spiridonov type and the others are two-body systems in which two supersymmetries are folded. In particular, we show that the first model admits a generalized 2-fold superalgebra
International Nuclear Information System (INIS)
Niyaz, P.
1993-01-01
Quantum Monte Carlo techniques were used to study two quantum many-body systems, the one-dimensional extended boson-Hubbard Hamiltonian, a model of superfluid-insulator quantum phase transitions, and the two-dimensional Holstein Model, a model for electron-phonon interactions. For the extended boson-Hubbard model, the authors studied the ground state properties at commensurate filling (density = 1) and half-integer filling (density = 1/2). At commensurate filling, the system has two possible insulating phases for strong coupling. If the on-site repulsion dominates, the system freezes into an insulating phase where each site is singly occupied. If the intersite repulsion dominates, doubly occupied and empty sites alternate. At weak coupling, the system becomes a superfluid. The authors investigated the order of phase transitions between these different phases. At half-integer filling, the authors found one strong coupling insulating phase, where singly occupied and empty sites alternate, and a weak coupling superfluid phase. The authors also investigated the possibility of a supersolid phase and found no clear evidence of such a new phase. For the electron-phonon (Holstein) model, the authors focused on the finite temperature phase transition from a metallic state to an insulating charge density wave (CDW) state as the temperature is lowered. The authors present the first calculation of the spectral density from Monte Carlo data for this system. The authors also investigated the formation of a CDW state as a function of various parameters characterizing the electron-phonon interactions. Using these numerical results as benchmarks, the authors then investigated different levels of Migdal approximations. The authors found the solutions of a set of gapped Migdal-Eliashberg equations agreed qualitatively with the Monte Carlo results
Donner, Tobias
2015-03-01
A Bose-Einstein condensate whose motional degrees of freedom are coupled to a high-finesse optical cavity via a transverse pump beam constitutes a dissipative quantum many-body system with long range interactions. These interactions can induce a structural phase transition from a flat to a density-modulated state. The transverse pump field simultaneously represents a probe of the atomic density via cavity- enhanced Bragg scattering. By spectrally analyzing the light field leaking out of the cavity, we measure non-destructively the dynamic structure factor of the fluctuating atomic density while the system undergoes the phase transition. An observed asymmetry in the dynamic structure factor is attributed to the coupling to dissipative baths. Critical exponents for both sides of the phase transition can be extracted from the data. We further discuss our progress in adding strong short-range interactions to this system, in order to explore Bose-Hubbard physics with cavity-mediated long-range interactions and self-organization in lower dimensions.
Quantum many-body effects in x-ray spectra efficiently computed using a basic graph algorithm
Liang, Yufeng; Prendergast, David
2018-05-01
The growing interest in using x-ray spectroscopy for refined materials characterization calls for an accurate electronic-structure theory to interpret the x-ray near-edge fine structure. In this work, we propose an efficient and unified framework to describe all the many-electron processes in a Fermi liquid after a sudden perturbation (such as a core hole). This problem has been visited by the Mahan-Noziéres-De Dominicis (MND) theory, but it is intractable to implement various Feynman diagrams within first-principles calculations. Here, we adopt a nondiagrammatic approach and treat all the many-electron processes in the MND theory on an equal footing. Starting from a recently introduced determinant formalism [Phys. Rev. Lett. 118, 096402 (2017), 10.1103/PhysRevLett.118.096402], we exploit the linear dependence of determinants describing different final states involved in the spectral calculations. An elementary graph algorithm, breadth-first search, can be used to quickly identify the important determinants for shaping the spectrum, which avoids the need to evaluate a great number of vanishingly small terms. This search algorithm is performed over the tree-structure of the many-body expansion, which mimics a path-finding process. We demonstrate that the determinantal approach is computationally inexpensive even for obtaining x-ray spectra of extended systems. Using Kohn-Sham orbitals from two self-consistent fields (ground and core-excited state) as input for constructing the determinants, the calculated x-ray spectra for a number of transition metal oxides are in good agreement with experiments. Many-electron aspects beyond the Bethe-Salpeter equation, as captured by this approach, are also discussed, such as shakeup excitations and many-body wave function overlap considered in Anderson's orthogonality catastrophe.
International Nuclear Information System (INIS)
Masiello, David J.; Reinhardt, William P.
2007-01-01
A time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, by construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states
Koop, E. J.; Lerescu, A. I.; Liu, J.; van Wees, B. J.; Reuter, D.; Wieck, A. D.; van der Wal, C. H.
The conductance of a quantum point contact (QPC) shows several features that result from many-body electron interactions. The spin degeneracy in zero magnetic field appears to be spontaneously lifted due to the so-called 0.7 anomaly. Further, the g-factor for electrons in the QPC is enhanced, and a
International Nuclear Information System (INIS)
Brueckner, K.A.
1980-01-01
This paper reviews the major steps in the development of many-body theory since the early 1950's. Very few systems permit an exact solution by selective diagram summation or by exact solution of a truncated Hamiltonian. Formal methods have usually had little success for real physical systems. Examples are all the quantum liquids such as nuclear matter, liquid He 3 , liquid He 4 , superconductors and metallic conductors. Atomic and molecular systems and finite nuclei present additional problems. Many-body theory has probably had its greatest success in the application to atomic properties and the development in recent years is reviewed. (Auth.)
Bruno, Patrick
2012-06-01
The (Berry-Aharonov-Anandan) geometric phase acquired during a cyclic quantum evolution of finite-dimensional quantum systems is studied. It is shown that a pure quantum state in a (2J+1)-dimensional Hilbert space (or, equivalently, of a spin-J system) can be mapped onto the partition function of a gas of independent Dirac strings moving on a sphere and subject to the Coulomb repulsion of 2J fixed test charges (the Majorana stars) characterizing the quantum state. The geometric phase may be viewed as the Aharonov-Bohm phase acquired by the Majorana stars as they move through the gas of Dirac strings. Expressions for the geometric connection and curvature, for the metric tensor, as well as for the multipole moments (dipole, quadrupole, etc.), are given in terms of the Majorana stars. Finally, the geometric formulation of the quantum dynamics is presented and its application to systems with exotic ordering such as spin nematics is outlined.
Jaschke, Daniel; Wall, Michael L.; Carr, Lincoln D.
2018-04-01
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z2 symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.
Quantum physics of light and matter a modern introduction to photons, atoms and many-body systems
Salasnich, Luca
2014-01-01
The book gives an introduction to the field quantization (second quantization) of light and matter with applications to atomic physics. The first chapter briefly reviews the origins of special relativity and quantum mechanics and the basic notions of quantum information theory and quantum statistical mechanics. The second chapter is devoted to the second quantization of the electromagnetic field, while the third chapter shows the consequences of the light field quantization in the description of electromagnetic transitions.In the fourth chapter it is analyzed the spin of the electron, and in particular its derivation from the Dirac equation, while the fifth chapter investigates the effects of external electric and magnetic fields on the atomic spectra (Stark and Zeeman effects). The sixth chapter describes the properties of systems composed by many interacting identical particles by introducing the Hartree-Fock variational method, the density functional theory, and the Born-Oppenheimer approximation. Finally,...
Czech Academy of Sciences Publication Activity Database
Dittrich, Jaroslav; Inozemtsev, V. I.
2009-01-01
Roč. 14, č. 2 (2009), s. 218-222 ISSN 1560-3547 R&D Projects: GA MŠk(CZ) LC06002; GA MŠk(CZ) LA08002 Institutional research plan: CEZ:AV0Z10480505 Keywords : quantum elliptic spin system * transposition * integrability Subject RIV: BE - Theoretical Physics Impact factor: 0.725, year: 2009
International Nuclear Information System (INIS)
Hubbard, J.
1980-01-01
The evolution of the discipline of many-body theory during the past 25 years is outlined and the developments originated in the Theoretical Physics Division, AERE, are discussed. Topics considered include; the connection between plasma oscillations and the dielectric properties of an electron gas, superconductivity, Fermi levels, ferromagnetism in metals, phase transformations, scaling laws, and quasi-one-dimensional solids. (UK)
Ziaei, Vafa; Bredow, Thomas
2017-03-17
The reliable calculation of the excited states of charge-transfer (CT) compounds poses a major challenge to the ab initio community because the frequently employed method, time-dependent density functional theory (TD-DFT), massively relies on the underlying density functional, resulting in heavily Hartree-Fock (HF) exchange-dependent excited-state energies. By applying the highly sophisticated many-body perturbation approach, we address the encountered unreliabilities and inconsistencies of not optimally tuned (standard) TD-DFT regarding photo-excited CT phenomena, and present results concerning accurate vertical transition energies and the correct energetic ordering of the CT and the first visible singlet state of a recently synthesized thermodynamically stable large hybrid perylene bisimide-macrocycle complex. This is a large-scale application of the quantum many-body perturbation approach to a chemically relevant CT system, demonstrating the system-size independence of the quality of the many-body-based excitation energies. Furthermore, an optimal tuning of the ωB97X hybrid functional can well reproduce the many-body results, making TD-DFT a suitable choice but at the expense of introducing a range-separation parameter, which needs to be optimally tuned. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Ma, Yue; Hoang, Thai M.; Gong, Ming; Li, Tongcang; Yin, Zhang-qi
2017-08-01
Hybrid spin-mechanical systems have great potential in sensing, macroscopic quantum mechanics, and quantum information science. In order to induce strong coupling between an electron spin and the center-of-mass motion of a mechanical oscillator, a large magnetic gradient usually is required, which is difficult to achieve. Here we show that strong coupling between the electron spin of a nitrogen-vacancy (NV) center and the torsional vibration of an optically levitated nanodiamond can be achieved in a uniform magnetic field. Thanks to the uniform magnetic field, multiple spins can strongly couple to the torsional vibration at the same time. We propose utilizing this coupling mechanism to realize the Lipkin-Meshkov-Glick (LMG) model by an ensemble of NV centers in a levitated nanodiamond. The quantum phase transition in the LMG model and finite number effects can be observed with this system. We also propose generating torsional superposition states and realizing torsional matter-wave interferometry with spin-torsional coupling.
Energy Technology Data Exchange (ETDEWEB)
Haemmerling, Jens; Gutkin, Boris; Guhr, Thomas, E-mail: jens.haemmerling@uni-due.d [Universitaet Duisburg-Essen, Lotharstrasse 1, 47048 Duisburg (Germany)
2010-07-02
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics.
International Nuclear Information System (INIS)
Haemmerling, Jens; Gutkin, Boris; Guhr, Thomas
2010-01-01
We study the emergence of collective dynamics in the integrable Hamiltonian system of two finite ensembles of coupled harmonic oscillators. After identification of a collective degree of freedom, the Hamiltonian is mapped onto a model of Caldeira-Leggett type, where the collective coordinate is coupled to an internal bath of phonons. In contrast to the usual Caldeira-Leggett model, the bath in the present case is part of the system. We derive an equation of motion for the collective coordinate which takes the form of a damped harmonic oscillator. We show that the distribution of quantum transition strengths induced by the collective mode is determined by its classical dynamics.
International Nuclear Information System (INIS)
Rihani, J.; Sedrine, N.B.; Sallet, V.; Oueslati, M.; Chtourou, R.
2008-01-01
InAs quantum dots (QDs) on GaAs (0 0 1) substrates were grown by Molecular Beam Epitaxy (MBE) using two growth temperatures. Photoluminescence (PL) pump power dependence measurements at low temperature were carried out for sample grown at higher temperature (520 deg. C). With increasing excitation density, the ground-state transition energy is found to decrease by 8 meV, while the excited-state transition energies exhibit resonance behaviour. The redshift of the ground-state emission was related to the band-gap renomalization (BGR) effect whereas the blueshift of the excited-state emissions was assigned to the compensation between filling of fine structure states and BGR effects. Using a quasi-resonant PL measurement, we have shown that the renormalization of the band-gap had to occur in the QD barrier
International Nuclear Information System (INIS)
Morimoto, T; Yumoto, N; Ujiie, Y; Aoki, N; Ochiai, Y; Bird, J P
2008-01-01
We investigate the behavior of interacting one-dimensional systems using linear (close to equilibrium) and non-linear transport measurements of split-gate quantum wires of varying channel length. Our measurements reveal a remarkable resonance effect in the differential conductance, which exhibits a pronounced peak, for a narrow range of source-drain voltage, at the transition from tunneling to open transport. This peak becomes more pronounced with increase of channel length, but is rapidly suppressed by increase of temperature or (in-plane) magnetic field. We believe that these unique features may arise from the dependence of transport on the electron density of states, and suggest a phenomenological model to account for this transport behavior
Bajaj, Pushp; Wang, Xiao-Gang; Carrington, Tucker; Paesani, Francesco
2018-03-01
Full-dimensional vibrational spectra are calculated for both X-(H2O) and X-(D2O) dimers (X = F, Cl, Br, I) at the quantum-mechanical level. The calculations are carried out on two sets of recently developed potential energy functions (PEFs), namely, Thole-type model energy (TTM-nrg) and many-body energy (MB-nrg), using the symmetry-adapted Lanczos algorithm with a product basis set including all six vibrational coordinates. Although both TTM-nrg and MB-nrg PEFs are derived from coupled-cluster single double triple-F12 data obtained in the complete basis set limit, they differ in how many-body effects are represented at short range. Specifically, while both models describe long-range interactions through the combination of two-body dispersion and many-body classical electrostatics, the relatively simple Born-Mayer functions employed in the TTM-nrg PEFs to represent short-range interactions are replaced in the MB-nrg PEFs by permutationally invariant polynomials to achieve chemical accuracy. For all dimers, the MB-nrg vibrational spectra are in close agreement with the available experimental data, correctly reproducing anharmonic and nuclear quantum effects. In contrast, the vibrational frequencies calculated with the TTM-nrg PEFs exhibit significant deviations from the experimental values. The comparison between the TTM-nrg and MB-nrg results thus reinforces the notion that an accurate representation of both short-range interactions associated with electron density overlap and long-range many-body electrostatic interactions is necessary for a correct description of hydration phenomena at the molecular level.
International Nuclear Information System (INIS)
Schwesinger, B.
1978-01-01
The solution of the many-body oscillator problem is used as a basis for a RPA-calculation of 16 O. The calculation is performed in a LS-coupling scheme with an interaction containing central, spin-orbit and tensor forces. The main differences with conventional RPA-calculations occur for the transition probabilities. (orig.) [de
Exact results for the many-body problem in one dimension with repulsive delta-function interaction
International Nuclear Information System (INIS)
Yang, C.N.
1983-01-01
The repulsive δ interaction problem in one dimension for N particles is reduced, through the use of Bethe's hypothesis, to an eigenvalue problem of matrices of the same sizes as the irreducible representations R of the permutation group S/sub N/. For some R's this eigenvalue problem itself is solved by a second use of Bethe's hypothesis, in a generalized form. In particular, the ground-state problem of spin-1/2 fermions is reduced to a generalized Fredholm equation
Back-of-the-envelope quantum mechanics with extensions to many-body systems and integrable PDEs
Olshanii, Maxim
2014-01-01
Dimensional and order-of-magnitude estimates are practiced by almost everybody but taught almost nowhere. When physics students engage in their first theoretical research project, they soon learn that exactly solvable problems belong only to textbooks, that numerical models are long and resource consuming, and that ""something else"" is needed to quickly gain insight into the system they are going to study. Qualitative methods are this ""something else"", but typically, students have never heard of them before. The aim of this book is to teach the craft of qualitative analysis using a set of p
Photon Subtraction by Many-Body Decoherence
DEFF Research Database (Denmark)
Murray, C. R.; Mirgorodskiy, I.; Tresp, C.
2018-01-01
We experimentally and theoretically investigate the scattering of a photonic quantum field from another stored in a strongly interacting atomic Rydberg ensemble. Considering the many-body limit of this problem, we derive an exact solution to the scattering-induced spatial decoherence of multiple...... stored photons, allowing for a rigorous understanding of the underlying dissipative quantum dynamics. Combined with our experiments, this analysis reveals a correlated coherence-protection process in which the scattering from one excitation can shield all others from spatial decoherence. We discuss how...... this effect can be used to manipulate light at the quantum level, providing a robust mechanism for single-photon subtraction, and experimentally demonstrate this capability....
Calogero, Francesco
2001-01-01
This book focuses on exactly treatable classical (i.e. non-quantal non-relativistic) many-body problems, as described by Newton's equation of motion for mutually interacting point particles. Most of the material is based on the author's research and is published here for the first time in book form. One of the main novelties is the treatment of problems in two- and three-dimensional space. Many related techniques are presented, e.g. the theory of generalized Lagrangian-type interpolation in higher-dimensional spaces. This book is written for students as well as for researchers; it works out detailed examples before going on to treat more general cases. Many results are presented via exercises, with clear hints pointing to their solutions.
Prethermalization in an isolated many body system
International Nuclear Information System (INIS)
Gring, M.
2012-01-01
Understanding the relaxation dynamics of complex non-equilibrium many-body quantum systems is a fundamental problem, arising in many areas of physics. However, experimental examples of non-equilibrium systems that are both controllable and suitable for detailed study are extremely rare. In this thesis one such example in the form of a coherently split one-dimensional (1d) ultra cold Bose gas in a double-well potential is studied in detail. Typical for the analysis of non-equilibrium systems, the key challenge in this study is the characterization of the complex transient states of the system. In the presented work this task is solved by employing measurements of the time evolution of the full quantum mechanical probability distribution functions (FDFs) of time-of-flight matter-wave interference patterns between the two halves of the split system. The dynamics of the FDFs reveal two distinct regimes of relaxation clearly demonstrating the multi-mode nature of 1d Bose gases. Moreover, after an initial rapid evolution, the FDFs exhibit the approach towards a thermal-like steady state of the system which however does not correspond to the true thermal equilibrium of the system. This surprising behaviour is also predicted by a recent theoretical work which puts the observations in a much broader context and classifies them as an example of prethermalization. Prethermalization is a general concept from relativistic quantum field theory and is currently the subject of intense theoretical research. Accordingly prethermalized states were recently predicted for a series of other many-body quantum systems. The work presented in this thesis represents a direct experimental observation of this phenomenon of prethermalization. (author) [de
Many body calculations in atomic physics
International Nuclear Information System (INIS)
Kelly, H.P.
1985-01-01
The use of the many-body perturbation theory for atomic calculations are reviewed. The major emphasis is on the use of the linked-cluster many-body perturbation theory derived by Brueckner and Goldstone. Applications of many-body theory to calculations of hyperfine structure are examined. Auger rates and parity violation are discussed. Photoionization is reviewed, and the authors show how many-body perturbation theory can be applied to problems ranging from structural properties such as correlation energies and hyperfine structure to dynamical properties such as transitions induced by weak neutral currents and photoionization cross sections
2016-06-03
Scientific conference, Quantum Physics REPORT DOCUMENTATION PAGE 11. SPONSOR/MONITOR’S REPORT NUMBER(S) 10. SPONSOR/MONITOR’S ACRONYM(S) ARO 8...publications (other than abstracts): Books Number of Manuscripts: 0.00Number of Presentations: Non Peer-Reviewed Conference Proceeding publications...other than abstracts): (d) Manuscripts Received Paper TOTAL: Received Paper TOTAL: Received Paper TOTAL: Received Book TOTAL: Patents Submitted
Introduction to many-body physics
Coleman, Piers
2015-01-01
A modern, graduate-level introduction to many-body physics in condensed matter, this textbook explains the tools and concepts needed for a research-level understanding of the correlated behavior of quantum fluids. Starting with an operator-based introduction to the quantum field theory of many-body physics, this textbook presents the Feynman diagram approach, Green's functions and finite-temperature many body physics before developing the path integral approach to interacting systems. Special chapters are devoted to the concepts of Fermi liquid theory, broken symmetry, conduction in disordered systems, superconductivity and the physics of local-moment metals. A strong emphasis on concepts and numerous exercises make this an invaluable course book for graduate students in condensed matter physics. It will also interest students in nuclear, atomic and particle physics.
International Nuclear Information System (INIS)
Schmid, K.W.
2001-01-01
The mathematical tools to restore Galilei invariance in the nuclear many-body problem with the help of projection techniques are presented. For simple oscillator configurations recursion relations for the various elementary contractions are derived. The method is then applied to simple configurations for the ground states of 4 He, 16 O and 40 Ca as well as to the corresponding one-hole and one-particle states. As a first application the spectral functions and spectroscopic factors for the above-mentioned doubly even nuclei are investigated. It turns out that the conventional picture of an uncorrelated system underestimates the single-particle strengths of the hole states from the last occupied shell while that of the higher excited hole states is overestimated considerably. These results are in complete agreement with those derived by Dieperink and de Forest using different methods. Similar effects are seen for the particle states which have not been studied before. All the calculations presented here are performed analytically and thus can be checked explicitly by the interested reader. (orig.)
A 2D Array of 100's of Ions for Quantum Simulation and Many-Body Physics in a Penning Trap
Bohnet, Justin; Sawyer, Brian; Britton, Joseph; Bollinger, John
2015-05-01
Quantum simulations promise to reveal new materials and phenomena for experimental study, but few systems have demonstrated the capability to control ensembles in which quantum effects cannot be directly computed. One possible platform for intractable quantum simulations may be a system of 100's of 9Be+ ions in a Penning trap, where the valence electron spins are coupled with an effective Ising interaction in a 2D geometry. Here we report on results from a new Penning trap designed for 2D quantum simulations. We characterize the ion crystal stability and describe progress towards bench-marking quantum effects of the spin-spin coupling using a spin-squeezing witness. We also report on the successful photodissociation of BeH+ contaminant molecular ions that impede the use of such crystals for quantum simulation. This work lays the foundation for future experiments such as the observation of spin dynamics under the quantum Ising Hamiltonian with a transverse field. Supported by a NIST-NRC Research Associateship.
Dynamically induced many-body localization
Choi, Soonwon; Abanin, Dmitry A.; Lukin, Mikhail D.
2018-03-01
We show that a quantum phase transition from ergodic to many-body localized (MBL) phases can be induced via periodic pulsed manipulation of spin systems. Such a transition is enabled by the interplay between weak disorder and slow heating rates. Specifically, we demonstrate that the Hamiltonian of a weakly disordered ergodic spin system can be effectively engineered, by using sufficiently fast coherent controls, to yield a stable MBL phase, which in turn completely suppresses the energy absorption from external control field. Our results imply that a broad class of existing many-body systems can be used to probe nonequilibrium phases of matter for a long time, limited only by coupling to external environment.
Many Body Structure of Strongly Interacting Systems
Arenhövel, Hartmuth; Drechsel, Dieter; Friedrich, Jörg; Kaiser, Karl-Heinz; Walcher, Thomas; Symposium on 20 Years of Physics at the Mainz Microtron MAMI
2006-01-01
This carefully edited proceedings volume provides an extensive review and analysis of the work carried out over the past 20 years at the Mainz Microtron (MAMI). This research centered around the application of Quantum Chromodynamics in the strictly nonperturbative regime at hadronic scales of about 1 fm. Due to the many degrees of freedom in hadrons at this scale the leitmotiv of this research is "Many body structure of strongly interacting systems". Further, an outlook on the research with the forthcoming upgrade of MAMI is given. This volume is an authoritative source of reference for everyone interested in the field of the electro-weak probing of the structure of hadrons.
The mathematical description of resonances in many-body systems
International Nuclear Information System (INIS)
Orth, A.
1985-01-01
We introduce a characterization for quantum-mechanical resonance and use it in order to detect for certain distinct physical states an especially slow decay behaviour. We apply these results to a model of the quantum-mechanical many-body problem and obtain so a mathematical description of the Auger effect (self-ionization of atoms). The class of the interaction potentials admitted for our theory is compared with other theories on resonances extremely large. We establish differentiability conditions and conditions on the fading behaviour in the infinite. Especially the Coulomb potential and the Yukawa potential belong to our class but also non-spherical-symmetric and non-analytic potentials with a Coulomb-like singularity in the origin, two- to threefold differentiable which tend to zero at the infinite. In the introduction we discuss extensively also by means of some examples the problematics of the quantum-mechanical resonance. (orig.) [de
Exactly solvable models in many-body theory
March, N H
2016-01-01
The book reviews several theoretical, mostly exactly solvable, models for selected systems in condensed states of matter, including the solid, liquid, and disordered states, and for systems of few or many bodies, both with boson, fermion, or anyon statistics. Some attention is devoted to models for quantum liquids, including superconductors and superfluids. Open problems in relativistic fields and quantum gravity are also briefly reviewed.The book ranges almost comprehensively, but concisely, across several fields of theoretical physics of matter at various degrees of correlation and at different energy scales, with relevance to molecular, solid-state, and liquid-state physics, as well as to phase transitions, particularly for quantum liquids. Mostly exactly solvable models are presented, with attention also to their numerical approximation and, of course, to their relevance for experiments.
Many-body orthogonal polynomial systems
International Nuclear Information System (INIS)
Witte, N.S.
1997-03-01
The fundamental methods employed in the moment problem, involving orthogonal polynomial systems, the Lanczos algorithm, continued fraction analysis and Pade approximants has been combined with a cumulant approach and applied to the extensive many-body problem in physics. This has yielded many new exact results for many-body systems in the thermodynamic limit - for the ground state energy, for excited state gaps, for arbitrary ground state avenges - and are of a nonperturbative nature. These results flow from a confluence property of the three-term recurrence coefficients arising and define a general class of many-body orthogonal polynomials. These theorems constitute an analytical solution to the Lanczos algorithm in that they are expressed in terms of the three-term recurrence coefficients α and β. These results can also be applied approximately for non-solvable models in the form of an expansion, in a descending series of the system size. The zeroth order order this expansion is just the manifestation of the central limit theorem in which a Gaussian measure and hermite polynomials arise. The first order represents the first non-trivial order, in which classical distribution functions like the binomial distributions arise and the associated class of orthogonal polynomials are Meixner polynomials. Amongst examples of systems which have infinite order in the expansion are q-orthogonal polynomials where q depends on the system size in a particular way. (author)
Pion-nuclear many body problems
International Nuclear Information System (INIS)
Weise, W.
1981-01-01
This chapter examines pion-nucleus scattering data produced at the meson factories in order to gain information about the ''optical'' branches of the pion-nuclear excitation spectrum. Discusses basic meson-baryon effective Lagrangians and elementary processes; pion-baryon vertex form factors; the spin-isospin dependent baryon-baryon interaction; pions in nuclear matter; nuclear spin-isospin correlations; the baryon-hole model; photon-induced excitation of baryon-hole states; high momentum transfer properties of pion-like nuclear states; a response function for pionic low-frequency modes in finite nuclei; and applications. Finds that there is no clear evidence for pionic critical opalescence, as in agreement with the expectation that the minimal density for the appearance of a pion condensate is certainly not lower than two or three times nuclear matter density
Non-equilibrium many body dynamics
International Nuclear Information System (INIS)
Creutz, M.; Gyulassy, M.
1997-01-01
This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop
Non-equilibrium many body dynamics
Energy Technology Data Exchange (ETDEWEB)
Creutz, M.; Gyulassy, M.
1997-09-22
This Riken BNL Research Center Symposium on Non-Equilibrium Many Body Physics was held on September 23-25, 1997 as part of the official opening ceremony of the Center at Brookhaven National Lab. A major objective of theoretical work at the center is to elaborate on the full spectrum of strong interaction physics based on QCD, including the physics of confinement and chiral symmetry breaking, the parton structure of hadrons and nuclei, and the phenomenology of ultra-relativistic nuclear collisions related to the up-coming experiments at RHIC. The opportunities and challenges of nuclear and particle physics in this area naturally involve aspects of the many body problem common to many other fields. The aim of this symposium was to find common theoretical threads in the area of non-equilibrium physics and modern transport theories. The program consisted of invited talks on a variety topics from the fields of atomic, condensed matter, plasma, astrophysics, cosmology, and chemistry, in addition to nuclear and particle physics. Separate abstracts have been indexed into the database for contributions to this workshop.
Many-body perturbation theory for ab initio nuclear structure
International Nuclear Information System (INIS)
Tichai, Alexander
2017-01-01
The solution of the quantum many-body problem for medium-mass nuclei using realistic nuclear interactions poses a superbe challenge for nuclear structure research. Because an exact solution can only be provided for the lightest nuclei, one has to rely on approximate solutions when proceeding to heavier systems. Over the past years, tremendous progress has been made in the development and application of systematically improvable expansion methods and an accurate description of nuclear observables has become viable up to mass number A ∼ 100. While closed-shell systems are consistently described via a plethora of different many-body methods, the extension to genuine open-shell systems still remains a major challenge and up to now there is no ab initio many-body method which applies equally well to systems with even and odd mass numbers. The goal of this thesis is the development and implementation of innovative perturbative approaches with genuine open-shell capabilities. This requires the extension of well-known single-reference approaches to more general vacua. In this work we choose two complementary routes for the usage of generalized reference states. First, we derive a new ab initio approach based on multi-configurational reference states that are conveniently derived from a prior no-core shell model calculation. Perturbative corrections are derived via second-order many-body perturbation theory, thus, merging configuration interaction and many-body perturbation theory. The generality of this ansatz enables for a treatment of medium-mass systems with arbitrary mass number, as well as the extension to low-lying excited states such that ground and excited states are treated on an equal footing. In a complementary approach, we use reference states that break a symmetry of the underlying Hamiltonian. In the simplest case this corresponds to the expansion around a particle-number-broken Hartree-Fock-Bogolyubov vacuum which is obtained from a mean-field calculation
Goldman, Iosif Ilich; Geilikman, B T
2006-01-01
This challenging book contains a comprehensive collection of problems in nonrelativistic quantum mechanics of varying degrees of difficulty. It features answers and completely worked-out solutions to each problem. Geared toward advanced undergraduates and graduate students, it provides an ideal adjunct to any textbook in quantum mechanics.
Exact many-body dynamics with stochastic one-body density matrix evolution
International Nuclear Information System (INIS)
Lacroix, D.
2004-05-01
In this article, we discuss some properties of the exact treatment of the many-body problem with stochastic Schroedinger equation (SSE). Starting from the SSE theory, an equivalent reformulation is proposed in terms of quantum jumps in the density matrix space. The technical details of the derivation a stochastic version of the Liouville von Neumann equation are given. It is shown that the exact Many-Body problem could be replaced by an ensemble of one-body density evolution, where each density matrix evolves according to its own mean-field augmented by a one-body noise. (author)
Many-body physics using cold atoms
Sundar, Bhuvanesh
Advances in experiments on dilute ultracold atomic gases have given us access to highly tunable quantum systems. In particular, there have been substantial improvements in achieving different kinds of interaction between atoms. As a result, utracold atomic gases oer an ideal platform to simulate many-body phenomena in condensed matter physics, and engineer other novel phenomena that are a result of the exotic interactions produced between atoms. In this dissertation, I present a series of studies that explore the physics of dilute ultracold atomic gases in different settings. In each setting, I explore a different form of the inter-particle interaction. Motivated by experiments which induce artificial spin-orbit coupling for cold fermions, I explore this system in my first project. In this project, I propose a method to perform universal quantum computation using the excitations of interacting spin-orbit coupled fermions, in which effective p-wave interactions lead to the formation of a topological superfluid. Motivated by experiments which explore the physics of exotic interactions between atoms trapped inside optical cavities, I explore this system in a second project. I calculate the phase diagram of lattice bosons trapped in an optical cavity, where the cavity modes mediates effective global range checkerboard interactions between the atoms. I compare this phase diagram with one that was recently measured experimentally. In two other projects, I explore quantum simulation of condensed matter phenomena due to spin-dependent interactions between particles. I propose a method to produce tunable spin-dependent interactions between atoms, using an optical Feshbach resonance. In one project, I use these spin-dependent interactions in an ultracold Bose-Fermi system, and propose a method to produce the Kondo model. I propose an experiment to directly observe the Kondo effect in this system. In another project, I propose using lattice bosons with a large hyperfine spin
Relativistic many-body XMCD theory including core degenerate effects
Fujikawa, Takashi
2009-11-01
A many-body relativistic theory to analyze X-ray Magnetic Circular Dichroism (XMCD) spectra has been developed on the basis of relativistic quantum electrodynamic (QED) Keldysh Green's function approach. This theoretical framework enables us to handle relativistic many-body effects in terms of correlated nonrelativistic Green's function and relativistic correction operator Q, which naturally incorporates radiation field screening and other optical field effects in addition to electron-electron interactions. The former can describe the intensity ratio of L2/L3 which deviates from the statistical weight (branching ratio) 1/2. In addition to these effects, we consider the degenerate or nearly degenerate effects of core levels from which photoelectrons are excited. In XPS spectra, for example in Rh 3d sub level excitations, their peak shapes are quite different: This interesting behavior is explained by core-hole moving after the core excitation. We discuss similar problems in X-ray absorption spectra in particular excitation from deep 2p sub levels which are degenerate in each sub levels and nearly degenerate to each other in light elements: The hole left behind is not frozen there. We derive practical multiple scattering formulas which incorporate all those effects.
Understanding many-body physics in one dimension from the Lieb–Liniger model
International Nuclear Information System (INIS)
Jiang Yu-Zhu; Chen Yang-Yang; Guan Xi-Wen
2015-01-01
This article presents an elementary introduction on various aspects of the prototypical integrable model the Lieb–Liniger Bose gas ranging from the cooperative to the collective features of many-body phenomena. In 1963, Lieb and Liniger first solved this quantum field theory many-body problem using Bethe’s hypothesis, i.e., a particular form of wavefunction introduced by Bethe in solving the one-dimensional Heisenberg model in 1931. Despite the Lieb–Liniger model is arguably the simplest exactly solvable model, it exhibits rich quantum many-body physics in terms of the aspects of mathematical integrability and physical universality. Moreover, the Yang–Yang grand canonical ensemble description for the model provides us with a deep understanding of quantum statistics, thermodynamics, and quantum critical phenomena at the many-body physical level. Recently, such fundamental physics of this exactly solved model has been attracting growing interest in experiments. Since 2004, there have been more than 20 experimental papers that reported novel observations of different physical aspects of the Lieb–Liniger model in the laboratory. So far the observed results are in excellent agreement with results obtained using the analysis of this simplest exactly solved model. Those experimental observations reveal the unique beauty of integrability. (topical review)
International Nuclear Information System (INIS)
Kumar, N.
1984-07-01
Quantum first passage problem (QUIPP) is formulated and solved in terms of a constrained Feynman path integral. The related paradox of blocking of unitary evolution by continuous observation on the system implicit in QUIPP is briefly discussed. (author)
International Nuclear Information System (INIS)
Girardeau, M.D.; Oregon Univ., Eugene
1981-01-01
Many problems in several areas of physics and chemistry involve many-body systems of interacting composite particles, in regimes where their internal transitions and/or reactive collisions (breakup, recombination, rearrangement) are important. Standard many-body Green's function and quantum field theoretic techniques are not well adapted to such situations. I discuss generalized representations which allow application of standard techniques to more complicated systems of interacting composite particles and their constituents. (orig./HSI)
Few-body correlations in many-body physics
Energy Technology Data Exchange (ETDEWEB)
Barth, Marcus
2015-12-01
In this thesis, various systems are analyzed in parameter regimes where the few-body aspects are dominant over the many-body behavior. Using the Operator Product Expansion from Quantum Field Theory, exact relations for observables of the electron gas as well as two-dimensional Fermi gases are derived. In addition, properties of both two-dimensional and three-dimensional cold quantum gases at small to moderate degeneracy are determined by means of a diagrammatic virial expansion.
Ziaei, Vafa; Bredow, Thomas
2018-05-01
An accurate theoretical prediction of ionization potential (IP) and electron affinity (EA) is key in understanding complex photochemical processes in aqueous environments. There have been numerous efforts in literature to accurately predict IP and EA of liquid water, however with often conflicting results depending on the level of theory and the underlying water structures. In a recent study based on hybrid-non-self-consistent many-body perturbation theory (MBPT) Gaiduk et al (2018 Nat. Commun. 9 247) predicted an IP of 10.2 eV and EA of 0.2 eV, resulting in an electronic band gap (i.e. electronic gap (IP-EA) as measured by photoelectron spectroscopy) of about 10 eV, redefining the widely cited experimental gap of 8.7 eV in literature. In the present work, we show that GW self-consistency and an implicit vertex correction in MBPT considerably affect recently reported EA values by Gaiduk et al (2018 Nat. Commun. 9 247) by about 1 eV. Furthermore, the choice of pseudo-potential is critical for an accurate determination of the absolute band positions. Consequently, the self-consistent GW approach with an implicit vertex correction based on projector augmented wave (PAW) method on top of quantum water structures predicts an IP of 10.2, an EA of 1.1, a fundamental gap of 9.1 eV and an exciton binding (Eb) energy of 0.9 eV for the first absorption band of liquid water via the Bethe–Salpeter equation (BSE). Only within such a self-consistent approach a simultanously accurate prediction of IP, EA, Eg, Eb is possible.
Thermalization dynamics in a quenched many-body state
Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus
2016-05-01
Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.
Entanglement between noncomplementary parts of many-body systems
International Nuclear Information System (INIS)
Wichterich, Hannu Christian
2011-01-01
This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient ''amount'' of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be ''harvested'' by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details. (orig.)
Many body perturbation calculations of photoionization
International Nuclear Information System (INIS)
Kelly, H.P.
1979-01-01
The application of many body perturbation theory to the calculation of atomic photoionization cross sections is reviewed. The choice of appropriate potential for the single-particle state is discussed and results are presented for several atoms including resonance structure. In addition to single photoionization, the process of double photoionization is considered and is found to be significant. (Auth.)
Review of many-body calculations
International Nuclear Information System (INIS)
Kelly, H.P.
1981-01-01
A brief review is given of many-body perturbation theory and its application to atomic physics. Particular attention is given to the choice of single-particle potential used to generate excited states. Applications to many atomic properties are discussed including hyperfine structure, photoabsorption including multiple processes, and parity non-conserving transitions in heavy atoms
Universal Properties of Many-Body Delocalization Transitions
Directory of Open Access Journals (Sweden)
Andrew C. Potter
2015-09-01
Full Text Available We study the dynamical melting of “hot” one-dimensional many-body localized systems. As disorder is weakened below a critical value, these nonthermal quantum glasses melt via a continuous dynamical phase transition into classical thermal liquids. By accounting for collective resonant tunneling processes, we derive and numerically solve an effective model for such quantum-to-classical transitions and compute their universal critical properties. Notably, the classical thermal liquid exhibits a broad regime of anomalously slow subdiffusive equilibration dynamics and energy transport. The subdiffusive regime is characterized by a continuously evolving dynamical critical exponent that diverges with a universal power at the transition. Our approach elucidates the universal long-distance, low-energy scaling structure of many-body delocalization transitions in one dimension, in a way that is transparently connected to the underlying microscopic physics. We discuss experimentally testable signatures of the predicted scaling properties.
Efficient numerical simulations of many-body localized systems
Energy Technology Data Exchange (ETDEWEB)
Pollmann, Frank [Max-Planck-Institut fuer Physik komplexer Systeme, 01187 Dresden (Germany); Khemani, Vedika; Sondhi, Shivaji [Physics Department, Princeton University, Princeton, NJ 08544 (United States)
2016-07-01
Many-body localization (MBL) occurs in isolated quantum systems when Anderson localization persists in the presence of finite interactions. To understand this phenomenon, the development of new, efficient numerical methods to find highly excited eigenstates is essential. We introduce a variant of the density-matrix renormalization group (DMRG) method that obtains individual highly excited eigenstates of MBL systems to machine precision accuracy at moderate-large disorder. This method explicitly takes advantage of the local spatial structure characterizing MBL eigenstates.
Entanglement replication in driven dissipative many-body systems.
Zippilli, S; Paternostro, M; Adesso, G; Illuminati, F
2013-01-25
We study the dissipative dynamics of two independent arrays of many-body systems, locally driven by a common entangled field. We show that in the steady state the entanglement of the driving field is reproduced in an arbitrarily large series of inter-array entangled pairs over all distances. Local nonclassical driving thus realizes a scale-free entanglement replication and long-distance entanglement distribution mechanism that has immediate bearing on the implementation of quantum communication networks.
Chiral symmetry and many-body forces in nuclei
International Nuclear Information System (INIS)
Nyman, E.M.; Rho, M.
1976-01-01
It is demonstrated that when quantum corrections are added, chiral Lagrangians need not generate strong many-body forces as they do in tree approximation. It is suggested that a physically reasonable procedure is to adjust the sigma-model parameters so as not to conflict with the current status of nuclear theory. As a consequence, the equilibrium density of abnormal states could be pushed up further, and the binding energy be considerably reduced. (Auth.)
Probing many-body interactions in an optical lattice clock
Energy Technology Data Exchange (ETDEWEB)
Rey, A.M., E-mail: arey@jilau1.colorado.edu [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Gorshkov, A.V. [Joint Quantum Institute, NIST and University of Maryland, Department of Physics, College Park, MD 20742 (United States); Kraus, C.V. [Institute for Quantum Optics and Quantum Information of the Austrian Academy of Sciences, A-6020 Innsbruck (Austria); Institute for Theoretical Physics, University of Innsbruck, A-6020 Innsbruck (Austria); Martin, M.J. [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Bishof, M.; Swallows, M.D.; Zhang, X.; Benko, C.; Ye, J. [JILA, NIST and University of Colorado, Department of Physics, Boulder, CO 80309 (United States); Lemke, N.D.; Ludlow, A.D. [National Institute of Standards and Technology, Boulder, CO 80305 (United States)
2014-01-15
We present a unifying theoretical framework that describes recently observed many-body effects during the interrogation of an optical lattice clock operated with thousands of fermionic alkaline earth atoms. The framework is based on a many-body master equation that accounts for the interplay between elastic and inelastic p-wave and s-wave interactions, finite temperature effects and excitation inhomogeneity during the quantum dynamics of the interrogated atoms. Solutions of the master equation in different parameter regimes are presented and compared. It is shown that a general solution can be obtained by using the so called Truncated Wigner Approximation which is applied in our case in the context of an open quantum system. We use the developed framework to model the density shift and decay of the fringes observed during Ramsey spectroscopy in the JILA {sup 87}Sr and NIST {sup 171}Yb optical lattice clocks. The developed framework opens a suitable path for dealing with a variety of strongly-correlated and driven open-quantum spin systems. -- Highlights: •Derived a theoretical framework that describes many-body effects in a lattice clock. •Validated the analysis with recent experimental measurements. •Demonstrated the importance of beyond mean field corrections in the dynamics.
Thermodynamical and Green function many-body Wick theorems
International Nuclear Information System (INIS)
Westwanski, B.
1987-01-01
The thermodynamical and Green function many-body reduction theorems of Wick type are proved for the arbitrary mixtures of the fermion, boson and spin systems. ''Many-body'' means that the operators used are the products of the arbitrary number of one-body standard basis operators [of the fermion or (and) spin types] with different site (wave vector) indices, but having the same ''time'' (in the interaction representation). The method of proving is based on'' 1) the first-order differential equation of Schwinger type for: 1a) anti T-product of operators; 1b) its average value; 2) KMS boundary conditions for this average. It is shown that the fermion, boson and spin systems can be unified in the many-body formulation (bosonification of the fermion systems). It is impossible in the one-body approach. Both of the many-body versions of the Wick theorem have the recurrent feature: nth order moment diagrams for the free energy or Green functions can be expressed by the (n-1)th order ones. This property corresponds to the automatic realization of: (i) summations over Bose-Einstein or (and) Fermi-Dirac frequencies; (ii) elimination of Bose-Einstein or (and) Fermi-Dirac distributions. The procedures (i) and (ii), being the results of using the Green function one-body reduction theorem, have constituted the significant difficulty up to now in the treatment of quantum systems. (orig.)
Nuclear, particle and many body physics
Morse, Philip M; Feshbach, Herman
2013-01-01
Nuclear, Particle and Many Body Physics, Volume II, is the second of two volumes dedicated to the memory of physicist Amos de-Shalit. The contributions in this volume are a testament to the respect he earned as a physicist and of the warm and rich affection he commanded as a personal friend. The book contains 41 chapters and begins with a study on the renormalization of rational Lagrangians. Separate chapters cover the scattering of high energy protons by light nuclei; approximation of the dynamics of proton-neutron systems; the scattering amplitude for the Gaussian potential; Coulomb excitati
Q-deformed algebras and many-body physics
Energy Technology Data Exchange (ETDEWEB)
Galetti, D; Lunardi, J T; Pimentel, B M [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil); Lima, C L [Sao Paulo Univ., SP (Brazil). Inst. de Fisica
1995-11-01
A review is presented of some applications of q-deformed algebras to many-body systems. The rotational and pairing nuclear problems will be discussed in the context of q-deformed algebras, before presenting a more microscopically based application of q-deformed concepts to many-fermion systems. (author). 30 refs., 5 figs.
Quantum Statistics and Entanglement Problems
Trainor, L. E. H.; Lumsden, Charles J.
2002-01-01
Interpretations of quantum measurement theory have been plagued by two questions, one concerning the role of observer consciousness and the other the entanglement phenomenon arising from the superposition of quantum states. We emphasize here the remarkable role of quantum statistics in describing the entanglement problem correctly and discuss the relationship to issues arising from current discussions of intelligent observers in entangled, decohering quantum worlds.
Solvable Family of Driven-Dissipative Many-Body Systems
Foss-Feig, Michael; Young, Jeremy T.; Albert, Victor V.; Gorshkov, Alexey V.; Maghrebi, Mohammad F.
2017-11-01
Exactly solvable models have played an important role in establishing the sophisticated modern understanding of equilibrium many-body physics. Conversely, the relative scarcity of solutions for nonequilibrium models greatly limits our understanding of systems away from thermal equilibrium. We study a family of nonequilibrium models, some of which can be viewed as dissipative analogues of the transverse-field Ising model, in that an effectively classical Hamiltonian is frustrated by dissipative processes that drive the system toward states that do not commute with the Hamiltonian. Surprisingly, a broad and experimentally relevant subset of these models can be solved efficiently. We leverage these solutions to compute the effects of decoherence on a canonical trapped-ion-based quantum computation architecture, and to prove a no-go theorem on steady-state phase transitions in a many-body model that can be realized naturally with Rydberg atoms or trapped ions.
International Nuclear Information System (INIS)
Amusia, M Ya
2011-01-01
Contrary to common wisdom, not everything is clear and simple in the structure of many-electron atoms. Complexity in atoms is mainly a result of interelectron interaction that leads to rather unusual behaviour. Most transparently this is manifested in photo-ionization processes of many-electron atoms and some multi-atomic objects e.g. endohedrals. Particular attention will be given to the approach describing the interaction of photons with many-electron atoms in the frame of the many-body theory based on the Feynman diagrams technique. As a suitable one-electron approximation the Hartree - Fock (HF) approach will be presented. On its ground we will include the so-called electron correlation effects and discuss the frequently used Random Phase Approximation with Exchange - RPAE. Some results of recent calculations will be presented.
Energy Technology Data Exchange (ETDEWEB)
Amusia, M Ya, E-mail: amusia@vms.huji.ac.il [Racah Institute of Physics, The Hebrew University, Jerusalem (Israel); Ioffe Physical-technical Institute, RAS, St. Petersburg (Russian Federation)
2011-09-16
Contrary to common wisdom, not everything is clear and simple in the structure of many-electron atoms. Complexity in atoms is mainly a result of interelectron interaction that leads to rather unusual behaviour. Most transparently this is manifested in photo-ionization processes of many-electron atoms and some multi-atomic objects e.g. endohedrals. Particular attention will be given to the approach describing the interaction of photons with many-electron atoms in the frame of the many-body theory based on the Feynman diagrams technique. As a suitable one-electron approximation the Hartree - Fock (HF) approach will be presented. On its ground we will include the so-called electron correlation effects and discuss the frequently used Random Phase Approximation with Exchange - RPAE. Some results of recent calculations will be presented.
Intermittent many-body dynamics at equilibrium
Danieli, C.; Campbell, D. K.; Flach, S.
2017-06-01
The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.
Current algebras and many-body physics
International Nuclear Information System (INIS)
Albertin, U.K.
1989-01-01
Several applications of current algebras in many body physics are examined. The first is the interacting Bose gas in three dimensions. Theories for phonons, vortices and rotons are all described within the current algebra formalism. Next the one dimensional electron gas is examined within the approximation of linear dispersion so that relativistic current algebra techniques may be used. The relation with Thirring strings and compactified boson models is examined, and points of enhanced symmetry in the compactified boson models are shown to lie on phase transition lines for the electron gas. Finally, mathematical aspects of the current algebra are studied. The theory of induced representations of the diffeomorphism group are used to describe the Aharanov-Bohm effect, the thermodynamics of the Bose gas, and the Bose gas in the presence of vortex filaments
Interferometric probes of many-body localization.
Serbyn, M; Knap, M; Gopalakrishnan, S; Papić, Z; Yao, N Y; Laumann, C R; Abanin, D A; Lukin, M D; Demler, E A
2014-10-03
We propose a method for detecting many-body localization (MBL) in disordered spin systems. The method involves pulsed coherent spin manipulations that probe the dephasing of a given spin due to its entanglement with a set of distant spins. It allows one to distinguish the MBL phase from a noninteracting localized phase and a delocalized phase. In particular, we show that for a properly chosen pulse sequence the MBL phase exhibits a characteristic power-law decay reflecting its slow growth of entanglement. We find that this power-law decay is robust with respect to thermal and disorder averaging, provide numerical simulations supporting our results, and discuss possible experimental realizations in solid-state and cold-atom systems.
Many-body approaches to nuclear physics
International Nuclear Information System (INIS)
Hjorth-Jensen, M.
1993-10-01
This thesis deals with applications of perturbative many-body theories to selected nuclear systems at low and intermediate energies. Examples are the properties of neutron stars, the calculation of shell-model effective interactions and the microscopic derivation of the optical-model potential for finite nuclei. The line of research leans on the microscopic approach, i.e. an approach which aims at describing nuclear properties from the underlying free interaction between the various hadrons where parameters like meson coupling constants define the Lagrangians. The emphasis is on the behavior of the various components of the free interaction in different nuclear media in order to understand how these components are affected by the studied nuclear correlations. 159 refs
Construction of exact constants of motion and effective models for many-body localized systems
Goihl, M.; Gluza, M.; Krumnow, C.; Eisert, J.
2018-04-01
One of the defining features of many-body localization is the presence of many quasilocal conserved quantities. These constants of motion constitute a cornerstone to an intuitive understanding of much of the phenomenology of many-body localized systems arising from effective Hamiltonians. They may be seen as local magnetization operators smeared out by a quasilocal unitary. However, accurately identifying such constants of motion remains a challenging problem. Current numerical constructions often capture the conserved operators only approximately, thus restricting a conclusive understanding of many-body localization. In this work, we use methods from the theory of quantum many-body systems out of equilibrium to establish an alternative approach for finding a complete set of exact constants of motion which are in addition guaranteed to represent Pauli-z operators. By this we are able to construct and investigate the proposed effective Hamiltonian using exact diagonalization. Hence, our work provides an important tool expected to further boost inquiries into the breakdown of transport due to quenched disorder.
Many-body optimization using an ab initio monte carlo method.
Haubein, Ned C; McMillan, Scott A; Broadbelt, Linda J
2003-01-01
Advances in computing power have made it possible to study solvated molecules using ab initio quantum chemistry. Inclusion of discrete solvent molecules is required to determine geometric information about solute/solvent clusters. Monte Carlo methods are well suited to finding minima in many-body systems, and ab initio methods are applicable to the widest range of systems. A first principles Monte Carlo (FPMC) method was developed to find minima in many-body systems, and emphasis was placed on implementing moves that increase the likelihood of finding minimum energy structures. Partial optimization and molecular interchange moves aid in finding minima and overcome the incomplete sampling that is unavoidable when using ab initio methods. FPMC was validated by studying the boron trifluoride-water system, and then the method was used to examine the methyl carbenium ion in water to demonstrate its application to solvation problems.
Aspects of Strongly Correlated Many-Body Fermi Systems
Porter, William J., III
A, by now, well-known signal-to-noise problem plagues Monte Carlo calculations of quantum-information-theoretic observables in systems of interacting fermions, particularly the Renyi entanglement entropies Sn, even in many cases where the infamous sign problem does not appear. Several methods have been put forward to circumvent this affliction including ensemble-switching techniques using auxiliary partition-function ratios. This dissertation presents an algorithm that modifies the recently proposed free-fermion decomposition in an essential way: we incorporate the entanglement-sensitive correlations directly into the probability measure in a natural way. Implementing this algorithm, we demonstrate that it is compatible with the hybrid Monte Carlo algorithm, the workhorse of the lattice quantum chromodynamics community and an essential tool for studying gauge theories that contain dynamical fermions. By studying a simple one-dimensional Hubbard model, we demonstrate that our method does not exhibit the same debilitating numerical difficulties that naive attempts to study entanglement often encounter. Following that, we illustrate some key probabilistic insights, using intuition derived from the previous method and its successes to construct a simpler, better behaved, and more elegant algorithm. Using this method, in combination with new identities which allow us to avoid seemingly necessary numerical difficulties, the inversion of the restricted one-body density matrices, we compute high order Renyi entropies and perform a thorough comparison to this new algorithm's predecessor using the Hubbard model mentioned before. Finally, we characterize non-perturbatively the Renyi entropies of degree n = 2,3,4, and 5 of three-dimensional, strongly coupled many-fermion systems in the scale-invariant regime of short interaction range and large scattering length, i.e. in the unitary limit using the algorithms detailed herein. We also detail an exact, few-body projective method
Many-body formalism for fermions: The partition function
Watson, D. K.
2017-09-01
The partition function, a fundamental tenet in statistical thermodynamics, contains in principle all thermodynamic information about a system. It encapsulates both microscopic information through the quantum energy levels and statistical information from the partitioning of the particles among the available energy levels. For identical particles, this statistical accounting is complicated by the symmetry requirements of the allowed quantum states. In particular, for Fermi systems, the enforcement of the Pauli principle is typically a numerically demanding task, responsible for much of the cost of the calculations. The interplay of these three elements—the structure of the many-body spectrum, the statistical partitioning of the N particles among the available levels, and the enforcement of the Pauli principle—drives the behavior of mesoscopic and macroscopic Fermi systems. In this paper, we develop an approach for the determination of the partition function, a numerically difficult task, for systems of strongly interacting identical fermions and apply it to a model system of harmonically confined, harmonically interacting fermions. This approach uses a recently introduced many-body method that is an extension of the symmetry-invariant perturbation method (SPT) originally developed for bosons. It uses group theory and graphical techniques to avoid the heavy computational demands of conventional many-body methods which typically scale exponentially with the number of particles. The SPT application of the Pauli principle is trivial to implement since it is done "on paper" by imposing restrictions on the normal-mode quantum numbers at first order in the perturbation. The method is applied through first order and represents an extension of the SPT method to excited states. Our method of determining the partition function and various thermodynamic quantities is accurate and efficient and has the potential to yield interesting insight into the role played by the Pauli
Fifth International Conference on Recent Progress in Many-Body Theories
Pajanne, E; Bishop, R; Recent Progress in MANY-BODY THEORIES
1988-01-01
The present volume contains the texts of the invited talks delivered at the Fifth International Conference on Recent Progress in Many-Body Theories held in Oulu, Finland during the period 3-8 August 1987. The general format and style of the meeting followed closely those which had evolved from the earlier conferences in the series: Trieste 1978, Oaxtepec 1981, Altenberg 1983 and San Francisco 1985. Thus, the conferences in this series are in tended, as far as is practicable, to cover in a broad and balanced fashion both the entire spectrum of theoretical tools developed to tackle the quan tum many-body problem, and their major fields of· application. One of the major aims of the series is to foster the exchange of ideas and techniques among physicists working in such diverse areas of application of many-body theories as nucleon-nucleon interactions, nuclear physics, astronomy, atomic and molecular physics, quantum chemistry, quantum fluids and plasmas, and solid-state and condensed matter physics. A spec...
Atomic many-body theory of giant resonances
International Nuclear Information System (INIS)
Kelly, H.P.; Altun, Z.
1987-01-01
In this paper the use of many-body perturbation theory (MBPT) to include effects of electron correlations is discussed. The various physical processes contributing to the broad photoionization cross sections of the rare gases are studied in terms of the relevant many-body diagrams. Use of the random phase approximation with exchange (RPAE) is discussed by Amusia and Cherepkov. Calculations using the relativistic RPAE are reviewed by Johnson. In addition, many-body perturbation theory (MBPT) is used to study resonances which are due to excitation of bound states degenerate with the continuum. Very interesting giant resonance structure can occur when an inner shell electron is excited into a vacant open-shell orbital of the same principal quantum number. A particular example which is studied is the neutral manganese atom 3p 6 3d 5 4s 2 ( 6 S), in which the spins of the five 3d electrons are aligned. A very large resonance occurs in the 3d and 4s cross sections due to 3p → 3d excitation near 51 eV, and calculations of this resonance by MBPT and RPAE are discussed. A second example of this type of resonance occurs in open-shell rare-earth atoms with configurations 4d 10 4f/sup n/5s 2 5p 6 s 2 . Calculations and experimental results will be discussed for the case of europium with a half-filled sub-shell 4f 7 . 71 references, 15 figures
Probing many-body localization with neural networks
Schindler, Frank; Regnault, Nicolas; Neupert, Titus
2017-06-01
We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.
International Nuclear Information System (INIS)
Amsterdamski, P.
1986-01-01
The standard cosmological model is reviewed and shown not to be self-sufficient in that it requires initial conditions most likely to be supplied by quantum cosmology. The possible approaches to the issue of initial conditions for cosmology are then discussed. In this thesis, the author considers three separate problems related to this issue. First, the possibility of inflation is investigated in detail by analyzing the evolution of metric perturbations and fluctuations in the expectation value of a scalar field prior to a phase transition; finite temperature effects are also included. Since the inhomogeneities were damped well before the onset of a phase transition. It is concluded that an inflation was possible. Next, the effective action of neutrino and photon fields is calculated for homogeneous spacetimes with small anisotropy; it is shown that quantum corrections to the action due to these fields influence the evolution of an early Universe in the Same way as do the analogous correction terms arising from a conformally invariant scalar which has been previously studied. Finally, the question of an early anisotropy is also discussed in a framework of Hartle-Hawking wave function of the Universe. A wave function of a Bianchi IX type Universe is calculated in a semiclassical approximation
Integrals of motion in the many-body localized phase
Directory of Open Access Journals (Sweden)
V. Ros
2015-02-01
Full Text Available We construct a complete set of quasi-local integrals of motion for the many-body localized phase of interacting fermions in a disordered potential. The integrals of motion can be chosen to have binary spectrum {0,1}, thus constituting exact quasiparticle occupation number operators for the Fermi insulator. We map the problem onto a non-Hermitian hopping problem on a lattice in operator space. We show how the integrals of motion can be built, under certain approximations, as a convergent series in the interaction strength. An estimate of its radius of convergence is given, which also provides an estimate for the many-body localization–delocalization transition. Finally, we discuss how the properties of the operator expansion for the integrals of motion imply the presence or absence of a finite temperature transition.
PREFACE: Advanced many-body and statistical methods in mesoscopic systems
Anghel, Dragos Victor; Sabin Delion, Doru; Sorin Paraoanu, Gheorghe
2012-02-01
It has increasingly been realized in recent times that the borders separating various subfields of physics are largely artificial. This is the case for nanoscale physics, physics of lower-dimensional systems and nuclear physics, where the advanced techniques of many-body theory developed in recent times could provide a unifying framework for these disciplines under the general name of mesoscopic physics. Other fields, such as quantum optics and quantum information, are increasingly using related methods. The 6-day conference 'Advanced many-body and statistical methods in mesoscopic systems' that took place in Constanta, Romania, between 27 June and 2 July 2011 was, we believe, a successful attempt at bridging an impressive list of topical research areas: foundations of quantum physics, equilibrium and non-equilibrium quantum statistics/fractional statistics, quantum transport, phases and phase transitions in mesoscopic systems/superfluidity and superconductivity, quantum electromechanical systems, quantum dissipation, dephasing, noise and decoherence, quantum information, spin systems and their dynamics, fundamental symmetries in mesoscopic systems, phase transitions, exactly solvable methods for mesoscopic systems, various extension of the random phase approximation, open quantum systems, clustering, decay and fission modes and systematic versus random behaviour of nuclear spectra. This event brought together participants from seventeen countries and five continents. Each of the participants brought considerable expertise in his/her field of research and, at the same time, was exposed to the newest results and methods coming from the other, seemingly remote, disciplines. The talks touched on subjects that are at the forefront of topical research areas and we hope that the resulting cross-fertilization of ideas will lead to new, interesting results from which everybody will benefit. We are grateful for the financial and organizational support from IFIN-HH, Ovidius
Neural network models: from biology to many - body phenomenology
International Nuclear Information System (INIS)
Clark, J.W.
1993-01-01
Theoretical work in neural networks has a strange feel for most physicists. In some cases the aspect of design becomes paramount. More comfortable ground at least for many body theorists may be found in realistic biological simulation, although the complexity of most problems is so awesome that incisive results will be hard won. It has also shown the impressive capabilities of artificial networks in pattern recognition and classification may be exploited to solve management problems in experimental physics and for discovery of radically new theoretical description of physical systems. This advance represents an important step towards the ultimate goal of neuro biological paradigm. (A.B.)
Many - body simulations using an array processor
International Nuclear Information System (INIS)
Rapaport, D.C.
1985-01-01
Simulations of microscopic models of water and polypeptides using molecular dynamics and Monte Carlo techniques have been carried out with the aid of an FPS array processor. The computational techniques are discussed, with emphasis on the development and optimization of the software to take account of the special features of the processor. The computing requirements of these simulations exceed what could be reasonably carried out on a normal 'scientific' computer. While the FPS processor is highly suited to the kinds of models described, several other computationally intensive problems in statistical mechanics are outlined for which alternative processor architectures are more appropriate
Chiral Floquet Phases of Many-Body Localized Bosons
Directory of Open Access Journals (Sweden)
Hoi Chun Po
2016-12-01
Full Text Available We construct and classify chiral topological phases in driven (Floquet systems of strongly interacting bosons, with finite-dimensional site Hilbert spaces, in two spatial dimensions. The construction proceeds by introducing exactly soluble models with chiral edges, which in the presence of many-body localization (MBL in the bulk are argued to lead to stable chiral phases. These chiral phases do not require any symmetry and in fact owe their existence to the absence of energy conservation in driven systems. Surprisingly, we show that they are classified by a quantized many-body index, which is well defined for any MBL Floquet system. The value of this index, which is always the logarithm of a positive rational number, can be interpreted as the entropy per Floquet cycle pumped along the edge, formalizing the notion of quantum-information flow. We explicitly compute this index for specific models and show that the nontrivial topology leads to edge thermalization, which provides an interesting link between bulk topology and chaos at the edge. We also discuss chiral Floquet phases in interacting fermionic systems and their relation to chiral bosonic phases.
Dynamical stability of a many-body Kapitza pendulum
Energy Technology Data Exchange (ETDEWEB)
Citro, Roberta, E-mail: citro@sa.infn.it [Dipartimento di Fisica “E. R. Caianiello” and Spin-CNR, Universita’ degli Studi di Salerno, Via Giovanni Paolo II, I-84084 Fisciano (Italy); Dalla Torre, Emanuele G., E-mail: emanuele.dalla-torre@biu.ac.il [Department of Physics, Bar Ilan University, Ramat Gan 5290002 (Israel); Department of Physics, Harvard University, Cambridge, MA 02138 (United States); D’Alessio, Luca [Department of Physics, The Pennsylvania State University, University Park, PA 16802 (United States); Department of Physics, Boston University, Boston, MA 02215 (United States); Polkovnikov, Anatoli [Department of Physics, Boston University, Boston, MA 02215 (United States); Babadi, Mehrtash [Department of Physics, Harvard University, Cambridge, MA 02138 (United States); Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, CA 91125 (United States); Oka, Takashi [Department of Applied Physics, University of Tokyo, Tokyo, 113-8656 (Japan); Demler, Eugene [Department of Physics, Harvard University, Cambridge, MA 02138 (United States)
2015-09-15
We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine–Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculation. Classical and quantum experiments are proposed to verify the validity of our results.
Many-Body Mean-Field Equations: Parallel implementation
International Nuclear Information System (INIS)
Vallieres, M.; Umar, S.; Chinn, C.; Strayer, M.
1993-01-01
We describe the implementation of Hartree-Fock Many-Body Mean-Field Equations on a Parallel Intel iPSC/860 hypercube. We first discuss the Nuclear Mean-Field approach in physical terms. Then we describe our parallel implementation of this approach on the Intel iPSC/860 hypercube. We discuss and compare the advantages and disadvantages of the domain partition versus the Hilbert space partition for this problem. We conclude by discussing some timing experiments on various computing platforms
Many-Body Green Function of Degenerate Systems
International Nuclear Information System (INIS)
Brouder, Christian; Panati, Gianluca; Stoltz, Gabriel
2009-01-01
A rigorous nonperturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H 0 leading to eigenstates of H 0 +V for degenerate systems. These initial states are eigenstates of P 0 VP 0 , where P 0 is the projection onto a degenerate eigenspace of H 0 . This result is used to give the proper definition of the Green function, the statistical Green function and the nonequilibrium Green function of degenerate systems. The convergence of these Green functions is established.
The quantum measurement problem.
Leggett, A J
2005-02-11
Despite the spectacular success of quantum mechanics (QM) over the last 80 years in explaining phenomena observed at the atomic and subatomic level, the conceptual status of the theory is still a topic of lively controversy. Most of the discussion centers around two famous paradoxes (or, as some would have it, pseudoparadoxes) associated, respectively, with the names of Einstein, Podolsky, and Rosen (EPR) and with Schrodinger's cat. In this Viewpoint, I will concentrate on the paradox of Schrodinger's cat or, as it is often known (to my mind somewhat misleadingly), the quantum measurement paradox.
de Raedt, Hans; von der Linden, W.; Binder, K
1995-01-01
In this chapter we review methods currently used to perform Monte Carlo calculations for quantum lattice models. A detailed exposition is given of the formalism underlying the construction of the simulation algorithms. We discuss the fundamental and technical difficulties that are encountered and
Nuclear collision theory with many-body correlations, 1
International Nuclear Information System (INIS)
Kurihara, Yukio.
1984-11-01
A generalized many-body correlation operator is introduced, following the Feshbach's formalism. Especially, the many-body correlation induced by the strong repulsion and attraction of the realistic NN interaction is concerned and the Feshbach's formalism is reformulated to describe such a many-body correlation well. And a method to estimate the many-body correlation operator is given from the multiple-scattering picture. The present formalism is compared with the resonating-group method. (author)
Advances in quantum mechanics contemporary trends and open problems
Dell'Antonio, Gianfausto
2017-01-01
This volume collects recent contributions on the contemporary trends in the mathematics of quantum mechanics, and more specifically in mathematical problems arising in quantum many-body dynamics, quantum graph theory, cold atoms, unitary gases, with particular emphasis on the developments of the specific mathematical tools needed, including: linear and non-linear Schrödinger equations, topological invariants, non-commutative geometry, resonances and operator extension theory, among others. Most of contributors are international leading experts or respected young researchers in mathematical physics, PDE, and operator theory. All their material is the fruit of recent studies that have already become a reference in the community. Offering a unified perspective of the mathematics of quantum mechanics, it is a valuable resource for researchers in the field.
Neural network models: from biology to many - body phenomenology
International Nuclear Information System (INIS)
Clark, J.W.
1993-01-01
The current surge of research on practical side of neural networks and their utility in memory storage/recall, pattern recognition and classification is given in this article. The initial attraction of neural networks as dynamical and statistical system has been investigated. From the view of many-body theorist, the neurons may be thought of as particles, and the weighted connection between the units, as the interaction between these particles. Finally, the author has seen the impressive capabilities of artificial neural networks in pattern recognition and classification may be exploited to solve data management problems in experimental physics and the discovery of radically new theoretically description of physical problems and neural networks can be used in physics. (A.B.)
Scalar meson field and many-body forces. Chapter 23
International Nuclear Information System (INIS)
Nyman, E.M.
1979-01-01
In applications of field theory to the theory of the nuclear forces, one has frequently assumed that there is a scalar meson. It will then be responsible for most of the medium-range attraction between the nucleons. According to current ideas, however, it is possible to account for the medium-range attraction without an elementary sigma meson. This approach requires a careful treatment of the exchange of interacting pairs of π mesons, such as to include those ππ interactions which are responsible for the formation and decay of the sigma meson. Recently, the scalar field in the nuclear many-body problem has begun to receive more attention. There are two reasons for this change of philosophy. One reason is the discovery of neutron stars. In neutron stars, the nucleon number density can be much higher than in nuclei. One therefore wants to derive the equation of state from a relativistic many-body theory. This forces one to deal explicitly with a set of mesons, such that in the non-relativistic limit one recovers the one-boson-exchange potential. (Auth.)
Effective evolution equations from many-body quantum mechanics
International Nuclear Information System (INIS)
Benedikter, Niels Patriz
2014-01-01
Systems of interest in physics often consist of a very large number of interacting particles. In certain physical regimes, effective non-linear evolution equations are commonly used as an approximation for making predictions about the time-evolution of such systems. Important examples are Bose-Einstein condensates of dilute Bose gases and degenerate Fermi gases. While the effective equations are well-known in physics, a rigorous justification is very difficult. However, a rigorous derivation is essential to precisely understand the range and the limits of validity and the quality of the approximation. In this thesis, we prove that the time evolution of Bose-Einstein condensates in the Gross-Pitaevskii regime can be approximated by the time-dependent Gross-Pitaevskii equation, a cubic non-linear Schroedinger equation. We then turn to fermionic systems and prove that the evolution of a degenerate Fermi gas can be approximated by the time-dependent Hartree-Fock equation (TDHF) under certain assumptions on the semiclassical structure of the initial data. Finally, we extend the latter result to fermions with relativistic kinetic energy. All our results provide explicit bounds on the error as the number of particles becomes large. A crucial methodical insight on bosonic systems is that correlations can be modeled by Bogolyubov transformations. We construct initial data appropriate for the Gross-Pitaevskii regime using a Bogolyubov transformation acting on a coherent state, which amounts to studying squeezed coherent states. As a crucial insight for fermionic systems, we point out a semiclassical structure in states close to the ground state of fermions in a trap. As a convenient language for studying the dynamics of fermionic systems, we use particle-hole transformations.
Quantum many-body systems in one dimension
Ha, N C Zachary
1996-01-01
The main theme of the book focuses on the intimate connection between the two families of exactly solvable models: the inverse-square exchange (ISE) and the nearest-neighbour exchange (NNE) models. Topics discussed include the Luttinger liquid concept and fractional statistics.
General coordinate invariance in quantum many-body systems
Czech Academy of Sciences Publication Activity Database
Brauner, Tomáš; Endlich, S.; Monin, A.; Penco, R.
2014-01-01
Roč. 90, č. 10 (2014), s. 105016 ISSN 1550-7998 Institutional support: RVO:61389005 Keywords : Chiral Perturbation-Theory * Planar Galilei Group * Lagrangians Subject RIV: BE - Theoretical Physics Impact factor: 4.643, year: 2014
Effective Lagrangians for quantum many-body systems
Czech Academy of Sciences Publication Activity Database
Andersen, J. O.; Brauner, Tomáš; Hofmann, C. P.; Vuorinen, A.
2014-01-01
Roč. 2014, č. 8 (2014), 088 ISSN 1029-8479 Institutional support: RVO:61389005 Keywords : spontaneous symmetry breaking * chiral lagrangian s * global symmetries Subject RIV: BE - Theoretical Physics Impact factor: 6.111, year: 2014
Three-body interactions in many-body effective field theory
International Nuclear Information System (INIS)
Furnstahl, R.J.
2004-01-01
This contribution is an advertisement for applying effective field theory (EFT) to many-body problems, including nuclei and cold atomic gases. Examples involving three-body interactions are used to illustrate how EFT's quantify and systematically eliminate model dependence, and how they make many-body calculations simpler and more powerful
Stochastic evaluation of second-order many-body perturbation energies.
Willow, Soohaeng Yoo; Kim, Kwang S; Hirata, So
2012-11-28
With the aid of the Laplace transform, the canonical expression of the second-order many-body perturbation correction to an electronic energy is converted into the sum of two 13-dimensional integrals, the 12-dimensional parts of which are evaluated by Monte Carlo integration. Weight functions are identified that are analytically normalizable, are finite and non-negative everywhere, and share the same singularities as the integrands. They thus generate appropriate distributions of four-electron walkers via the Metropolis algorithm, yielding correlation energies of small molecules within a few mE(h) of the correct values after 10(8) Monte Carlo steps. This algorithm does away with the integral transformation as the hotspot of the usual algorithms, has a far superior size dependence of cost, does not suffer from the sign problem of some quantum Monte Carlo methods, and potentially easily parallelizable and extensible to other more complex electron-correlation theories.
Relativistic many-body theory of high density matter
International Nuclear Information System (INIS)
Chin, S.A.
1977-01-01
A fully relativistic quantum many-body theory is applied to the study of high-density matter. The latter is identified with the zero-temperature ground state of a system of interacting baryons. In accordance with the observed short-range repulsive and long-range attractive character of the nucleon--nucleon force, baryons are described as interacting with each other via a massive scalar and a massive vector meson exchange. In the Hartree approximation, the theory yields the same result as the mean-field theory, but with additional vacuum fluctuation corrections. The resultant equation of state for neutron matter is used to determine properties of neutron stars. The relativistic exchange energy, its corresponding single-particle excitation spectrum, and its effect on the neutron matter equation of state, are calculated. The correlation energy from summing the set of ring diagrams is derived directly from the energy-momentum tensor, with renormalization carried out by adding counterterms to the original Lagrangian and subtracting purely vacuum expectation values. Terms of order g 4 lng 2 are explicitly given. Effects of scalar-vector mixing are discussed. Collective modes corresponding to macroscopic density fluctuation are investigated. Two basic modes are found, a plasma-like mode and zero sound, with the latter dominant at high density. The stability and damping of these modes are studied. Last, the effect of vacuum polarization in high-density matter is examined
Petascale Many Body Methods for Complex Correlated Systems
Pruschke, Thomas
2012-02-01
Correlated systems constitute an important class of materials in modern condensed matter physics. Correlation among electrons are at the heart of all ordering phenomena and many intriguing novel aspects, such as quantum phase transitions or topological insulators, observed in a variety of compounds. Yet, theoretically describing these phenomena is still a formidable task, even if one restricts the models used to the smallest possible set of degrees of freedom. Here, modern computer architectures play an essential role, and the joint effort to devise efficient algorithms and implement them on state-of-the art hardware has become an extremely active field in condensed-matter research. To tackle this task single-handed is quite obviously not possible. The NSF-OISE funded PIRE collaboration ``Graduate Education and Research in Petascale Many Body Methods for Complex Correlated Systems'' is a successful initiative to bring together leading experts around the world to form a virtual international organization for addressing these emerging challenges and educate the next generation of computational condensed matter physicists. The collaboration includes research groups developing novel theoretical tools to reliably and systematically study correlated solids, experts in efficient computational algorithms needed to solve the emerging equations, and those able to use modern heterogeneous computer architectures to make then working tools for the growing community.
Kinetic approach to the initial value problem in quantum field theory
International Nuclear Information System (INIS)
Lin Chi Yong; Toledo Piza, A.F.R. de.
1989-06-01
Time-dependente projection techniques developed to derive kinetic equations in the context of the quantum many-body problem are applied to φ 4 field theory. The approach is illustrated by working out the 0+1 dimensional case explicitly, including numerical solutions of the kinetic equations. Extension to higher dimensions is briefly discussed. (author) [pt
The proceedings of the 9th international conference on recent progress in many-body theories
International Nuclear Information System (INIS)
Neilson, D.; Bishop, R. F.
1998-01-01
This inaugural volume in this new World Scientific Publications series, 'Advances in Quantum Many-Body Theory' records the invited and contributed papers given at the Ninth International Conference on Recent Progress in Many-Body Theories. This conference was held in the School of Physics at The University of New South Wales in Sydney in July, 1997. The conference was also the seventh in the University's series of Gordon Godfrey International Workshop on Theoretical Physics. The style and format of the conference followed the accepted pattern for the series, focusing on the development, refinement, and important applications of many-body methods. A major aim of the series has been to foster an exchange of ideas among physicists working in such diverse areas as nuclear and subnuclear physics, quantum chemistry, complex systems, quantum field theory, strongly correlated electronic systems, magnetism, quantum fluids and condensed matter physics. A special feature of this ninth conference was a session devoted to theories for many-electron systems in zero dimensions (quantum dots), one dimension (quantum wires) and two dimensions (electron layers). These new systems are now firmly established as fertile sources of novel and challenging many-body phenomena
Typical Relaxation of Isolated Many-Body Systems Which Do Not Thermalize
Balz, Ben N.; Reimann, Peter
2017-05-01
We consider isolated many-body quantum systems which do not thermalize; i.e., expectation values approach an (approximately) steady longtime limit which disagrees with the microcanonical prediction of equilibrium statistical mechanics. A general analytical theory is worked out for the typical temporal relaxation behavior in such cases. The main prerequisites are initial conditions which appreciably populate many energy levels and do not give rise to significant spatial inhomogeneities on macroscopic scales. The theory explains very well the experimental and numerical findings in a trapped-ion quantum simulator exhibiting many-body localization, in ultracold atomic gases, and in integrable hard-core boson and X X Z models.
A semiclassical approach to many-body interference in Fock-space
Energy Technology Data Exchange (ETDEWEB)
Engl, Thomas
2015-11-01
Many-body systems draw ever more physicists' attention. Such an increase of interest often comes along with the development of new theoretical methods. In this thesis, a non-perturbative semiclassical approach is developed, which allows to analytically study many-body interference effects both in bosonic and fermionic Fock space and is expected to be applicable to many research areas in physics ranging from Quantum Optics and Ultracold Atoms to Solid State Theory and maybe even High Energy Physics. After the derivation of the semiclassical approximation, which is valid in the limit of large total number of particles, first applications manifesting the presence of many-body interference effects are shown. Some of them are confirmed numerically thus verifying the semiclassical predictions. Among these results are coherent back-/forward-scattering in bosonic and fermionic Fock space as well as a many-body spin echo, to name only the two most important ones.
Many-body localization from one particle density matrix
Energy Technology Data Exchange (ETDEWEB)
Bera, Soumya; Bardarson, Jens [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany); Schomerus, Henning [Lancaster University, Lancaster (United Kingdom); Heidrich-Meisner, Fabian [Ludwig-Maximilians-Universitaet Muenchen (Germany)
2016-07-01
We show that the one-particle density matrix ρ can be used to characterize the interaction-driven many-body localization transition in isolated fermionic systems. The natural orbitals (the eigenstates) are localized in the many-body localized phase and spread out when one enters the delocalized phase, while the occupation spectrum (the set of eigenvalues) reveals the distinctive Fock- space structure of the many-body eigenstates, exhibiting a step-like discontinuity in the localized phase. The associated one-particle occupation entropy is small in the localized phase and large in the delocalized phase, with diverging fluctuations at the transition.
Stochastic many-body perturbation theory for anharmonic molecular vibrations
Energy Technology Data Exchange (ETDEWEB)
Hermes, Matthew R. [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); Hirata, So, E-mail: sohirata@illinois.edu [Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States); CREST, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012 (Japan)
2014-08-28
A new quantum Monte Carlo (QMC) method for anharmonic vibrational zero-point energies and transition frequencies is developed, which combines the diagrammatic vibrational many-body perturbation theory based on the Dyson equation with Monte Carlo integration. The infinite sums of the diagrammatic and thus size-consistent first- and second-order anharmonic corrections to the energy and self-energy are expressed as sums of a few m- or 2m-dimensional integrals of wave functions and a potential energy surface (PES) (m is the vibrational degrees of freedom). Each of these integrals is computed as the integrand (including the value of the PES) divided by the value of a judiciously chosen weight function evaluated on demand at geometries distributed randomly but according to the weight function via the Metropolis algorithm. In this way, the method completely avoids cumbersome evaluation and storage of high-order force constants necessary in the original formulation of the vibrational perturbation theory; it furthermore allows even higher-order force constants essentially up to an infinite order to be taken into account in a scalable, memory-efficient algorithm. The diagrammatic contributions to the frequency-dependent self-energies that are stochastically evaluated at discrete frequencies can be reliably interpolated, allowing the self-consistent solutions to the Dyson equation to be obtained. This method, therefore, can compute directly and stochastically the transition frequencies of fundamentals and overtones as well as their relative intensities as pole strengths, without fixed-node errors that plague some QMC. It is shown that, for an identical PES, the new method reproduces the correct deterministic values of the energies and frequencies within a few cm{sup −1} and pole strengths within a few thousandths. With the values of a PES evaluated on the fly at random geometries, the new method captures a noticeably greater proportion of anharmonic effects.
Substantiating problems of quantum mechanics
International Nuclear Information System (INIS)
Gottlieb, J.
1978-05-01
Some basic problems, related to the spaces and the operators necessary to describe quantum-mechanical phenomena, are entered upon from a new axiomatic standpoint. Some generalizations are operated, required by convergence criteria, concerning the Fourier transform, the Fourier product and the equation of eigen-values. Physical arguments are brought to support such generalizations and an analysis in view of organizing the structure of the proposed spaces is undertaken. (author)
Another New Solvable Many-Body Model of Goldfish Type
Directory of Open Access Journals (Sweden)
Francesco Calogero
2012-07-01
Full Text Available A new solvable many-body problem is identified. It is characterized by nonlinear Newtonian equations of motion (''acceleration equal force'' featuring one-body and two-body velocity-dependent forces ''of goldfish type'' which determine the motion ofan arbitrary number $N$ of unit-mass point-particles in a plane. The $N$ (generally complex values $z_{n}(t$ at time $t$ ofthe $N$ coordinates of these moving particles are given by the $N$eigenvalues of a time-dependent $Nimes N$ matrix $U(t$explicitly known in terms of the $2N$ initial data $z_{n}(0$and $dot{z}_{n}(0 $. This model comes in two dif/ferentvariants, one featuring 3 arbitrary coupling constants, the other only 2; for special values of these parameters all solutions are completely periodic with the same period independent of the initial data (''isochrony''; for other special values of these parameters this property holds up to corrections vanishing exponentially as $tightarrow infty$ (''asymptotic isochrony''. Other isochronous variants of these models are also reported. Alternative formulations, obtained by changing the dependent variables from the $N$ zeros of a monic polynomial of degree $N$ to its $N$ coefficients, are also exhibited. Some mathematical findings implied by some of these results - such as Diophantine properties of the zeros of certain polynomials - are outlined, but their analysis is postponed to a separate paper.
Quantum complexity of graph and algebraic problems
International Nuclear Information System (INIS)
Doern, Sebastian
2008-01-01
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Quantum complexity of graph and algebraic problems
Energy Technology Data Exchange (ETDEWEB)
Doern, Sebastian
2008-02-04
This thesis is organized as follows: In Chapter 2 we give some basic notations, definitions and facts from linear algebra, graph theory, group theory and quantum computation. In Chapter 3 we describe three important methods for the construction of quantum algorithms. We present the quantum search algorithm by Grover, the quantum amplitude amplification and the quantum walk search technique by Magniez et al. These three tools are the basis for the development of our new quantum algorithms for graph and algebra problems. In Chapter 4 we present two tools for proving quantum query lower bounds. We present the quantum adversary method by Ambainis and the polynomial method introduced by Beals et al. The quantum adversary tool is very useful to prove good lower bounds for many graph and algebra problems. The part of the thesis containing the original results is organized in two parts. In the first part we consider the graph problems. In Chapter 5 we give a short summary of known quantum graph algorithms. In Chapter 6 to 8 we study the complexity of our new algorithms for matching problems, graph traversal and independent set problems on quantum computers. In the second part of our thesis we present new quantum algorithms for algebraic problems. In Chapter 9 to 10 we consider group testing problems and prove quantum complexity bounds for important problems from linear algebra. (orig.)
Nonlinear field theories and non-Gaussian fluctuations for near-critical many-body systems
International Nuclear Information System (INIS)
Tuszynski, J.A.; Dixon, J.M.; Grundland, A.M.
1994-01-01
This review article outlines a number of efforts made over the past several decades to understand the physics of near critical many-body systems. Beginning with the phenomenological theories of Landau and Ginzburg the paper discusses the two main routes adopted in the past. The first approach is based on statistical calculations while the second investigates the underlying nonlinear field equations. In the last part of the paper we outline a generalisation of these methods which combines classical and quantum properties of the many-body systems studied. (orig.)
Local conservation laws and the structure of the many-body localized states.
Serbyn, Maksym; Papić, Z; Abanin, Dmitry A
2013-09-20
We construct a complete set of local integrals of motion that characterize the many-body localized (MBL) phase. Our approach relies on the assumption that local perturbations act locally on the eigenstates in the MBL phase, which is supported by numerical simulations of the random-field XXZ spin chain. We describe the structure of the eigenstates in the MBL phase and discuss the implications of local conservation laws for its nonequilibrium quantum dynamics. We argue that the many-body localization can be used to protect coherence in the system by suppressing relaxation between eigenstates with different local integrals of motion.
Relativistic many-body theory of atomic transitions: the relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.N.
1981-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated using techniques of quantum field theory. To reduce the equation of motion to a tractable form which is appropriate for numerical calculations, a graphical method is employed to resolve the complication arising from the antisymmetrization and angular momentum coupling. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
Many-body-localization: strong disorder perturbative approach for the local integrals of motion
Monthus, Cécile
2018-05-01
For random quantum spin models, the strong disorder perturbative expansion of the local integrals of motion around the real-spin operators is revisited. The emphasis is on the links with other properties of the many-body-localized phase, in particular the memory in the dynamics of the local magnetizations and the statistics of matrix elements of local operators in the eigenstate basis. Finally, this approach is applied to analyze the many-body-localization transition in a toy model studied previously from the point of view of the entanglement entropy.
Vortex matter stabilized by many-body interactions
Wolf, S.; Vagov, A.; Shanenko, A. A.; Axt, V. M.; Aguiar, J. Albino
2017-10-01
This work investigates interactions of vortices in superconducting materials between standard types I and II, in the domain of the so-called intertype (IT) superconductivity. Contrary to common expectations, the many-body (many-vortex) contribution is not a correction to the pair-vortex interaction here but plays a crucial role in the formation of the IT vortex matter. In particular, the many-body interactions stabilize vortex clusters that otherwise could not exist. Furthermore, clusters with large numbers of vortices become more stable when approaching the boundary between the intertype domain and type I. This indicates that IT superconductors develop a peculiar unconventional type of the vortex matter governed by the many-body interactions of vortices.
Problems and solutions in quantum physics
Ficek, Zbigniew
2016-01-01
This book contains tutorial problems with solutions for the textbook Quantum Physics for Beginners. The reader studying the abstract field of quantum physics needs to solve plenty of practical, especially quantitative, problems. This book places emphasis on basic problems of quantum physics together with some instructive, simulating, and useful applications. A considerable range of complexity is presented by these problems, and not too many of them can be solved using formulas alone.
PREFACE: 17th International Conference on Recent Progress in Many-Body Theories (MBT17)
Reinholz, Heidi; Boronat, Jordi
2014-08-01
These are the proceedings of the XVII International Conference on Recent Progress in Many-Body Theories, which was held from 8-13 September 2013 in Rostock, Germany. The conference continued the triennial series initiated in Trieste in 1978 and was devoted to new developments in the field of many-body theories. The conference series encourages the exchange of ideas between physicists working in such diverse areas as nuclear physics, quantum chemistry, lattice Hamiltonians or quantum uids. Many-body theories are an integral part in different fields of theoretical physics such as condensed matter, nuclear matter and field theory. Phase transitions and macroscopic quantum effects such as magnetism, Bose-Einstein condensation, super uidity or superconductivity have been investigated within ultra-cold gases, finite systems or various nanomaterials. The conference series on Recent Progress in Many-Body Theories is devoted to foster the interaction and to cross-fertilize between different fields and to discuss future lines of research. The topics of the 17th meeting were Cluster Physics Cold Gases High Energy Density Matter and Intense Lasers Magnetism New Developments in Many-Body Techniques Nuclear Many-Body and Relativistic Theories Quantum Fluids and Solids Quantum Phase Transitions Topological Insulators and Low Dimensional Systems. 109 participants from 20 countries participated. 44 talks and 61 posters werde presented. As a particular highlight of the conference, The Eugene Feenberg Memorial Medal for outstanding results in the field of many-body theory and The Hermann Kümmel Early Achievement Award in Many-Body Physics for young scientists in that field were awarded. The Feenberg Medal went jointly to Patrick Lee (MIT, USA) for his fundamental contributions to condensed-matter theory, especially in regard to the quantum Hall effect, to universal conductance uctuations, and to the Kondo effect in quantum dots, and Douglas Scalapino (UC Santa Barbara, USA) for his
Importance-truncated no-core shell model for fermionic many-body systems
Energy Technology Data Exchange (ETDEWEB)
Spies, Helena
2017-03-15
The exact solution of quantum mechanical many-body problems is only possible for few particles. Therefore, numerical methods were developed in the fields of quantum physics and quantum chemistry for larger particle numbers. Configuration Interaction (CI) methods or the No-Core Shell Model (NCSM) allow ab initio calculations for light and intermediate-mass nuclei, without resorting to phenomenology. An extension of the NCSM is the Importance-Truncated No-Core Shell Model, which uses an a priori selection of the most important basis states. The importance truncation was first developed and applied in quantum chemistry in the 1970s and latter successfully applied to models of light and intermediate mass nuclei. Other numerical methods for calculations for ultra-cold fermionic many-body systems are the Fixed-Node Diffusion Monte Carlo method (FN-DMC) and the stochastic variational approach with Correlated Gaussian basis functions (CG). There are also such method as the Coupled-Cluster method, Green's Function Monte Carlo (GFMC) method, et cetera, used for calculation of many-body systems. In this thesis, we adopt the IT-NCSM for the calculation of ultra-cold Fermi gases at unitarity. Ultracold gases are dilute, strongly correlated systems, in which the average interparticle distance is much larger than the range of the interaction. Therefore, the detailed radial dependence of the potential is not resolved, and the potential can be replaced by an effective contact interaction. At low energy, s-wave scattering dominates and the interaction can be described by the s-wave scattering length. If the scattering length is small and negative, Cooper-pairs are formed in the Bardeen-Cooper-Schrieffer (BCS) regime. If the scattering length is small and positive, these Cooper-pairs become strongly bound molecules in a Bose-Einstein-Condensate (BEC). In between (for large scattering lengths) is the unitary limit with universal properties. Calculations of the energy spectra
Many-body localization of bosons in optical lattices
Sierant, Piotr; Zakrzewski, Jakub
2018-04-01
Many-body localization for a system of bosons trapped in a one-dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose–Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.
Many body effects in the van der Waals force
International Nuclear Information System (INIS)
Perez, P.; Claro, F.
1985-08-01
A classical model of fluctuating dipoles is proposed for the evaluation of many-body effects in the van der Waals force between neutral polarizable particles. The method is applied to solid xenon giving the correct low temperature stable structure, unlike the usual two-body potential result. (author)
Properties of exponential many-body interatomic potentials
Czech Academy of Sciences Publication Activity Database
Ostapovets, Andrej; Paidar, Václav
2009-01-01
Roč. 47, č. 3 (2009), s. 193-199 ISSN 0023-432X R&D Projects: GA AV ČR IAA100100920 Institutional research plan: CEZ:AV0Z10100520 Keywords : many-body potentials * elastic constants * multilayer surface relaxations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.345, year: 2007
Many-body forces in nuclear shell-model
International Nuclear Information System (INIS)
Rath, P.K.
1985-01-01
In the microscopic derivation of the effective Hamiltonian for the nuclear shell model many-body forces between the valence nucleons occur. These many-body forces can be discriminated in ''real'' many-body forces, which can be related to mesonic and internal degrees of freedom of the nucleons, and ''effective'' many-body forces, which arise by the confinement of the nucleonic Hilbert space to the finite-dimension shell-model space. In the present thesis the influences of such three-body forces on the spectra of sd-shell nuclei are studied. For this the two common techniques for shell-model calculations (Oak Ridge-Rochester and Glasgow representation) are extended in such way that a general three-body term in the Hamiltonian can be regarded. The studies show that the repulsive contributions of the considered three-nucleon forces become more important with increasing number of valence nucleons. By this the particle-number dependence of empirical two-nucleon forces can be qualitatively explained. A special kind of effective many-body force occurs in the folded diagram expansion of the energy-dependent effective Hamiltonian for the shell model. Thereby it is shown that the contributions of the folded diagrams with three nucleons are just as important as those with two nucleons. Thus it is to be suspected that the folded diagram expansion contains many-particle terms with arbitrary particle number. The present studies however show that four nucleon effects are neglegible so that the folded diagram expansion can be confined to two- and three-particle terms. In shell-model calculations which extend over several main shells the influences of the spurious center-of-mass motion must be regarded. A procedure is discussed by which these spurious degrees of freedom can be exactly separated. (orig.) [de
Exploiting Quantum Resonance to Solve Combinatorial Problems
Zak, Michail; Fijany, Amir
2006-01-01
Quantum resonance would be exploited in a proposed quantum-computing approach to the solution of combinatorial optimization problems. In quantum computing in general, one takes advantage of the fact that an algorithm cannot be decoupled from the physical effects available to implement it. Prior approaches to quantum computing have involved exploitation of only a subset of known quantum physical effects, notably including parallelism and entanglement, but not including resonance. In the proposed approach, one would utilize the combinatorial properties of tensor-product decomposability of unitary evolution of many-particle quantum systems for physically simulating solutions to NP-complete problems (a class of problems that are intractable with respect to classical methods of computation). In this approach, reinforcement and selection of a desired solution would be executed by means of quantum resonance. Classes of NP-complete problems that are important in practice and could be solved by the proposed approach include planning, scheduling, search, and optimal design.
Medders, Gregory R; Paesani, Francesco
2015-03-10
Vibrational spectroscopy is a powerful technique to probe the structure and dynamics of water. However, deriving an unambiguous molecular-level interpretation of the experimental spectral features remains a challenge due to the complexity of the underlying hydrogen-bonding network. In this contribution, we present an integrated theoretical and computational framework (named many-body molecular dynamics or MB-MD) that, by systematically removing uncertainties associated with existing approaches, enables a rigorous modeling of vibrational spectra of water from quantum dynamical simulations. Specifically, we extend approaches used to model the many-body expansion of interaction energies to develop many-body representations of the dipole moment and polarizability of water. The combination of these "first-principles" representations with centroid molecular dynamics simulations enables the simulation of infrared and Raman spectra of liquid water under ambient conditions that, without relying on any ad hoc parameters, are in good agreement with the corresponding experimental results. Importantly, since the many-body energy, dipole, and polarizability surfaces employed in the simulations are derived independently from accurate fits to correlated electronic structure data, MB-MD allows for a systematic analysis of the calculated spectra in terms of both electronic and dynamical contributions. The present analysis suggests that, while MB-MD correctly reproduces both the shifts and the shapes of the main spectroscopic features, an improved description of quantum dynamical effects possibly combined with a dissociable water potential may be necessary for a quantitative representation of the OH stretch band.
Many-body localization proximity effects in platforms of coupled spins and bosons
Marino, J.; Nandkishore, R. M.
2018-02-01
We discuss the onset of many-body localization in a one-dimensional system composed of a XXZ quantum spin chain and a Bose-Hubbard model linearly coupled together. We consider two complementary setups, depending whether spatial disorder is initially imprinted on spins or on bosons; in both cases, we explore the conditions for the disordered portion of the system to localize by proximity of the other clean half. Assuming that the dynamics of one of the two parts develops on shorter time scales than the other, we can adiabatically eliminate the fast degrees of freedom, and derive an effective Hamiltonian for the system's remainder using projection operator techniques. Performing a locator expansion on the strength of the many-body interaction term or on the hopping amplitude of the effective Hamiltonian thus derived, we present results on the stability of the many-body localized phases induced by proximity effect. We also briefly comment on the feasibility of the proposed model through modern quantum optics architectures, with the long-term perspective to realize experimentally, in composite open systems, Anderson or many-body localization proximity effects.
Relativistic Many-Body Theory A New Field-Theoretical Approach
Lindgren, Ingvar
2011-01-01
Relativistic Many-Body Theory treats — for the first time — the combination of relativistic atomic many-body theory with quantum-electrodynamics (QED) in a unified manner. This book can be regarded as a continuation of the book by Lindgren and Morrison, Atomic Many-Body Theory (Springer 1986), which deals with the non-relativistic theory of many-electron systems, describing several means of treating the electron correlation to essentially all orders of perturbation theory. The treatment of the present book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insuffici...
Quantum cryptography as a retrodiction problem.
Werner, A H; Franz, T; Werner, R F
2009-11-27
We propose a quantum key distribution protocol based on a quantum retrodiction protocol, known as the Mean King problem. The protocol uses a two way quantum channel. We show security against coherent attacks in a transmission-error free scenario, even if Eve is allowed to attack both transmissions. This establishes a connection between retrodiction and key distribution.
Parallel implementation of many-body mean-field equations
International Nuclear Information System (INIS)
Chinn, C.R.; Umar, A.S.; Vallieres, M.; Strayer, M.R.
1994-01-01
We describe the numerical methods used to solve the system of stiff, nonlinear partial differential equations resulting from the Hartree-Fock description of many-particle quantum systems, as applied to the structure of the nucleus. The solutions are performed on a three-dimensional Cartesian lattice. Discretization is achieved through the lattice basis-spline collocation method, in which quantum-state vectors and coordinate-space operators are expressed in terms of basis-spline functions on a spatial lattice. All numerical procedures reduce to a series of matrix-vector multiplications and other elementary operations, which we perform on a number of different computing architectures, including the Intel Paragon and the Intel iPSC/860 hypercube. Parallelization is achieved through a combination of mechanisms employing the Gram-Schmidt procedure, broadcasts, global operations, and domain decomposition of state vectors. We discuss the approach to the problems of limited node memory and node-to-node communication overhead inherent in using distributed-memory, multiple-instruction, multiple-data stream parallel computers. An algorithm was developed to reduce the communication overhead by pipelining some of the message passing procedures
Relativistic many-body bound systems. Monograph report
International Nuclear Information System (INIS)
Danos, M.; Gillet, V.
1975-04-01
The principles and the mathematical details of a fully relativistic nuclear theory are given. Since the concept of nuclear forces is a strictly non-relativistic construct, it must be abandoned, and the forces must be replaced explicitly by their physical origin, i.e., by the interaction between nucleons and mesons. Thus, in this monograph the description of a nucleus has been formulated as a problem of relativistic quantum field theory which is solved by nuclear physics methods; to wit: the physics is described by specifying a Lagrangian which is a functional of the constituent fields (= of the parton fields); the solutions for the physical systems then are obtained in a time-independent treatment as expansions in the parton fields: both particles and nuclei are composite systems, made up of parton configurations, which define a representation of the Hamiltonian (associated with the specified Lagrangian)
Many-Body Localization Dynamics from Gauge Invariance
Brenes, Marlon; Dalmonte, Marcello; Heyl, Markus; Scardicchio, Antonello
2018-01-01
We show how lattice gauge theories can display many-body localization dynamics in the absence of disorder. Our starting point is the observation that, for some generic translationally invariant states, the Gauss law effectively induces a dynamics which can be described as a disorder average over gauge superselection sectors. We carry out extensive exact simulations on the real-time dynamics of a lattice Schwinger model, describing the coupling between U(1) gauge fields and staggered fermions. Our results show how memory effects and slow, double-logarithmic entanglement growth are present in a broad regime of parameters—in particular, for sufficiently large interactions. These findings are immediately relevant to cold atoms and trapped ion experiments realizing dynamical gauge fields and suggest a new and universal link between confinement and entanglement dynamics in the many-body localized phase of lattice models.
Almost conserved operators in nearly many-body localized systems
Pancotti, Nicola; Knap, Michael; Huse, David A.; Cirac, J. Ignacio; Bañuls, Mari Carmen
2018-03-01
We construct almost conserved local operators, that possess a minimal commutator with the Hamiltonian of the system, near the many-body localization transition of a one-dimensional disordered spin chain. We collect statistics of these slow operators for different support sizes and disorder strengths, both using exact diagonalization and tensor networks. Our results show that the scaling of the average of the smallest commutators with the support size is sensitive to Griffiths effects in the thermal phase and the onset of many-body localization. Furthermore, we demonstrate that the probability distributions of the commutators can be analyzed using extreme value theory and that their tails reveal the difference between diffusive and subdiffusive dynamics in the thermal phase.
Quasiparticle many-body dynamics of the Anderson model
International Nuclear Information System (INIS)
Kuzemskij, A.L.
1996-01-01
The paper addresses the many-body quasiparticle dynamics of the Anderson impurity model at finite temperatures in the framework of the equation-of-motion method. We find a new exact identity relating the one-particle and many-particle Green's Functions. Using this identity we present a consistent and general scheme for a construction of generalised mean fields (elastic scattering corrections) and self-energy (inelastic scattering) in terms of the Dyson equation. A new approach for the complex expansion for the single-particle propagator in terms of the Coulomb repulsion U and hybridization V is proposed. Using the exact identity, the essentially new many-body dynamical solution of SIAM has been derived. This approach offers a new way for the systematic construction of the approximative interpolating dynamical solutions of the strongly correlated electron systems. 47 refs
Many-body interactions in quasi-freestanding graphene
Energy Technology Data Exchange (ETDEWEB)
Siegel, David; Park, Cheol-Hwan; Hwang, Choongyu; Deslippe, Jack; Fedorov, Alexei; Louie, Steven; Lanzara, Alessandra
2011-06-03
The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the long-standing puzzles in this field. Here we present such a study in quasi-freestanding graphene by using high-resolution angle-resolved photoemission spectroscopy. We see the electron-electron and electron-phonon interactions go through substantial changes when the semimetallic regime is approached, including renormalizations due to strong electron-electron interactions with similarities to marginal Fermi liquid behavior. These findings set a new benchmark in our understanding of many-body physics in graphene and a variety of novel materials with Dirac fermions.
Theory of many-body localization in periodically driven systems
International Nuclear Information System (INIS)
Abanin, Dmitry A.; De Roeck, Wojciech; Huveneers, François
2016-01-01
We present a theory of periodically driven, many-body localized (MBL) systems. We argue that MBL persists under periodic driving at high enough driving frequency: The Floquet operator (evolution operator over one driving period) can be represented as an exponential of an effective time-independent Hamiltonian, which is a sum of quasi-local terms and is itself fully MBL. We derive this result by constructing a sequence of canonical transformations to remove the time-dependence from the original Hamiltonian. When the driving evolves smoothly in time, the theory can be sharpened by estimating the probability of adiabatic Landau–Zener transitions at many-body level crossings. In all cases, we argue that there is delocalization at sufficiently low frequency. We propose a phase diagram of driven MBL systems.
Many-Body Coulomb Gauge Exotic and Charmed Hybrids
Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2000-01-01
Utilizing a QCD Coulomb gauge Hamiltonian with linear confinement specified by lattice, we report a relativistic many-body calculation for the light exotic and charmed hybrid mesons. The Hamiltonian successfully describes both quark and gluon sectors, with vacuum and quasiparticle properties generated by a BCS transformation and more elaborate TDA and RPA diagonalizations for the meson ($q\\bar{q}$) and glueball ($gg$) masses. Hybrids entail a computationally intense relativistic three quasipa...
On nonequilibrium many-body systems III: nonlinear transport theory
International Nuclear Information System (INIS)
Luzzi, R.; Vasconcellos, A.R.; Algarte, A.C.S.
1986-01-01
A nonlinear transport theory for many-body systems arbitrarily away from equilibrium, based on the nonequilibrium statistical operator (NSO) method, is presented. Nonlinear transport equations for a basis set of dynamical quantities are derived using two equivalent treatments that may be considered far reaching generalizations of the Hilbert-Chapman-Enskog method and Mori's generalized Langevin equations method. The first case is considered in some detail and the general characteristics of the theory are discussed. (Author) [pt
The transformation of elementary particle physics into many-body physics
International Nuclear Information System (INIS)
Hove, L. van
1986-01-01
The author illustrates the domains of particle physics where the theoretical problems and methods have much in common with many-body and condensed-matter physics. The multitude of diverse physical systems accessible to experimentation in condensed-matter physics, and the numerous concepts developed for their theoretical understanding provide a rich store of ideas and analogies to the particle physicist. This can help him to overcome the great handicap that in his own discipline the experimental facts are very hard to come by and are often extremely incomplete. On the other hand, particle physics brought us such truly fundamental advances as non-Abelian gauge theories, electroweak unification with the heavy weak bosons, and quantum chromodynamics with the confinement principle for the field quanta. As our understanding of these novel schemes deepens, possibly with further progress toward unification, one can expect that they will slowly have an impact on the rest of physics, just as the concepts and techniques of Abelian field theories have gradually invaded most of condensed-matter physics. (Auth.)
Density functional and many-body theories of Hydrogen plasmas
International Nuclear Information System (INIS)
Perrot, F.; Dharma-Wardana, M.W.C.
1983-11-01
This work is an attempt to go beyond the standard description of hot condensed matter using the well-known ''average atom model''. The first part describes a static model using ''Density functional theory'' to calculate self-consistent coupled electron and ion density profiles of the plasma not restricted to a single average atomic sphere. In a second part, the results are used as ingredients for a many-body approach to electronic properties: the one-particle Green-function self-energy is calculated, from which shifted levels, populations and level-widths are deduced. Results for the Hydrogen plasma are reported, with emphasis on the 1s bound state
Many-Body Theory for Positronium-Atom Interactions
Green, D. G.; Swann, A. R.; Gribakin, G. F.
2018-05-01
A many-body-theory approach has been developed to study positronium-atom interactions. As first applications, we calculate the elastic scattering and momentum-transfer cross sections and the pickoff annihilation rate 1Zeff for Ps collisions with He and Ne. For He the cross section is in agreement with previous coupled-state calculations, while comparison with experiment for both atoms highlights discrepancies between various sets of measured data. In contrast, the calculated 1Zeff (0.13 and 0.26 for He and Ne, respectively) are in excellent agreement with the measured values.
Porter-Thomas distribution in unstable many-body systems
International Nuclear Information System (INIS)
Volya, Alexander
2011-01-01
We use the continuum shell model approach to explore the resonance width distribution in unstable many-body systems. The single-particle nature of a decay, the few-body character of the interaction Hamiltonian, and the collectivity that emerges in nonstationary systems due to the coupling to the continuum of reaction states are discussed. Correlations between the structures of the parent and daughter nuclear systems in the common Fock space are found to result in deviations of decay width statistics from the Porter-Thomas distribution.
Correlation functions for Hermitian many-body systems: Necessary conditions
International Nuclear Information System (INIS)
Brown, E.B.
1994-01-01
Lee [Phys. Rev. B 47, 8293 (1993)] has shown that the odd-numbered derivatives of the Kubo autocorrelation function vanish at t=0. We show that this condition is based on a more general property of nondiagonal Kubo correlation functions. This general property provides that certain functional forms (e.g., simple exponential decay) are not admissible for any symmetric or antisymmetric Kubo correlation function in a Hermitian many-body system. Lee's result emerges as a special case of this result. Applications to translationally invariant systems and systems with rotational symmetries are also demonstrated
Many-Body Potentials For Binary Immiscible liquid Metal Alloys
International Nuclear Information System (INIS)
Karaguelle, H.
2004-01-01
The modified analytic embedded atom method (MAEAM) type many- body potentials have been constructed for three binary liquid immiscible alloy systems: Al-Pb, Ag-Ni, Ag- Cu. The MAEAM potential functions are fitted to both solid and liquid state properties for only liquid pure metals which consist the immiscible alloy. In order to test the reliability of the constructed MAEAM effective potentials, partial structure factors and pair distribution functions of these binary liquid metal alloys have been calculated using the thermodynamically self-consistent variational modified hypernetted chain (VMHNC) theory of liquids. A good agreement with the available experimental data for structure has
Adiabatic quantum search algorithm for structured problems
International Nuclear Information System (INIS)
Roland, Jeremie; Cerf, Nicolas J.
2003-01-01
The study of quantum computation has been motivated by the hope of finding efficient quantum algorithms for solving classically hard problems. In this context, quantum algorithms by local adiabatic evolution have been shown to solve an unstructured search problem with a quadratic speedup over a classical search, just as Grover's algorithm. In this paper, we study how the structure of the search problem may be exploited to further improve the efficiency of these quantum adiabatic algorithms. We show that by nesting a partial search over a reduced set of variables into a global search, it is possible to devise quantum adiabatic algorithms with a complexity that, although still exponential, grows with a reduced order in the problem size
Quantum Computing's Classical Problem, Classical Computing's Quantum Problem
Van Meter, Rodney
2013-01-01
Tasked with the challenge to build better and better computers, quantum computing and classical computing face the same conundrum: the success of classical computing systems. Small quantum computing systems have been demonstrated, and intermediate-scale systems are on the horizon, capable of calculating numeric results or simulating physical systems far beyond what humans can do by hand. However, to be commercially viable, they must surpass what our wildly successful, highly advanced classica...
Relativistic many-body theory of atomic transitions. The relativistic equation-of-motion approach
International Nuclear Information System (INIS)
Huang, K.
1982-01-01
An equation-of-motion approach is used to develop the relativistic many-body theory of atomic transitions. The relativistic equations of motion for transition matrices are formulated with the use of techniques of quantum-field theory. To reduce the equations of motion to a tractable form which is appropriate for numerical calculations, a graphical method to resolve the complication arising from the antisymmetrization and angular-momentum coupling is employed. The relativistic equation-of-motion method allows an ab initio treatment of correlation and relativistic effects in both closed- and open-shell many-body systems. A special case of the present formulation reduces to the relativistic random-phase approximation
Modified potentials in many-body perturbation theory
International Nuclear Information System (INIS)
Silver, D.M.; Bartlett, R.J.
1976-01-01
Many-body perturbation-theory calculations of the pair-correlation energy within the regime of various finite expansions in two-center Slater-type basis sets are performed using a wide variety of modified potentials for the determination of unoccupied orbitals. To achieve meaningful convergence, it appears that the perturbation series must be carried through third order, using shifted denominators to include contributions from various higher-order diagrams. Moreover, certain denominator shifts are found necessary to ensure that a negative-definite resolvent accompanies the perturbation scheme when an arbitrary modified potential is employed. Through third order with denominator shifts, well-behaved modified potentials are found to give results that are equivalent, within 1 kcal/mole, to those obtained for pair-correlation energies with the standard self-consistent-field-V/sup N/ potential
Structure of the many-body wavefunction for scattering
International Nuclear Information System (INIS)
L'Huillier, M.; Redish, E.F.; Tandy, P.C.
1978-01-01
We show that the scattered part of the many-body wavefunction initiated by two incoming clusters is given by a fully connected operator acting on the initial channel state. The structure of this operator suggests a division of the full wavefunction into two-cluster components. A set of coupled equations in both the differential and integral form is then derived for these components. These equations have structure and properties similar to the three-body equations of Faddeev. We demonstrate that each component has outgoing waves in a unique two-cluster partition. The transition amplitude for any final arrangement can therefore be extracted directly from the outgoing waves in the relevant components
The partition function of an interacting many body system
International Nuclear Information System (INIS)
Rummel, C.; Ankerhold, J.
2002-01-01
Based on the path integral approach the partition function of a many body system with separable two body interaction is calculated in the sense of a semiclassical approximation. The commonly used Gaussian type of approximation, known as the perturbed static path approximation (PSPA), breaks down near a crossover temperature due to instabilities of the classical mean field solution. It is shown how the PSPA is systematically improved within the crossover region by taking into account large non-Gaussian fluctuation and an approximation applicable down to very low temperatures is carried out. These findings are tested against exact results for the archetypical cases of a particle moving in a one dimensional double well and the exactly solvable Lipkin-Meshkov-Glick model. The extensions should have applications in finite systems at low temperatures as in nuclear physics and mesoscopic systems, e. g. for gap fluctuations in nano-scale superconducting devices previously studied within a PSPA type of approximation. (author)
Nuclear collision theory with many-body correlations, 2
International Nuclear Information System (INIS)
Kurihara, Yukio.
1984-12-01
A nuclear collision theory, in which the many-body correlation induced by the strong short-ranged repulsion and medium-ranged attraction of the realistic NN interaction is explicitly included, is applied to the deuteron+deuteron elastic scattering at low energies. Pair correlation functions calculated by the present theory are very different from the Hackenbroich et al. 's one. They contain not only the short-ranged suppressive correlation, but also the medium-ranged enhancing correlation. The former changes the shape of the d-d potential from the wine-bottle one. And the latter makes the d-d potential much more attractive. This effect is necessary for reproducing a bump around thatesub(cm)=90 0 in the experimental elastic differential cross section. The phase shifts evaluated by the present theory are compared with those from the resonating-group method. (author)
Relativistic many-body theory of atomic structures
International Nuclear Information System (INIS)
Cheng, K.T.
1983-01-01
The main objective of this program is to improve our understanding of the effect of relativity and electron correlations on atomic processes. Current efforts include hyperfine structure (hfs) studies using the multiconfiguration Dirac-Fock (MCDF) technique. Atomic hfs are known to be sensitive to relativity and electron correlations, and provide important tests of relativistic atomic many-body theories. Preliminary results on the hfs of the 4f 12 3 H ground state of 68 Er 167 are shown and are in good agreement with experiment. This shows that the MCDF technique can be an efficient and powerful method for atomic hfs studies. Further tests of this method are in progress. We are also studying the absorption spectra for Xe-like ions in the region of 4d → nf, epsilonf transitions
Many-body theory and Energy Density Functionals
Energy Technology Data Exchange (ETDEWEB)
Baldo, M. [INFN, Catania (Italy)
2016-07-15
In this paper a method is first presented to construct an Energy Density Functional on a microscopic basis. The approach is based on the Kohn-Sham method, where one introduces explicitly the Nuclear Matter Equation of State, which can be obtained by an accurate many-body calculation. In this way it connects the functional to the bare nucleon-nucleon interaction. It is shown that the resulting functional can be performing as the best Gogny force functional. In the second part of the paper it is shown how one can go beyond the mean-field level and the difficulty that can appear. The method is based on the particle-vibration coupling scheme and a formalism is presented that can handle the correct use of the vibrational degrees of freedom within a microscopic approach. (orig.)
Many-body physics with alkaline-earth Rydberg lattices
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, R; Nath, R; Pohl, T [Max Planck Institute for the Physics of Complex Systems, Noethnitzer Strasse 38, 01187 Dresden (Germany); Millen, J; Jones, M P A, E-mail: rick@pks.mpg.de [Department of Physics, Durham University, Durham DH1 3LE (United Kingdom)
2011-09-28
We explore the prospects for confining alkaline-earth Rydberg atoms in an optical lattice via optical dressing of the secondary core-valence electron. Focussing on the particular case of strontium, we identify experimentally accessible magic wavelengths for simultaneous trapping of ground and Rydberg states. A detailed analysis of relevant loss mechanisms shows that the overall lifetime of such a system is limited only by the spontaneous decay of the Rydberg state, and is not significantly affected by photoionization or autoionization. The van der Waals C{sub 6} coefficients for the Sr(5sns {sup 1}S{sub 0}) Rydberg series are calculated, and we find that the interactions are attractive. Finally we show that the combination of magic-wavelength lattices and attractive interactions could be exploited to generate many-body Greenberger-Horne-Zeilinger states.
Problems in Quantum Mechanics with Solutions
d'Emilio, Emilio
2011-01-01
242 solved problems of several degrees of difficulty in nonrelativistic Quantum Mechanics, ranging from the themes of the crisis of classical physics, through the achievements in the framework of modern atomic physics, down to the still alive, more intriguing aspects connected e.g. with the EPR paradox, the Aharonov--Bohm effect, quantum teleportation.
Physics: Quantum problems solved through games
Maniscalco, Sabrina
2016-04-01
Humans are better than computers at performing certain tasks because of their intuition and superior visual processing. Video games are now being used to channel these abilities to solve problems in quantum physics. See Letter p.210
Quantum resonance for simulating combinatorial problems
International Nuclear Information System (INIS)
Zak, Michail; Fijany, Amir
2005-01-01
Quantum computing by simulations is based upon similarity between mathematical formalism of a quantum phenomenon and phenomena to be analyzed. In this Letter, the mathematical formalism of quantum resonance combined with tensor product decomposability of unitary evolutions is mapped onto a class of NP-complete combinatorial problems. It has been demonstrated that nature has polynomial resources for solving NP-complete problems and that will help to develop a new strategy for artificial intelligence, as well as to re-evaluate the role of natural selection in biological evolution
Towards quantum gravity via quantum field theory. Problems and perspectives
Energy Technology Data Exchange (ETDEWEB)
Fredenhagen, Klaus [II. Institut fuer Theoretische Physik, Universitaet Hamburg (Germany)
2016-07-01
General Relativity is a classical field theory; the standard methods for constructing a corresponding quantum field theory, however, meet severe difficulties, in particular perturbative non-renormalizability and the problem of background independence. Nevertheless, modern approaches to quantum field theory have significantly lowered these obstacles. On the side of non-renormalizability, this is the concept of effective theories, together with indications for better non-perturbative features of the renormalization group flow. On the side of background independence the main progress comes from an improved understanding of quantum field theories on generic curved spacetimes. Combining these informations, a promising approach to quantum gravity is an expansion around a classical solution which then is a quantum field theory on a given background, augmented by an identity which expresses independence against infinitesimal shifts of the background. The arising theory is expected to describe small corrections to classical general relativity. Inflationary cosmology is expected to arise as a lowest order approximation.
Communication: Random phase approximation renormalized many-body perturbation theory
International Nuclear Information System (INIS)
Bates, Jefferson E.; Furche, Filipp
2013-01-01
We derive a renormalized many-body perturbation theory (MBPT) starting from the random phase approximation (RPA). This RPA-renormalized perturbation theory extends the scope of single-reference MBPT methods to small-gap systems without significantly increasing the computational cost. The leading correction to RPA, termed the approximate exchange kernel (AXK), substantially improves upon RPA atomization energies and ionization potentials without affecting other properties such as barrier heights where RPA is already accurate. Thus, AXK is more balanced than second-order screened exchange [A. Grüneis et al., J. Chem. Phys. 131, 154115 (2009)], which tends to overcorrect RPA for systems with stronger static correlation. Similarly, AXK avoids the divergence of second-order Møller-Plesset (MP2) theory for small gap systems and delivers a much more consistent performance than MP2 across the periodic table at comparable cost. RPA+AXK thus is an accurate, non-empirical, and robust tool to assess and improve semi-local density functional theory for a wide range of systems previously inaccessible to first-principles electronic structure calculations
Many-body delocalization with random vector potentials
Cheng, Chen; Mondaini, Rubem
In this talk we present the ergodic properties of excited states in a model of interacting fermions in quasi-one dimensional chains subjected to a random vector potential. In the non-interacting limit, we show that arbitrarily small values of this complex off-diagonal disorder triggers localization for the whole spectrum; the divergence of the localization length in the single particle basis is characterized by a critical exponent ν which depends on the energy density being investigated. However, when short-ranged interactions are included, the localization is lost and the system is ergodic regardless of the magnitude of disorder in finite chains. Our numerical results suggest a delocalization scheme for arbitrary small values of interactions. This finding indicates that the standard scenario of the many-body localization cannot be obtained in a model with random gauge fields. This research is financially supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. U1530401 and 11674021). RM also acknowledges support from NSFC (Grant No. 11650110441).
Detecting many-body-localization lengths with cold atoms
Guo, Xuefei; Li, Xiaopeng
2018-03-01
Considering ultracold atoms in optical lattices, we propose experimental protocols to study many-body-localization (MBL) length and criticality in quench dynamics. Through numerical simulations with exact diagonalization, we show that in the MBL phase the perturbed density profile following a local quench remains exponentially localized in postquench dynamics. The size of this density profile after long-time-dynamics defines a localization length, which tends to diverge at the MBL-to-ergodic transition as we increase the system size. The determined localization transition point agrees with previous exact diagonalization calculations using other diagnostics. Our numerical results provide evidence for violation of the Harris-Chayes bound for the MBL criticality. The critical exponent ν can be extracted from our proposed dynamical procedure, which can then be used directly in experiments to determine whether the Harris-Chayes-bound holds for the MBL transition. These proposed protocols to detect localization criticality are justified by benchmarking to the well-established results for the noninteracting three-dimensional Anderson localization.
Spectral statistics of chaotic many-body systems
International Nuclear Information System (INIS)
Dubertrand, Rémy; Müller, Sebastian
2016-01-01
We derive a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger (or Gross–Pitaevski) equation. Our formula applies to bosonic systems with discretised positions, such as the Bose–Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. We use the trace formula to investigate the spectral statistics of these systems, by studying interference between solutions of the nonlinear Schrödinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner–Dyson ensembles of random matrix theory. The conditions for Wigner–Dyson statistics involve a gap in the spectrum of the Frobenius–Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties. (paper)
Many-body theory of effective mass in degenerate semiconductors
Tripathi, G. S.; Shadangi, S. K.
2018-03-01
We derive the many-body theory of the effective mass in the effective mass representation (EMR). In the EMR, we need to solve the equation of motion of an electron in the presence of electron-electron interactions, where the wavefunction is expanded over a complete set of Luttinger-Kohn wavefunctions. We use the Luttinger-Ward thermodynamic potential and the Green’s function perturbation to derive an expression for the band effective mass by taking into account the electron-electron interactions. Both quasi-particle and the correlation contributions are considered. We show that had we considered only the quasi-particle contribution, we would have missed important cancellations. Thus the correlated motion of electrons has important effects in the renormalization of the effective mass. Considering the exchange self-energy in the band model, we derive a tractable expression for the band effective mass. We apply the theory to n-type degenerate semiconductors, PbTe and SnTe, and analyze the impact of the theory on the anisotropic effective mass of the conduction bands in these systems.
From Discrete Breathers to Many Body Localization and Flatbands
Flach, Sergej
Discrete breathers (DB) and intrinsic localized modes (ILM) are synonymic dynamical states on nonlinear lattices - periodic in time and localized in space, and widely observed in many applications. I will discuss the connections between DBs and many-body localization (MBL) and the properties of DBs on flatband networks. A dense quantized gas of strongly excited DBs can lead to a MBL phase in a variety of different lattice models. Its classical counterpart corresponds to a 'nonergodic metal' in the MBL language, or to a nonGibbsean selftrapped state in the language of nonlinear dynamics. Flatband networks are lattices with small amplitude waves exhibiting macroscopic degeneracy in their band structure due to local symmetries, destructive interference, compact localized eigenstates and horizontal flat bands. DBs can preserve the compactness of localization in the presence of nonlinearity with properly tuned internal phase relationships, making them promising tools for control of the phase coherence of waves. Also at New Zealand Institute of Advanced Study, Massey University, Auckland, New Zealand.
Many body effects in nuclear matter QCD sum rules
Drukarev, E. G.; Ryskin, M. G.; Sadovnikova, V. A.
2017-12-01
We calculate the single-particle nucleon characteristics in symmetric nuclear matter with inclusion of the 3N and 4N interactions. We calculated the contribution of the 3N interactions earlier, now we add that of the 4N ones. The contribution of the 4N forces to nucleon self energies is expressed in terms of the nonlocal scalar condensate (d = 3) and of the configurations of the vector-scalar and the scalar-scalar quark condensates (d = 6) in which two diquark operators act on two different nucleons of the matter.These four-quark condensates are obtained in the model-independent way. The density dependence of the nucleon effective mass, of the vector self energy and of the single-particle potential energy are obtained. We traced the dependence of the nucleon characteristics on the actual value of the pion-nucleon sigma term. We obtained also the nucleon characteristics in terms of the quasifree nucleons, with the noninteracting nucleons surrounded by their pion clouds as the starting point. This approach leads to strict hierarchy of the many body forces.
Workshop on Kadanoff-Baym Equations : Progress and Perspectives for Many-Body Physics
2000-01-01
Equilibrium and nonequilibrium properties of correlated many-body systems are of growing interest in many fields of physics, including condensed matter, dense plasmas, nuclear matter and particles. The most powerful and general method which applies equally to all these areas is given by quantum field theory.Written by the leading experts and understandable to non-specialists, this book provides an overview on the basic ideas and concepts of the method of nonequilibrium Green's functions. It is complemented by modern applications of the method to a variety of topics, such as optics and transpor
First-principles many-body theory for ultra-cold atoms
International Nuclear Information System (INIS)
Drummond, Peter D.; Hu Hui; Liu Xiaji
2010-01-01
Recent breakthroughs in the creation of ultra-cold atoms in the laboratory have ushered in unprecedented changes in physical science. These enormous changes in the coldest temperatures available in the laboratory mean that many novel experiments are possible. There is unprecedented control and simplicity in these novel systems, meaning that quantum many-body theory is now facing severe challenges in quantitatively understanding these new results. We discuss some of the new experiments and recently developed theoretical techniques required to predict the results obtained.
Off-shell effects and consistency of many-body treatments of dense matter
International Nuclear Information System (INIS)
Krippa, Boris; Birse, Michael C.; McGovern, Judith A.; Walet, Niels R.
2003-01-01
Effective field theory requires all observables to be independent of the representation used for the quantum field operators. It means that off-shell properties of the interactions should not lead to any observable effects. We analyze this issue in the context of many-body approaches to nuclear matter, where it should be possible to shift the contributions of lowest order in purely off-shell two-body interactions into three-body forces. We show that none of the commonly used truncations of the two-body scattering amplitude such as the ladder, Brueckner-Hartree-Fock, or parquet approximations respect this requirement
Electromagnetic interactions in relativistic systems of many bodies
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Cook, A.H.
1987-09-01
In a previous report (Cook, 1986, 1987) on a formulation of a quasi-relativistic quantum mechanical equation of motion for many particles, little was said of the electromagnetic interactions that keep a set of particles in a bound state. That omission is to some extent repaired in this report. (author). 3 refs
Holographic Duality with a View Toward Many-Body Physics
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John McGreevy
2010-01-01
Full Text Available These are notes based on a series of lectures given at the KITP workshop Quantum Criticality and the AdS/CFT Correspondence in July, 2009. The goal of the lectures was to introduce condensed matter physicists to the AdS/CFT correspondence. Discussion of string theory and of supersymmetry is avoided to the extent possible.
Highly Enhanced Many-Body Interactions in Anisotropic 2D Semiconductors.
Sharma, Ankur; Yan, Han; Zhang, Linglong; Sun, Xueqian; Liu, Boqing; Lu, Yuerui
2018-05-15
Atomically thin two-dimensional (2D) semiconductors have presented a plethora of opportunities for future optoelectronic devices and photonics applications, made possible by the strong light matter interactions at the 2D quantum limit. Many body interactions between fundamental particles in 2D semiconductors are strongly enhanced compared with those in bulk semiconductors because of the reduced dimensionality and, thus, reduced dielectric screening. These enhanced many body interactions lead to the formation of robust quasi-particles, such as excitons, trions, and biexcitons, which are extremely important for the optoelectronics device applications of 2D semiconductors, such as light emitting diodes, lasers, and optical modulators, etc. Recently, the emerging anisotropic 2D semiconductors, such as black phosphorus (termed as phosphorene) and phosphorene-like 2D materials, such as ReSe 2 , 2D-perovskites, SnS, etc., show strong anisotropic optical and electrical properties, which are different from conventional isotropic 2D semiconductors, such as transition metal dichalcogenide (TMD) monolayers. This anisotropy leads to the formation of quasi-one-dimensional (quasi-1D) excitons and trions in a 2D system, which results in even stronger many body interactions in anisotropic 2D materials, arising from the further reduced dimensionality of the quasi-particles and thus reduced dielectric screening. Many body interactions have been heavily investigated in TMD monolayers in past years, but not in anisotropic 2D materials yet. The quasi-particles in anisotropic 2D materials have fractional dimensionality which makes them perfect candidates to serve as a platform to study fundamental particle interactions in fractional dimensional space. In this Account, we present our recent progress related to 2D phosphorene, a 2D system with quasi-1D excitons and trions. Phosphorene, because of its unique anisotropic properties, provides a unique 2D platform for investigating the
Many-body Anderson localization of strongly interacting bosons in random lattices
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Katzer, Roman
2015-05-01
In the present work, we investigate the problem of many-body localization of strongly interacting bosons in random lattices within the disordered Bose-Hubbard model. This involves treating both the local Mott-Hubbard physics as well as the non-local quantum interference processes, which give rise to the phenomenon of Anderson localization, within the same theory. In order to determine the interaction induced transition to the Mott insulator phase, it is necessary to treat the local particle interaction exactly. Therefore, here we use a mean-field approach that approximates only the kinetic term of the Hamiltonian. This way, the full problem of interacting bosons on a random lattice is reduced to a local problem of a single site coupled to a particle bath, which has to be solved self-consistently. In accordance to previous works, we find that a finite disorder width leads to a reduced size of the Mott insulating regions. The transition from the superfluid phase to the Bose glass phase is driven by the non-local effect of Anderson localization. In order to describe this transition, one needs to work within a theory that is non-local as well. Therefore, here we introduce a new approach to the problem. Based on the results for the local excitation spectrum obtained within the mean-field theory, we reduce the full, interacting model to an effective, non-interacting model by applying a truncation scheme to the Hilbert space. Evaluating the long-ranged current density within this approximation, we identify the transition from the Bose glass to the superfluid phase with the Anderson transition of the effective model. Resolving this transition using the self-consistent theory of localization, we obtain the full phase diagram of the disordered Bose-Hubbard model in the regime of strong interaction and larger disorder. In accordance to the theorem of inclusions, we find that the Mott insulator and the superfluid phase are always separated by the compressible, but insulating
Many-body dynamics with cold atoms and molecules in optical lattices
International Nuclear Information System (INIS)
Schachenmayer, J.
2012-01-01
Systems of cold atoms or molecules, trapped in a periodic potential formed from standing waves of laser light, provide an experimental possibility to study strongly correlated many-body lattice models, which are traditionally used in condensed matter physics. Due to the relatively weak energy scales in these ''optical lattices'' (next-neighbor tunneling energies are typically on the order of tens of Hertz), the time-scales of the dynamics in these systems is relatively slow and can be observed in experiments. Furthermore, the microscopic parameters of the models can be very well controlled by lattice laser intensities and external fields. Thus, optical lattices provide an excellent framework to study many-body quantum non-equilibrium dynamics, which on the theoretical level is the topic of this thesis. This thesis contains a study of many-body dynamics in optical lattices for both idealized isolated models and realistic models with imperfections. It is centered around four main topics: The first two topics are studies of coherent many-body dynamics. This contains explicitly: (i) an analysis of the possibility to dynamically prepare crystalline states of Rydberg atoms or polar molecules by adiabatically tuning laser parameters; and (ii) a study of the collapses and revivals of the momentum-distribution of a Bose-Einstein condensate with a fixed number of atoms, which is suddenly loaded into a deep optical lattice. The third main topic is entanglement and specifically the dynamical growth of entanglement between portions of an optical lattice in quench experiments. A method to create and measure large-scale entanglement is presented in this thesis. The fourth main topic addresses classical noise. Specifically, a system of atoms in an optical lattice, which is created from lasers with intensity fluctuations, is analyzed in this work. The noisy evolution of many-body correlation functions is studied and a method to cancel this noise in a realistic experimental setup is
Optimization problem in quantum cryptography
International Nuclear Information System (INIS)
Brandt, Howard E
2003-01-01
A complete optimization was recently performed, yielding the maximum information gain by a general unitary entangling probe in the four-state protocol of quantum cryptography. A larger set of optimum probe parameters was found than was known previously from an incomplete optimization. In the present work, a detailed comparison is made between the complete and incomplete optimizations. Also, a new set of optimum probe parameters is identified for the four-state protocol
On the quantum inverse scattering problem
International Nuclear Information System (INIS)
Maillet, J.M.; Terras, V.
2000-01-01
A general method for solving the so-called quantum inverse scattering problem (namely the reconstruction of local quantum (field) operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given. The principal requirement being the initial condition (R(0)=P, the permutation operator) for the quantum R-matrix solving the Yang-Baxter equation, it applies not only to most known integrable fundamental lattice models (such as Heisenberg spin chains) but also to lattice models with arbitrary number of impurities and to the so-called fused lattice models (including integrable higher spin generalizations of Heisenberg chains). Our method is then applied to several important examples like the sl n XXZ model, the XYZ spin-((1)/(2)) chain and also to the spin-s Heisenberg chains
Engineering Topological Many-Body Materials in Microwave Cavity Arrays
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Brandon M. Anderson
2016-12-01
Full Text Available We present a scalable architecture for the exploration of interacting topological phases of photons in arrays of microwave cavities, using established techniques from cavity and circuit quantum electrodynamics. A time-reversal symmetry-breaking (nonreciprocal flux is induced by coupling the microwave cavities to ferrites, allowing for the production of a variety of topological band structures including the α=1/4 Hofstadter model. To induce photon-photon interactions, the cavities are coupled to superconducting qubits; we find these interactions are sufficient to stabilize a ν=1/2 bosonic Laughlin puddle. Exact diagonalization studies demonstrate that this architecture is robust to experimentally achievable levels of disorder. These advances provide an exciting opportunity to employ the quantum circuit toolkit for the exploration of strongly interacting topological materials.
On nonequilibrium many-body systems V: ultrafast transport phenomena
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Freire, V.N.; Vasconcellos, A.R.; Luzzi, R.
1989-01-01
The monequilibrium statistical operator method and its accompanying nonlinear quantum transport theory, are used to perform an analytical study of the ultrafast mobility transient of central-valley photoinjected carriers in direct-gap polar semiconductors. Expressions for the time-resolved mobility of the hot carriers are derived. A brief discussion of the carriers' diffusion coefficient is done. (A.C.A.S.) [pt
Complexity of Quantum Impurity Problems
Bravyi, Sergey; Gosset, David
2017-12-01
We give a quasi-polynomial time classical algorithm for estimating the ground state energy and for computing low energy states of quantum impurity models. Such models describe a bath of free fermions coupled to a small interacting subsystem called an impurity. The full system consists of n fermionic modes and has a Hamiltonian {H=H_0+H_{imp}}, where H 0 is quadratic in creation-annihilation operators and H imp is an arbitrary Hamiltonian acting on a subset of O(1) modes. We show that the ground energy of H can be approximated with an additive error {2^{-b}} in time {n^3 \\exp{[O(b^3)]}}. Our algorithm also finds a low energy state that achieves this approximation. The low energy state is represented as a superposition of {\\exp{[O(b^3)]}} fermionic Gaussian states. To arrive at this result we prove several theorems concerning exact ground states of impurity models. In particular, we show that eigenvalues of the ground state covariance matrix decay exponentially with the exponent depending very mildly on the spectral gap of H 0. A key ingredient of our proof is Zolotarev's rational approximation to the {√{x}} function. We anticipate that our algorithms may be used in hybrid quantum-classical simulations of strongly correlated materials based on dynamical mean field theory. We implemented a simplified practical version of our algorithm and benchmarked it using the single impurity Anderson model.
Theoretical physics 3. Quantum mechanics 1 with problems in MAPLE
International Nuclear Information System (INIS)
Reineker, P.; Schulz, M.; Schulz, B.M.
2007-01-01
The following topics are dealt with: Historically heuristic introduction to quantum mechanics, the Schroedinger equation, foundations of quantum mechanics, the linear harmonic oscillator, quantum-mechanical motion in the central field, approximation methods for the solution of quantum mechanical problems, motion of particles in the electromagnetic field, spin and magnetic moment of the electron, many-particle systems, conceptional problems of quantum mechanics
Introduction to integrable many-body systems II
International Nuclear Information System (INIS)
Samaj, L.
2010-01-01
This is the second part of a three-volume introductory course about integrable systems of interacting bodies. The models of interest are quantum spin chains with nearest-neighbor interactions between spin operators, in particular Heisenberg spin- 2 models. The Ising model in a transverse field, expressible as a quadratic fermion form by using the Jordan-Wigner transformation, is the subject of Sect. 12. The derivation of the coordinate Bethe ansatz for the XXZ Heisenberg chain and the determination of its absolute ground state in various regions of the anisotropy parameter are presented in Sect. 13. The magnetic properties of the ground state are explained in Sect. 14. Sect. 15 concerns excited states and the zero-temperature thermodynamics of the XXZ model. The thermodynamics of the XXZ Heisenberg chain is derived on the basis of the string hypothesis in Sect. 16; the thermodynamic Bethe ansatz equations are analyzed in high-temperature and low-temperature limits. An alternative derivation of the thermodynamics without using strings, leading to a non-linear integral equation determining the free energy, is the subject of Sect. 17. A nontrivial application of the Quantum Inverse Scattering method to the fully anisotropic XYZ Heisenberg chain is described in Section 18. Section 19 deals with integrable cases of isotropic spin chains with an arbitrary spin. (Author)
Diagrammatic many-body perturbation expansion for atoms and molecules. Pt. 6
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Moncrieff, D.; Baker, D.J.; Wilson, S.
1989-01-01
The efficient evaluation of the second-order expression in the many-body perturbation theory expansion for the correlation energy on vector processing and parallel processing computers is discussed. It is argued that the linked diagram theorem not only leads to the well known theoretical advantages of the many-body perturbation theory approach which allows the calculation of correlation energies for large (i.e. extended molecules or species containing heavy atoms) systems but also decouples the many-electron problem allowing efficient implementation on parallel processing machines. Furthermore, the computation associated with each of the resulting subproblems is very well suited to vector processing machines. Timing tests are reported for the CRAY 1 and CDC Cyber 205 vector processors, for a 1 processor implementation on the CRAY X-MP/48 and the ETA-10E, and for a 4 processor implementation on the Cray X-MP/48. (orig.)
Method for the Direct Solve of the Many-Body Schrödinger Wave Equation
Jerke, Jonathan; Tymczak, C. J.; Poirier, Bill
We report on theoretical and computational developments towards a computationally efficient direct solve of the many-body Schrödinger wave equation for electronic systems. This methodology relies on two recent developments pioneered by the authors: 1) the development of a Cardinal Sine basis for electronic structure calculations; and 2) the development of a highly efficient and compact representation of multidimensional functions using the Canonical tensor rank representation developed by Belykin et. al. which we have adapted to electronic structure problems. We then show several relevant examples of the utility and accuracy of this methodology, scaling with system size, and relevant convergence issues of the methodology. Method for the Direct Solve of the Many-Body Schrödinger Wave Equation.
Simulation of non-equilibrium many body electrons in RTD
Directory of Open Access Journals (Sweden)
A. H. Rezvani
2001-06-01
Full Text Available We inspected the exact solution of double barrier quantum well. The choice of proper boundary conditions has been taken into account. We eveluated the mechanism of resonant in this device. The density correlation matrix was calculated by using the exact solution of the time-dependent generalized nonlinear Schrodinger equation in the presence of electron-electron interaction. The result shows that there is no correlation dependence among the electrons at the equilibrium between contact regions. After biasing, we have calculated the density correlation matrix in the transient and steady state. The results of our calculations show the oscillatory plasmon current in the state of transient, while in the steaby state the correlation among the phase of electrons observed to be oscillatory in the whole region of the device.
Introduction to integrable many-body systems III
International Nuclear Information System (INIS)
Bajnok, Z.; Samaj, L.
2011-01-01
This is the third part of a three-volume introductory course about integrable systems of interacting bodies. The emphasis is put onto the method of Thermodynamic Bethe Ansatz. Two kinds of integrable models are studied. Systems of itinerant electrons, forming a part of Condensed Matter Physics, involve the Hubbard lattice model of electrons with short-ranged one-site interactions (Sect. 20) and the s-d exchange Kondo model (Sect. 21), describing the scattering of conduction electrons on a spin-s impurity. Methods and basic concepts used in Quantum Field Theory are explained on the integrable (1 + 1)-dimensional sine-Gordon model. We start with the classical description of the model in Sect. 22, analyze its finite energy field configurations (soliton, anti-soliton and breathers) and show its classical integrability. The model is quantized by using two schemes: the conformal (Sect. 23) and Lagrangian (Sect. 24) quantizations. The scattering matrix of the sine-Gordon theory is derived at the full quantum level in the bootstrap scheme and is compared to its classical limit in Sect. 25. The parameters of the scattering matrix are related to those of the Lagrangian by calculating the ground-state energy in an applied magnetic field in two ways: Conformal perturbation theory and Thermodynamic Bethe Ansatz (Sect. 26). The relation of the sine-Gordon theory to the XXZ Heisenberg model, which provides a complete solution of the sine-Gordon model in a finite volume, is pointed out in Sect. 27. The obtained results are applied in Sect. 28. to the derivation of the exact thermodynamics for the (symmetric) two-component Coulomb gas; this is the first classical two-dimensional fluid with exactly solvable thermodynamics (Authors)
The use of many-body expansions and geometry optimizations in fragment-based methods.
Fedorov, Dmitri G; Asada, Naoya; Nakanishi, Isao; Kitaura, Kazuo
2014-09-16
Conspectus Chemists routinely work with complex molecular systems: solutions, biochemical molecules, and amorphous and composite materials provide some typical examples. The questions one often asks are what are the driving forces for a chemical phenomenon? How reasonable are our views of chemical systems in terms of subunits, such as functional groups and individual molecules? How can one quantify the difference in physicochemical properties of functional units found in a different chemical environment? Are various effects on functional units in molecular systems additive? Can they be represented by pairwise potentials? Are there effects that cannot be represented in a simple picture of pairwise interactions? How can we obtain quantitative values for these effects? Many of these questions can be formulated in the language of many-body effects. They quantify the properties of subunits (fragments), referred to as one-body properties, pairwise interactions (two-body properties), couplings of two-body interactions described by three-body properties, and so on. By introducing the notion of fragments in the framework of quantum chemistry, one obtains two immense benefits: (a) chemists can finally relate to quantum chemistry, which now speaks their language, by discussing chemically interesting subunits and their interactions and (b) calculations become much faster due to a reduced computational scaling. For instance, the somewhat academic sounding question of the importance of three-body effects in water clusters is actually another way of asking how two hydrogen bonds affect each other, when they involve three water molecules. One aspect of this is the many-body charge transfer (CT), because the charge transfers in the two hydrogen bonds are coupled to each other (not independent). In this work, we provide a generalized view on the use of many-body expansions in fragment-based methods, focusing on the general aspects of the property expansion and a contraction of a
Theoretical approaches to many-body perturbation theory and the challenges
International Nuclear Information System (INIS)
Barrett, Bruce R
2005-01-01
A brief review of the history of many-body perturbation theory (MBPT) and its applications in nuclear physics is given. Problems regarding its application to nuclear-structure calculations are discussed and analysed. It is concluded that the usefulness of nuclear MBPT in terms of an expansion in the nuclear reaction matrix G for the calculation of effective interactions in shell-model investigations is severely challenged and restricted by the problems and uncertainties connected with this approach. New methods based on unitary transformation approaches have proven to be more accurate and reliable, particularly for light nuclei
The brachistochrone problem in open quantum systems
International Nuclear Information System (INIS)
Rotter, Ingrid
2007-01-01
Recently, the quantum brachistochrone problem has been discussed in the literature by using non-Hermitian Hamilton operators of different types. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al for the transmission through microwave cavities of different shapes are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can not be described in the framework of the standard quantum mechanics with the Hermitian Hamilton operator and consideration of S matrix poles
Functional integral representation of the nuclear many-body grand partition function
International Nuclear Information System (INIS)
Kerman, A.K.; Troudet, T.
1984-01-01
A local functional integral formulation of the nuclear many-body problem is proposed which is a generalization of the method previously developed. Its most interesting feature is that it allows an expansion of the many-body evolution operator around any arbitrary mean-field which takes into account the pairing correlations between the nucleons. This is explicitly illustrated for the nuclear many-body grand partition function for which special attention is paid to the static temperature-dependent Hartree-Fock-Bogolyubov (H.F.B.) approximation. Indeed, the temperature-dependent H.F.B. configuration appears to be the optimal choice from a variational point of view among all the possible independent quasi-particle motion approximations. An analytic approximation of the energy level density rho (E,A) is given using explicitly the arbitrariness in the choice of the mean-field and a possible numerical application is proposed. Finally, a new compact formulation of our functional integral that might be useful for future Monte Carlo calculations is proposed
Sous, John; Grant, Edward
2018-03-01
We argue that the quenched ultracold plasma presents an experimental platform for studying the quantum many-body physics of disordered systems in the long-time and finite energy-density limits. We consider an experiment that quenches a plasma of nitric oxide to an ultracold system of Rydberg molecules, ions, and electrons that exhibits a long-lived state of arrested relaxation. The qualitative features of this state fail to conform with classical models. Here, we develop a microscopic quantum description for the arrested phase based on an effective many-body spin Hamiltonian that includes both dipole-dipole and van der Waals interactions. This effective model appears to offer a way to envision the essential quantum disordered nonequilibrium physics of this system.
Operator approximant problems arising from quantum theory
Maher, Philip J
2017-01-01
This book offers an account of a number of aspects of operator theory, mainly developed since the 1980s, whose problems have their roots in quantum theory. The research presented is in non-commutative operator approximation theory or, to use Halmos' terminology, in operator approximants. Focusing on the concept of approximants, this self-contained book is suitable for graduate courses.
Exploring one-particle orbitals in large many-body localized systems
Villalonga, Benjamin; Yu, Xiongjie; Luitz, David J.; Clark, Bryan K.
2018-03-01
Strong disorder in interacting quantum systems can give rise to the phenomenon of many-body localization (MBL), which defies thermalization due to the formation of an extensive number of quasilocal integrals of motion. The one-particle operator content of these integrals of motion is related to the one-particle orbitals (OPOs) of the one-particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015), 10.1103/PhysRevLett.115.046603; Ann. Phys. 529, 1600356 (2017), 10.1002/andp.201600356]. We study the properties of the OPOs of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS, a matrix product state method to target highly excited many-body eigenstates introduced previously [Phys. Rev. Lett. 118, 017201 (2017), 10.1103/PhysRevLett.118.017201], we are able to obtain accurate results for large systems of sizes up to L =64 . We find that the OPOs drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the OPOs decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find that the probability distribution of the strength of the large-range coupling constants of the number operators generated by the OPOs approach a log-uniform distribution at strong disorder.
Quantum game application to spectrum scarcity problems
Zabaleta, O. G.; Barrangú, J. P.; Arizmendi, C. M.
2017-01-01
Recent spectrum-sharing research has produced a strategy to address spectrum scarcity problems. This novel idea, named cognitive radio, considers that secondary users can opportunistically exploit spectrum holes left temporarily unused by primary users. This presents a competitive scenario among cognitive users, making it suitable for game theory treatment. In this work, we show that the spectrum-sharing benefits of cognitive radio can be increased by designing a medium access control based on quantum game theory. In this context, we propose a model to manage spectrum fairly and effectively, based on a multiple-users multiple-choice quantum minority game. By taking advantage of quantum entanglement and quantum interference, it is possible to reduce the probability of collision problems commonly associated with classic algorithms. Collision avoidance is an essential property for classic and quantum communications systems. In our model, two different scenarios are considered, to meet the requirements of different user strategies. The first considers sensor networks where the rational use of energy is a cornerstone; the second focuses on installations where the quality of service of the entire network is a priority.
Energy Technology Data Exchange (ETDEWEB)
Padmanabhan, Pramod [Fields, Gravity & Strings, CTPU, Institute for Basic Science,Daejeon 34037 (Korea, Republic of); Rey, Soo-Jong [Fields, Gravity & Strings, CTPU, Institute for Basic Science,Daejeon 34037 (Korea, Republic of); School of Physics and Astronomy & Center for Theoretical Physics, Seoul National University,Seoul 06544 (Korea, Republic of); Department of Basic Sciences, University of Science and Technology, Daejeon 34113 (Korea, Republic of); Teixeira, Daniel; Trancanelli, Diego [Institute of Physics, University of São Paulo, 05314-970 São Paulo (Brazil)
2017-05-25
Partial symmetries are described by generalized group structures known as symmetric inverse semigroups. We use the algebras arising from these structures to realize supersymmetry in (0+1) dimensions and to build many-body quantum systems on a chain. This construction consists in associating appropriate supercharges to chain sites, in analogy to what is done in spin chains. For simple enough choices of supercharges, we show that the resulting states have a finite non-zero Witten index, which is invariant under perturbations, therefore defining supersymmetric phases of matter protected by the index. The Hamiltonians we obtain are integrable and display a spectrum containing both product and entangled states. By introducing disorder and studying the out-of-time-ordered correlators (OTOC), we find that these systems are in the many-body localized phase and do not thermalize. Finally, we reformulate a theorem relating the growth of the second Rényi entropy to the OTOC on a thermal state in terms of partial symmetries.
Relativistic many-body theory a new field-theoretical approach
Lindgren, Ingvar
2016-01-01
This revised second edition of the author’s classic text offers readers a comprehensively updated review of relativistic atomic many-body theory, covering the many developments in the field since the publication of the original title. In particular, a new final section extends the scope to cover the evaluation of QED effects for dynamical processes. The treatment of the book is based upon quantum-field theory, and demonstrates that when the procedure is carried to all orders of perturbation theory, two-particle systems are fully compatible with the relativistically covariant Bethe-Salpeter equation. This procedure can be applied to arbitrary open-shell systems, in analogy with the standard many-body theory, and it is also applicable to systems with more than two particles. Presently existing theoretical procedures for treating atomic systems are, in several cases, insufficient to explain the accurate experimental data recently obtained, particularly for highly charged ions. The main text is divided into...
Many-body localization transition: Schmidt gap, entanglement length, and scaling
Gray, Johnnie; Bose, Sougato; Bayat, Abolfazl
2018-05-01
Many-body localization has become an important phenomenon for illuminating a potential rift between nonequilibrium quantum systems and statistical mechanics. However, the nature of the transition between ergodic and localized phases in models displaying many-body localization is not yet well understood. Assuming that this is a continuous transition, analytic results show that the length scale should diverge with a critical exponent ν ≥2 in one-dimensional systems. Interestingly, this is in stark contrast with all exact numerical studies which find ν ˜1 . We introduce the Schmidt gap, new in this context, which scales near the transition with an exponent ν >2 compatible with the analytical bound. We attribute this to an insensitivity to certain finite-size fluctuations, which remain significant in other quantities at the sizes accessible to exact numerical methods. Additionally, we find that a physical manifestation of the diverging length scale is apparent in the entanglement length computed using the logarithmic negativity between disjoint blocks.
Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom
International Nuclear Information System (INIS)
Dorfner, Florian Guenter
2017-01-01
dimension also during time evolution. For the polaron problem on an infinite chain Krylov-space time evolution in a limited functional space has been shown to be very efficient. We adapt this algorithm to periodic boundary conditions and show that it is the most efficient method compared to standard Krylov space time evolution and the time-evolving block decimation method. We also study the properties of the local reduced density matrix as a function of model parameters and under non-equilibrium conditions in three different models: the Bose-Bose resonance model, the Holstein model and the Hubbard-Holstein model. It was shown for fermionic and spin models that the single-site von Neumann entropy is an indicator for phase transitions. In the Bose-Bose resonance model we find that both, the local von Neumann entropy and the eigenstates of the local reduced density matrix show features in the vicinity of a phase boundary. Also, we find that the eigenstates of the local reduced density matrix depend on time in quantum quench dynamics. Further, we study the relaxation dynamics of a single electron coupled to Holstein phonons in all parameter regimes. In the adiabatic case a net energy transfer from electron to phonons happens and we provide an analytic formula for the relaxation time in the weak-coupling adiabatic regime. Another main topic in this thesis is thermalization in closed quantum many-body systems. Our first example is the temporal decay of Neel order in the one-dimensional Fermi-Hubbard model. We find evidence that the relaxation dynamics of spin-related quantities are, in the long-time regime, controlled by spin excitations. Further, we study the thermalization of the double occupancy in the framework of the eigenstate thermalization hypothesis and find that it does not thermalize due to integrability of the model. As a second example, we consider many-body localization in a one-dimensional system of spinless fermions with attractive interactions. It is known for
Numerical methods for strongly correlated many-body systems with bosonic degrees of freedom
Energy Technology Data Exchange (ETDEWEB)
Dorfner, Florian Guenter
2017-02-23
dimension also during time evolution. For the polaron problem on an infinite chain Krylov-space time evolution in a limited functional space has been shown to be very efficient. We adapt this algorithm to periodic boundary conditions and show that it is the most efficient method compared to standard Krylov space time evolution and the time-evolving block decimation method. We also study the properties of the local reduced density matrix as a function of model parameters and under non-equilibrium conditions in three different models: the Bose-Bose resonance model, the Holstein model and the Hubbard-Holstein model. It was shown for fermionic and spin models that the single-site von Neumann entropy is an indicator for phase transitions. In the Bose-Bose resonance model we find that both, the local von Neumann entropy and the eigenstates of the local reduced density matrix show features in the vicinity of a phase boundary. Also, we find that the eigenstates of the local reduced density matrix depend on time in quantum quench dynamics. Further, we study the relaxation dynamics of a single electron coupled to Holstein phonons in all parameter regimes. In the adiabatic case a net energy transfer from electron to phonons happens and we provide an analytic formula for the relaxation time in the weak-coupling adiabatic regime. Another main topic in this thesis is thermalization in closed quantum many-body systems. Our first example is the temporal decay of Neel order in the one-dimensional Fermi-Hubbard model. We find evidence that the relaxation dynamics of spin-related quantities are, in the long-time regime, controlled by spin excitations. Further, we study the thermalization of the double occupancy in the framework of the eigenstate thermalization hypothesis and find that it does not thermalize due to integrability of the model. As a second example, we consider many-body localization in a one-dimensional system of spinless fermions with attractive interactions. It is known for
Density-density functionals and effective potentials in many-body electronic structure calculations
International Nuclear Information System (INIS)
Reboredo, Fernando A.; Kent, Paul R.
2008-01-01
We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.
Many-body dynamics of driven-dissipative Rydberg cavity polaritons
Pistorius, Tim; Fan, Jingtao; Weimer, Hendrik
2017-04-01
The usage of photons as long-range information carriers has greatly increased the interest in systems with nonlinear optical properties in recent years. The nonlinearity is easily achievable in Rydberg mediums through the strong van der Waals interaction which makes them one of the best candidates for such a system. Here, we propose a way to analyze the steady state solutions of a Rydberg medium in a cavity through the combination of the variational principle for open quantum systems and the P-distribution of the density matrix. To get a better understanding of the many-body-dynamics a transformation into the polariton picture is performed and investigated. Volkswagen Foundation, Deutsche Forschungsgemeinschaft.
General variational many-body theory with complete self-consistency for trapped bosonic systems
International Nuclear Information System (INIS)
Streltsov, Alexej I.; Alon, Ofir E.; Cederbaum, Lorenz S.
2006-01-01
In this work we develop a complete variational many-body theory for a system of N trapped bosons interacting via a general two-body potential. The many-body solution of this system is expanded over orthogonal many-body basis functions (configurations). In this theory both the many-body basis functions and the respective expansion coefficients are treated as variational parameters. The optimal variational parameters are obtained self-consistently by solving a coupled system of noneigenvalue--generally integro-differential--equations to get the one-particle functions and by diagonalizing the secular matrix problem to find the expansion coefficients. We call this theory multiconfigurational Hartree theory for bosons or MCHB(M), where M specifies explicitly the number of one-particle functions used to construct the configurations. General rules for evaluating the matrix elements of one- and two-particle operators are derived and applied to construct the secular Hamiltonian matrix. We discuss properties of the derived equations. We show that in the limiting cases of one configuration the theory boils down to the well-known Gross-Pitaevskii and the recently developed multi-orbital mean fields. The invariance of the complete solution with respect to unitary transformations of the one-particle functions is utilized to find the solution with the minimal number of contributing configurations. In the second part of our work we implement and apply the developed theory. It is demonstrated that for any practical computation where the configurational space is restricted, the description of trapped bosonic systems strongly depends on the choice of the many-body basis set used, i.e., self-consistency is of great relevance. As illustrative examples we consider bosonic systems trapped in one- and two-dimensional symmetric and asymmetric double well potentials. We demonstrate that self-consistency has great impact on the predicted physical properties of the ground and excited states
Gritsev, Vladimir; Demler, Eugene; Lukin, Mikhail; Polkovnikov, Anatoli
2007-11-16
We study the problem of rapid change of the interaction parameter (quench) in a many-body low-dimensional system. It is shown that, measuring the correlation functions after the quench, the information about a spectrum of collective excitations in a system can be obtained. This observation is supported by analysis of several integrable models and we argue that it is valid for nonintegrable models as well. Our conclusions are supplemented by performing exact numerical simulations on finite systems. We propose that measuring the power spectrum in a dynamically split 1D Bose-Einsten condensate into two coupled condensates can be used as an experimental test of our predictions.
Many-Body Theory of Pyrochlore Iridates and Related Materials
Wang, Runzhi
In this thesis we focus on two problems. First we propose a numerical method for generating optimized Wannier functions with desired properties. Second we perform the state of the art density functional plus dynamical mean-field calculations in pyrochlore iridates, to investigate the physics induced by the cooperation of spin-orbit coupling and electron correlation. We begin with the introduction for maximally localized Wannier functions and other related extensions. Then we describe the current research in the field of spin-orbit coupling and its interplay with correlation effects, followed by a brief introduction of the `hot' materials of iridates. Before the end of the introduction, we discuss the numerical methods employed in our work, including the density functional theory; dynamical mean-field theory and its combination with the exact diagonalization impurity solver. Then we propose our approach for constructing an optimized set of Wannier functions, which is a generalization of the functionality of the classic maximal localization method put forward by Marzari and Vanderbilt. Our work is motivated by the requirement of the effective description of the local subspace of the Hamiltonian by the beyond density functional theory methods. In extensions of density functional theory such as dynamical mean-field theory, one may want highly accurate description of particular local orbitals, including correct centers and symmetries; while the basis for the remaining degrees of freedom is unimportant. Therefore, we develop the selectively localized Wannier function approach which allows for a greater localization in the selected subset of Wannier functions and at the same time allows us to fix the centers and ensure the point symmetries. Applications in real materials are presented to demonstrate the power of our approach. Next we move to the investigation of pyrochlore iridates, focussing on the metal-insulator transition and material dependence in these compounds. We
Problems in quantum mechanics with solutions
d'Emilio, Emilio
2017-01-01
This second edition of an extremely well-received book presents more than 250 nonrelativistic quantum mechanics problems of varying difficulty with the aim of providing students didactic material of proven value, allowing them to test their comprehension and mastery of each subject. The coverage is extremely broad, from themes related to the crisis of classical physics through achievements within the framework of modern atomic physics to lively debated, intriguing aspects relating to, for example, the EPR paradox, the Aharonov-Bohm effect, and quantum teleportation. Compared with the first edition, a variety of improvements have been made and additional topics of interest included, especially focusing on elementary potential scattering. The problems themselves range from standard and straightforward ones to those that are complex but can be considered essential because they address questions of outstanding importance or aspects typically overlooked in primers. The book offers students both an excellent tool f...
Destructive quantum interference in spin tunneling problems
von Delft, Jan; Henley, Christopher L.
1992-01-01
In some spin tunneling problems, there are several different but symmetry-related tunneling paths that connect the same initial and final configurations. The topological phase factors of the corresponding tunneling amplitudes can lead to destructive interference between the different paths, so that the total tunneling amplitude is zero. In the study of tunneling between different ground state configurations of the Kagom\\'{e}-lattice quantum Heisenberg antiferromagnet, this occurs when the spi...
Some basic problems of quantum electrodynamics
International Nuclear Information System (INIS)
Steinmann, O.
1981-01-01
QED (= quantum electrodynamics) is often said to be one of the most successful theories, if not 'the' most successful one, that we possess in physics. That it is a theory is, however, not yet established beyond possible doubt. In this talk I report on the present state of this problem. The question is whether the computational rules of QED, which stand up so well to all practical tests, can be founded logically in a consistent, exactly formulizable, theory. (orig./HSI)
Solving satisfiability problems by the ground-state quantum computer
International Nuclear Information System (INIS)
Mao Wenjin
2005-01-01
A quantum algorithm is proposed to solve the satisfiability (SAT) problems by the ground-state quantum computer. The scale of the energy gap of the ground-state quantum computer is analyzed for the 3-bit exact cover problem. The time cost of this algorithm on the general SAT problems is discussed
Long-distance entanglement in many-body atomic and optical systems
Energy Technology Data Exchange (ETDEWEB)
Giampaolo, Salvatore M; Illuminati, Fabrizio [Dipartimento di Matematica e Informatica, Universita degli Studi di Salerno, Via Ponte don Melillo, I-84084 Fisciano, SA (Italy)], E-mail: illuminati@sa.infn.it
2010-02-15
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
Long-distance entanglement in many-body atomic and optical systems
International Nuclear Information System (INIS)
Giampaolo, Salvatore M; Illuminati, Fabrizio
2010-01-01
We discuss the phenomenon of long-distance entanglement (LDE) in the ground state of quantum spin models, its use in high-fidelity and robust quantum communication, and its realization in many-body systems of ultracold atoms in optical lattices and in arrays of coupled optical cavities. We investigate XX quantum spin models on one-dimensional lattices with open ends and different patterns of site-dependent interaction couplings, singling out two general settings: patterns that allow for perfect LDE in the ground state of the system, namely such that the end-to-end entanglement remains finite in the thermodynamic limit, and patterns of quasi-long-distance entanglement (QLDE) in the ground state of the system, namely such that the end-to-end entanglement vanishes with a very slow power-law decay as the length of the spin chain is increased. We discuss physical realizations of these models in ensembles of ultracold bosonic atoms loaded in optical lattices. We show how, using either suitably engineered super-lattice structures or exploiting the presence of edge impurities in lattices with single periodicity, it is possible to realize models endowed with nonvanishing LDE or QLDE. We then study how to realize models that optimize the robustness of QLDE at finite temperature and in the presence of imperfections using suitably engineered arrays of coupled optical cavities. For both cases the numerical estimates of the end-to-end entanglement in the actual physical systems are thoroughly compared with the analytical results obtained for the spin model systems. We finally introduce LDE-based schemes of long-distance quantum teleportation in linear arrays of coupled cavities, and show that they allow for high-fidelity and high success rates even at moderately high temperatures.
Problems and solutions in quantum chemistry and physics
Johnson, Charles S
1988-01-01
Unusually varied problems, with detailed solutions, cover quantum mechanics, wave mechanics, angular momentum, molecular spectroscopy, scattering theory, more. 280 problems, plus 139 supplementary exercises.
Many-body theory of electrical, thermal and optical response of molecular heterojunctions
Bergfield, Justin Phillip
In this work, we develop a many-body theory of electronic transport through single molecule junctions based on nonequilibrium Green's functions (NEGFs). The central quantity of this theory is the Coulomb self-energy matrix of the junction SigmaC. SigmaC is evaluated exactly in the sequential-tunneling limit, and the correction due to finite lead-molecule tunneling is evaluated using a conserving approximation based on diagrammatic perturbation theory on the Keldysh contour. In this way, tunneling processes are included to infinite order, meaning that any approximation utilized is a truncation in the physical processes considered rather than in the order of those processes. Our theory reproduces the key features of both the Coulomb blockade and coherent transport regimes simultaneously in a single unified theory. Nonperturbative effects of intramolecular correlations are included, which are necessary to accurately describe the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap, essential for a quantitative theory of transport. This work covers four major topics related to transport in single-molecule junctions. First, we use our many-body theory to calculate the nonlinear electrical response of the archetypal Au-1,4-benzenedithiol-Au junction and find irregularly shaped 'molecular diamonds' which have been experimentally observed in some larger molecules but which are inaccessible to existing theoretical approaches. Next, we extend our theory to include heat transport and develop an exact expression for the heat current in an interacting nanostructure. Using this result, we discover that quantum coherence can strongly enhance the thermoelectric response of a device, a result with a number of technological applications. We then develop the formalism to include multi-orbital lead-molecule contacts and multi-channel leads, both of which strongly affect the observable transport. Lastly, we include a dynamic screening correction to
Nonlinear many-body reaction theories from nuclear mean field approximations
International Nuclear Information System (INIS)
Griffin, J.J.
1983-01-01
Several methods of utilizing nonlinear mean field propagation in time to describe nuclear reaction have been studied. The property of physical asymptoticity is analyzed in this paper, which guarantees that the prediction by a reaction theory for the physical measurement of internal fragment properties shall not depend upon the precise location of the measuring apparatus. The physical asymptoticity is guaranteed in the Schroedinger collision theory of a scuttering system with translationally invariant interaction by the constancy of the S-matrix elements and by the translational invariance of the internal motion for well-separated fragments. Both conditions are necessary for the physical asymptoticity. The channel asymptotic single-determinantal propagation can be described by the Dirac-TDHF (time dependent Hartree-Fock) time evolution. A new asymptotic Hartree-Fock stationary phase (AHFSP) description together with the S-matrix time-dependent Hartree-Fock (TD-S-HF) theory constitute the second example of a physically asymptotic nonlinear many-body reaction theory. A review of nonlinear mean field many-body reaction theories shows that initial value TDHF is non-asymptotic. The TD-S-HF theory is asymptotic by the construction. The gauge invariant periodic quantized solution of the exact Schroedinger problem has been considered to test whether it includes all of the exact eigenfunctions as it ought to. It did, but included as well an infinity of all spurions solutions. (Kato, T.)
Experimental realization of the quantum box problem
International Nuclear Information System (INIS)
Resch, K.J.; Lundeen, J.S.; Steinberg, A.M.
2004-01-01
The three-box problem is a gedankenexperiment designed to elucidate some interesting features of quantum measurement and locality. A particle is prepared in a particular superposition of three boxes, and later found in a different (but nonorthogonal) superposition. It was predicted that appropriate 'weak' measurements of particle position in the interval between preparation and post-selection would find the particle in two different places, each with certainty. We verify these predictions in an optical experiment and address the issues of locality and of negative probability
Computational approach to large quantum dynamical problems
International Nuclear Information System (INIS)
Friesner, R.A.; Brunet, J.P.; Wyatt, R.E.; Leforestier, C.; Binkley, S.
1987-01-01
The organizational structure is described for a new program that permits computations on a variety of quantum mechanical problems in chemical dynamics and spectroscopy. Particular attention is devoted to developing and using algorithms that exploit the capabilities of current vector supercomputers. A key component in this procedure is the recursive transformation of the large sparse Hamiltonian matrix into a much smaller tridiagonal matrix. An application to time-dependent laser molecule energy transfer is presented. Rate of energy deposition in the multimode molecule for systematic variations in the molecular intermode coupling parameters is emphasized
Many-Body Energy Decomposition with Basis Set Superposition Error Corrections.
Mayer, István; Bakó, Imre
2017-05-09
The problem of performing many-body decompositions of energy is considered in the case when BSSE corrections are also performed. It is discussed that the two different schemes that have been proposed go back to the two different interpretations of the original Boys-Bernardi counterpoise correction scheme. It is argued that from the physical point of view the "hierarchical" scheme of Valiron and Mayer should be preferred and not the scheme recently discussed by Ouyang and Bettens, because it permits the energy of the individual monomers and all the two-body, three-body, etc. energy components to be free of unphysical dependence on the arrangement (basis functions) of other subsystems in the cluster.
Energy Technology Data Exchange (ETDEWEB)
Zakharov, A.Yu., E-mail: Anatoly.Zakharov@novsu.ru; Zakharov, M.A., E-mail: ma_zakharov@list.ru
2016-01-28
The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems. - Highlights: • A new form of equation of motion of classical many-body system is proposed. • Interactions retardation as one of the mechanisms of many-body system irreversibility. • Irreversibility and determinism without probabilities. • The possible way to microscopic foundation of thermodynamics.
Comment on "Many-body localization in Ising models with random long-range interactions"
Maksymov, Andrii O.; Rahman, Noah; Kapit, Eliot; Burin, Alexander L.
2017-11-01
This Comment is dedicated to the investigation of many-body localization in a quantum Ising model with long-range power-law interactions r-α, relevant for a variety of systems ranging from electrons in Anderson insulators to spin excitations in chains of cold atoms. It has earlier been argued [arXiv:cond-mat/0611387 (2005); Phys. Rev. B 91, 094202 (2015), 10.1103/PhysRevB.91.094202] that this model obeys the dimensional constraint suggesting the delocalization of all finite-temperature states in the thermodynamic limit for α ≤2 d in a d -dimensional system. This expectation conflicts with the recent numerical studies of the specific interacting spin model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625]. To resolve this controversy we reexamine the model of Li et al. [Phys. Rev. A 94, 063625 (2016), 10.1103/PhysRevA.94.063625] and demonstrate that the infinite-temperature states there obey the dimensional constraint. The earlier developed scaling theory for the critical system size required for delocalization is extended to small exponents 0 ≤α ≤d . The disagreements between the two works are explained by the nonstandard selection of investigated states in the ordered phase in the work of Li et al. [Phys. Rev. A 94, 063625 (2016)type="doi" specific-use="suppress-display">10.1103/PhysRevA.94.063625].
Many-body dispersion effects in the binding of adsorbates on metal surfaces
Energy Technology Data Exchange (ETDEWEB)
Maurer, Reinhard J. [Department of Chemistry, Yale University, New Haven, Connecticut 06520 (United States); Ruiz, Victor G.; Tkatchenko, Alexandre [Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, D-14195 Berlin (Germany)
2015-09-14
A correct description of electronic exchange and correlation effects for molecules in contact with extended (metal) surfaces is a challenging task for first-principles modeling. In this work, we demonstrate the importance of collective van der Waals dispersion effects beyond the pairwise approximation for organic–inorganic systems on the example of atoms, molecules, and nanostructures adsorbed on metals. We use the recently developed many-body dispersion (MBD) approach in the context of density-functional theory [Tkatchenko et al., Phys. Rev. Lett. 108, 236402 (2012) and Ambrosetti et al., J. Chem. Phys. 140, 18A508 (2014)] and assess its ability to correctly describe the binding of adsorbates on metal surfaces. We briefly review the MBD method and highlight its similarities to quantum-chemical approaches to electron correlation in a quasiparticle picture. In particular, we study the binding properties of xenon, 3,4,9,10-perylene-tetracarboxylic acid, and a graphene sheet adsorbed on the Ag(111) surface. Accounting for MBD effects, we are able to describe changes in the anisotropic polarizability tensor, improve the description of adsorbate vibrations, and correctly capture the adsorbate–surface interaction screening. Comparison to other methods and experiment reveals that inclusion of MBD effects improves adsorption energies and geometries, by reducing the overbinding typically found in pairwise additive dispersion-correction approaches.
Categorization of Quantum Mechanics Problems by Professors and Students
Lin, Shih-Yin; Singh, Chandralekha
2010-01-01
We discuss the categorization of 20 quantum mechanics problems by physics professors and undergraduate students from two honours-level quantum mechanics courses. Professors and students were asked to categorize the problems based upon similarity of solution. We also had individual discussions with professors who categorized the problems. Faculty…
Approximate motion integrals and the quantum chaos problem
International Nuclear Information System (INIS)
Bunakov, V.E.; Ivanov, I.B.
2001-01-01
One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru
Photoionization cross sections and Auger rates calculated by many-body perturbation theory
International Nuclear Information System (INIS)
Kelly, H.P.
1976-01-01
Methods for applying the many body perturbation theory to atomic calculations are discussed with particular emphasis on calculation of photoionization cross sections and Auger rates. Topics covered include: Rayleigh--Schroedinger theory; many body perturbation theory; calculations of photoionization cross sections; and Auger rates
Maximizing kinetic energy transfer in one-dimensional many-body collisions
International Nuclear Information System (INIS)
Ricardo, Bernard; Lee, Paul
2015-01-01
The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions. (paper)
Maximizing kinetic energy transfer in one-dimensional many-body collisions
Ricardo, Bernard; Lee, Paul
2015-03-01
The main problem discussed in this paper involves a simple one-dimensional two-body collision, in which the problem can be extended into a chain of one-dimensional many-body collisions. The result is quite interesting, as it provides us with a thorough mathematical understanding that will help in designing a chain system for maximum energy transfer for a range of collision types. In this paper, we will show that there is a way to improve the kinetic energy transfer between two masses, and the idea can be applied recursively. However, this method only works for a certain range of collision types, which is indicated by a range of coefficients of restitution. Although the concept of momentum, elastic and inelastic collision, as well as Newton’s laws, are taught in junior college physics, especially in Singapore schools, students in this level are not expected to be able to do this problem quantitatively, as it requires rigorous mathematics, including calculus. Nevertheless, this paper provides nice analytical steps that address some common misconceptions in students’ way of thinking about one-dimensional collisions.
Monthus, Cécile
2018-03-01
For the many-body-localized phase of random Majorana models, a general strong disorder real-space renormalization procedure known as RSRG-X (Pekker et al 2014 Phys. Rev. X 4 011052) is described to produce the whole set of excited states, via the iterative construction of the local integrals of motion (LIOMs). The RG rules are then explicitly derived for arbitrary quadratic Hamiltonians (free-fermions models) and for the Kitaev chain with local interactions involving even numbers of consecutive Majorana fermions. The emphasis is put on the advantages of the Majorana language over the usual quantum spin language to formulate unified RSRG-X rules.
An implementation problem for boson fields and quantum Girsanov transform
Energy Technology Data Exchange (ETDEWEB)
Ji, Un Cig, E-mail: uncigji@chungbuk.ac.kr [Department of Mathematics, Research Institute of Mathematical Finance, Chungbuk National University, Cheongju 361-763 (Korea, Republic of); Obata, Nobuaki, E-mail: obata@math.is.tohoku.ac.jp [Graduate School of Information Sciences, Tohoku University, Sendai 980-8579 (Japan)
2016-08-15
We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.
An implementation problem for boson fields and quantum Girsanov transform
International Nuclear Information System (INIS)
Ji, Un Cig; Obata, Nobuaki
2016-01-01
We study an implementation problem for quadratic functions of annihilation and creation operators on a boson field in terms of quantum white noise calculus. The implementation problem is shown to be equivalent to a linear differential equation for white noise operators containing quantum white noise derivatives. The solution is explicitly obtained and turns out to form a class of white noise operators including generalized Fourier–Gauss and Fourier–Mehler transforms, Bogoliubov transform, and a quantum extension of the Girsanov transform.
PREFACE: Many-body correlations from dilute to dense nuclear systems
Otsuka, Takaharu; Urban, Michael; Yamada, Taiichi
2011-09-01
The International EFES-IN2P3 conference on "Many body correlations from dilute to dense nuclear systems" was held at the Institut Henri Poincaré (IHP), Paris, France, from 15-18 February 2011, on the occasion of the retirement of our colleague Peter Schuck. Correlations play a decisive role in various many-body systems such as nuclear systems, condensed matter and quantum gases. Important examples include: pairing correlations (Cooper pairs) which give rise to nuclear superfluidity (analogous to superconductivity in condensed matter); particle-hole (RPA) correlations in the description of the ground state beyond mean-field theory; clusters; and α-particle correlations in certain nuclei. Also, the nucleons themselves can be viewed as clusters of three quarks. During the past few years, researchers have started to study how the character of these correlations changes with the variation of the density. For instance, the Cooper pairs in dense matter can transform into a Bose-Einstein condensate (BEC) of true bound states at low density (this is the BCS-BEC crossover studied in ultracold Fermi gases). Similar effects play a role in neutron matter at low density, e.g., in the "neutron skin" of exotic nuclei. The α-cluster correlation becomes particularly important at lower density, such as in the excited states of some nuclei (e.g., the α-condensate-like structure in the Hoyle state of 12C) or in the formation of compact stars. In addition to nuclear physics, topics from astrophysics (neutron stars), condensed matter, and quantum gases were discussed in 48 talks and 19 posters, allowing the almost 90 participants from different communities to exchange their ideas, experiences and methods. The conference dinner took place at the Musée d'Orsay, and all the participants enjoyed the very pleasant atmosphere. One session of the conference was dedicated to the celebration of Peter's retirement. We would like to take this opportunity to wish Peter all the best and we hope
Inverse problems in classical and quantum physics
International Nuclear Information System (INIS)
Almasy, A.A.
2007-01-01
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
Inverse problems in classical and quantum physics
Energy Technology Data Exchange (ETDEWEB)
Almasy, A.A.
2007-06-29
The subject of this thesis is in the area of Applied Mathematics known as Inverse Problems. Inverse problems are those where a set of measured data is analysed in order to get as much information as possible on a model which is assumed to represent a system in the real world. We study two inverse problems in the fields of classical and quantum physics: QCD condensates from tau-decay data and the inverse conductivity problem. Despite a concentrated effort by physicists extending over many years, an understanding of QCD from first principles continues to be elusive. Fortunately, data continues to appear which provide a rather direct probe of the inner workings of the strong interactions. We use a functional method which allows us to extract within rather general assumptions phenomenological parameters of QCD (the condensates) from a comparison of the time-like experimental data with asymptotic space-like results from theory. The price to be paid for the generality of assumptions is relatively large errors in the values of the extracted parameters. Although we do not claim that our method is superior to other approaches, we hope that our results lend additional confidence to the numerical results obtained with the help of methods based on QCD sum rules. EIT is a technology developed to image the electrical conductivity distribution of a conductive medium. The technique works by performing simultaneous measurements of direct or alternating electric currents and voltages on the boundary of an object. These are the data used by an image reconstruction algorithm to determine the electrical conductivity distribution within the object. In this thesis, two approaches of EIT image reconstruction are proposed. The first is based on reformulating the inverse problem in terms of integral equations. This method uses only a single set of measurements for the reconstruction. The second approach is an algorithm based on linearisation which uses more then one set of measurements. A
Students' Epistemological Framing in Quantum Mechanics Problem Solving
Modir, Bahar; Thompson, John D.; Sayre, Eleanor C.
2017-01-01
Students' difficulties in quantum mechanics may be the result of unproductive framing and not a fundamental inability to solve the problems or misconceptions about physics content. We observed groups of students solving quantum mechanics problems in an upper-division physics course. Using the lens of epistemological framing, we investigated four…
Ballistic near-field heat transport in dense many-body systems
Latella, Ivan; Biehs, Svend-Age; Messina, Riccardo; Rodriguez, Alejandro W.; Ben-Abdallah, Philippe
2018-01-01
Radiative heat transport mediated by near-field interactions is known to be superdiffusive in dilute, many-body systems. Here we use a generalized Landauer theory of radiative heat transfer in many-body planar systems to demonstrate a nonmonotonic transition from superdiffusive to ballistic transport in dense systems. We show that such a transition is associated to a change of the polarization of dominant modes. Our findings are complemented by a quantitative study of the relaxation dynamics of the system in the different regimes of heat transport. This result could have important consequences on thermal management at nanoscale of many-body systems.
Applications of the random-state approach to quantum many-body dynamics
Zhao, Peiliang
2017-01-01
The work described in the thesis focuses on computer simulation algorithms to compute the electronic properties of exotic materials such as graphene. The effects of disorder on the electronic properties of these materials are studied and the fingerprints of the different kinds of disorder are
Topological interactions of Nambu-Goldstone bosons in quantum many-body systems
Czech Academy of Sciences Publication Activity Database
Brauner, Tomáš; Moroz, S.
2014-01-01
Roč. 90, č. 12 (2014), s. 121701 ISSN 1550-7998 Institutional support: RVO:61389005 Keywords : Chiral Perturbation-theory * hall ferromagnets * Lagrangians Subject RIV: BE - Theoretical Physics Impact factor: 4.643, year: 2014
2013-07-31
to drive stimulated Raman transitions [41, 42]. At the ion chain, the beam R1 with frequency ωL per- 4 pendicularly intersects a multi-colored beam R2...1996). [17] E. Farhi et al., Science 292, 472 (2001). [18] J. I. Cirac and P. Zoller, Nat. Phys. 8, 264 (2012). [19] K. Kim et al., Nature 465, 590
Scaling of the polarization amplitude in quantum many-body systems in one dimension
Kobayashi, Ryohei; Nakagawa, Yuya O.; Fukusumi, Yoshiki; Oshikawa, Masaki
2018-04-01
Resta proposed a definition of the electric polarization in one-dimensional systems in terms of the ground-state expectation value of the large gauge transformation operator. Vanishing of the expectation value in the thermodynamic limit implies that the system is a conductor. We study Resta's polarization amplitude (expectation value) in the S =1 /2 XXZ chain and its several generalizations, in the gapless conducting Tomonaga-Luttinger liquid phase. We obtain an analytical expression in the lowest-order perturbation theory about the free fermion point (XY chain) and an exact result for the Haldane-Shastry model with long-range interactions. We also obtain numerical results, mostly using the exact diagonalization method. We find that the amplitude exhibits a power-law scaling in the system size (chain length) and vanishes in the thermodynamic limit. On the other hand, the exponent depends on the model even when the low-energy limit is described by the Tomonaga-Luttinger liquid with the same Luttinger parameter. We find that a change in the exponent occurs when the Umklapp term(s) are eliminated, suggesting the importance of the Umklapp terms.
Spontaneous Symmetry Breaking and Nambu-Goldstone Bosons in Quantum Many-Body Systems
Czech Academy of Sciences Publication Activity Database
Brauner, Tomáš
2010-01-01
Roč. 2, č. 2 (2010), s. 609-657 ISSN 2073-8994 Institutional support: RVO:61389005 Keywords : spontaneous symmetry breaking * Nambu-Goldstone bosons * effective field theory Subject RIV: BE - Theoretical Physics
Spontaneous Symmetry Breaking and Nambu–Goldstone Bosons in Quantum Many-Body Systems
Directory of Open Access Journals (Sweden)
Tomáš Brauner
2010-04-01
Full Text Available Spontaneous symmetry breaking is a general principle that constitutes the underlying concept of a vast number of physical phenomena ranging from ferromagnetism and superconductivity in condensed matter physics to the Higgs mechanism in the standard model of elementary particles. I focus on manifestations of spontaneously broken symmetries in systems that are not Lorentz invariant, which include both nonrelativistic systems as well as relativistic systems at nonzero density, providing a self-contained review of the properties of spontaneously broken symmetries specific to such theories. Topics covered include: (i Introduction to the mathematics of spontaneous symmetry breaking and the Goldstone theorem. (ii Minimization of Higgs-type potentials for higher-dimensional representations. (iii Counting rules for Nambu–Goldstone bosons and their dispersion relations. (iv Construction of effective Lagrangians. Specific examples in both relativistic and nonrelativistic physics are worked out in detail.
The problem of time quantum mechanics versus general relativity
Anderson, Edward
2017-01-01
This book is a treatise on time and on background independence in physics. It first considers how time is conceived of in each accepted paradigm of physics: Newtonian, special relativity, quantum mechanics (QM) and general relativity (GR). Substantial differences are moreover uncovered between what is meant by time in QM and in GR. These differences jointly source the Problem of Time: Nine interlinked facets which arise upon attempting concurrent treatment of the QM and GR paradigms, as is required in particular for a background independent theory of quantum gravity. A sizeable proportion of current quantum gravity programs - e.g. geometrodynamical and loop quantum gravity approaches to quantum GR, quantum cosmology, supergravity and M-theory - are background independent in this sense. This book's foundational topic is thus furthermore of practical relevance in the ongoing development of quantum gravity programs. This book shows moreover that eight of the nine facets of the Problem of Time already occur upon ...
Solutions to selected exercise problems in quantum chemistry and spectroscopy
DEFF Research Database (Denmark)
Spanget-Larsen, Jens
2016-01-01
Suggested solutions to a number of problems from the collection "Exercise Problems in Quantum Chemistry and Spectroscopy", previously published on ResearchGate (DOI: 10.13140/RG.2.1.4024.8162).......Suggested solutions to a number of problems from the collection "Exercise Problems in Quantum Chemistry and Spectroscopy", previously published on ResearchGate (DOI: 10.13140/RG.2.1.4024.8162)....
On the basis of molecular orbitals for relativistic bound systems of many bodies
International Nuclear Information System (INIS)
Cook, A.H.
1987-09-01
The quasi-relativistic Hamiltonian for bound states of many bodies proposed in previous articles (Cook, 1986, 1987a) is shown to provide a basis for the molecular orbital scheme of constructing wavefunctions and calculating eigenenergies. (author). 5 refs
Heuristic method for determining outgoing waves in many-body wave functions
International Nuclear Information System (INIS)
Redish, E.F.; Tandy, P.C.; L'Huillier, M.
1975-12-01
A new and simple method is proposed for determining the kinds of outgoing waves present in a given many-body wave function. Whether any particular wave function contains ''hidden'' rearrangement components can be determined. 1 figure
Theory of many-body radiative heat transfer without the constraint of reciprocity
Zhu, Linxiao; Guo, Yu; Fan, Shanhui
2018-03-01
Using a self-consistent scattered field approach based on fluctuational electrodynamics, we develop compact formulas for radiative heat transfer in many-body systems without the constraint of reciprocity. The formulas allow for efficient numerical calculation for a system consisting of a large number of bodies, and are in principle exact. As a demonstration, for a nonreciprocal many-body system, we investigate persistent heat current at thermal equilibrium and directional heat transfer when the system is away from thermal equilibrium.
Many-body effects in X-ray photoemission spectroscopy and electronic properties of solids
International Nuclear Information System (INIS)
Kohiki, S.
1999-01-01
Photoemission from a solid is evidently a many-body process since the motion of each electron cannot be independent of the motions of other electrons. In this article we review the reported many-body effects in X-ray photoemission such as extra-atomic relaxation energy, charge transfer satellite and energy loss structure which are informative in relation to the characteristics of solids. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Loop corrections and other many-body effects in relativistic field theories
International Nuclear Information System (INIS)
Ainsworth, T.L.; Brown, G.E.; Prakash, M.; Weise, W.
1988-01-01
Incorporation of effective masses into negative energy states (nucleon loop corrections) gives rise to repulsive many-body forces, as has been known for some time. Rather than renormalizing away the three- and four-body terms, we introduce medium corrections into the effective σ-exchange, which roughly cancel the nucleon loop terms for densities ρ ≅ ρ nm , where ρ nm is nuclear matter density. Going to higher densities, the repulsive contributions tend to saturate whereas the attractive ones keep on growing in magnitude. The latter is achieved through use of a density-dependent effective mass for the σ-particle, m σ = m σ (ρ), such that m σ (ρ) decreases with increasing density. Such a behavior is seen e.g. in the Nambu-Jona-Lasinio model. It is argued that a smooth transition to chiral restoration implies a similar behavior. The resulting nuclear equation of state is, because of the self-consistency in the problem, immensely insensitive to changes in the mass or coupling constant of the σ-particle. (orig.)
The reality problem in quantum mechanics
International Nuclear Information System (INIS)
Flamm, D.
1988-01-01
A series of 12 lectures on quantum mechanics and its inter-pretations: The more specific part begins with chapter 8: spin and polarization measurements; the Einstein-Podolski-Rosen paradoxon; Bell's inequations; interpretations of quantum theory; the role of the observer and the wave function of the world. 40 refs., 11 figs. (qui)
Continuous-Variable Quantum Computation of Oracle Decision Problems
Adcock, Mark R. A.
Quantum information processing is appealing due its ability to solve certain problems quantitatively faster than classical information processing. Most quantum algorithms have been studied in discretely parameterized systems, but many quantum systems are continuously parameterized. The field of quantum optics in particular has sophisticated techniques for manipulating continuously parameterized quantum states of light, but the lack of a code-state formalism has hindered the study of quantum algorithms in these systems. To address this situation, a code-state formalism for the solution of oracle decision problems in continuously-parameterized quantum systems is developed. Quantum information processing is appealing due its ability to solve certain problems quantitatively faster than classical information processing. Most quantum algorithms have been studied in discretely parameterized systems, but many quantum systems are continuously parameterized. The field of quantum optics in particular has sophisticated techniques for manipulating continuously parameterized quantum states of light, but the lack of a code-state formalism has hindered the study of quantum algorithms in these systems. To address this situation, a code-state formalism for the solution of oracle decision problems in continuously-parameterized quantum systems is developed. In the infinite-dimensional case, we study continuous-variable quantum algorithms for the solution of the Deutsch--Jozsa oracle decision problem implemented within a single harmonic-oscillator. Orthogonal states are used as the computational bases, and we show that, contrary to a previous claim in the literature, this implementation of quantum information processing has limitations due to a position-momentum trade-off of the Fourier transform. We further demonstrate that orthogonal encoding bases are not unique, and using the coherent states of the harmonic oscillator as the computational bases, our formalism enables quantifying
International Nuclear Information System (INIS)
Nam, H; Stoitsov, M; Nazarewicz, W; Hagen, G; Kortelainen, M; Pei, J C; Bulgac, A; Maris, P; Vary, J P; Roche, K J; Schunck, N; Thompson, I; Wild, S M
2012-01-01
The demands of cutting-edge science are driving the need for larger and faster computing resources. With the rapidly growing scale of computing systems and the prospect of technologically disruptive architectures to meet these needs, scientists face the challenge of effectively using complex computational resources to advance scientific discovery. Multi-disciplinary collaborating networks of researchers with diverse scientific backgrounds are needed to address these complex challenges. The UNEDF SciDAC collaboration of nuclear theorists, applied mathematicians, and computer scientists is developing a comprehensive description of nuclei and their reactions that delivers maximum predictive power with quantified uncertainties. This paper describes UNEDF and identifies attributes that classify it as a successful computational collaboration. We illustrate significant milestones accomplished by UNEDF through integrative solutions using the most reliable theoretical approaches, most advanced algorithms, and leadership-class computational resources.
The many-body problem an encyclopedia of exactly solved models in one dimension
1993-01-01
This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space - such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz - can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developmen
A guide to Feynman diagrams in the many-body problem
Mattuck, Richard D
1976-01-01
Until this book, most treatments of this topic were inaccessible to nonspecialists. A superb introduction to important areas of modern physics, it covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and much more. ""A great delight to read."" - Physics Today. 1974 edition.
UNEDF: Advanced Scientific Computing Transforms the Low-Energy Nuclear Many-Body Problem
International Nuclear Information System (INIS)
Stoitsov, Mario; Nam, Hai Ah; Nazarewicz, Witold; Bulgac, Aurel; Hagen, Gaute; Kortelainen, E.M.; Pei, Junchen; Roche, K.J.; Schunck, N.; Thompson, I.; Vary, J.P.; Wild, S.
2011-01-01
The UNEDF SciDAC collaboration of nuclear theorists, applied mathematicians, and computer scientists is developing a comprehensive description of nuclei and their reactions that delivers maximum predictive power with quantified uncertainties. This paper illustrates significant milestones accomplished by UNEDF through integration of the theoretical approaches, advanced numerical algorithms, and leadership class computational resources.
Correlations in clusters and related systems. New perspectives on the many-body problem
International Nuclear Information System (INIS)
Connerade, J.P.
1996-01-01
The contents of the present volume are the proceedings of an Adriatico Research Conference, held at the International Centre for Theoretical Physics in Trieste from 26 to 29 July 1994. The theme of the conference covered many aspects of cooperative effects, beginning with giant resonances in many-electron systems, and particularly in new objects such as metallic clusters, in which collective electron dynamics are a novel feature. The relationship of these resonances with comparable features in nuclear and solid state physics was extensively discussed. Related effects, such as instabilities of valence both in clusters and in solids were explored. Clusters allow one to track the evolution of certain properties from the free atom to the solid state limits as a function of size. The giant resonances concerned not only intra-atomic excitations, but also correlated motions of all delocalized electrons within the cluster. Other systems with unusual properties, such as negative ions, in which correlations play an important role, were also considered. Finally, dynamical effects and the possible interactions between electron-electron correlations and high laser fields were envisaged
Density functional approach to the many-body problem : Key concepts and exact functionals
van Leeuwen, Robert
2003-01-01
We give an overview of the fundamental concepts of density functional theory. We give a careful discussion of the several density functionals and their differentiability properties. We show that for nondegenerate ground states we can calculate the necessary functional derivatives by means of linear
A Quantum Approach to Subset-Sum and Similar Problems
Daskin, Ammar
2017-01-01
In this paper, we study the subset-sum problem by using a quantum heuristic approach similar to the verification circuit of quantum Arthur-Merlin games. Under described certain assumptions, we show that the exact solution of the subset sum problem my be obtained in polynomial time and the exponential speed-up over the classical algorithms may be possible. We give a numerical example and discuss the complexity of the approach and its further application to the knapsack problem.
Canonical transformations in problems of quantum statistical mechanics
International Nuclear Information System (INIS)
Sankovich, D.P.
1985-01-01
The problem of general canonical transformations in quantum systems possessing a classical analog is considered. The main role plays the Weyl representation of dynamic variables of the quantum system considered. One managed to build a general diagram of canonical transformations in a quantum case and to develop a method for reducing one or another operator to the simplest canonical form. In this case the procedure, being analogous to the Poincare-Birkhof normalization based on the Lie series theory, occurs
Quantum algorithms for the ordered search problem via semidefinite programming
International Nuclear Information System (INIS)
Childs, Andrew M.; Landahl, Andrew J.; Parrilo, Pablo A.
2007-01-01
One of the most basic computational problems is the task of finding a desired item in an ordered list of N items. While the best classical algorithm for this problem uses log 2 N queries to the list, a quantum computer can solve the problem using a constant factor fewer queries. However, the precise value of this constant is unknown. By characterizing a class of quantum query algorithms for the ordered search problem in terms of a semidefinite program, we find quantum algorithms for small instances of the ordered search problem. Extending these algorithms to arbitrarily large instances using recursion, we show that there is an exact quantum ordered search algorithm using 4 log 605 N≅0.433 log 2 N queries, which improves upon the previously best known exact algorithm
Homogeneous nucleation: a problem in nonequilibrium quantum statistical mechanics
International Nuclear Information System (INIS)
1978-08-01
The master equation for cluster growth and evaporation is derived for many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory is generalized to include system and reservoir states that are not separate entities. Formulas for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulas for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure, volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud chamber and nozzle experiments, which measure water. Comparison with other theories reveals that classical theory only accidently agrees with experiment and that the Helmholtz free-energy formula used in the Lothe--Pound theory is incomplete. 27 figures, 3 tables, 149 references
Students' Conceptual Difficulties in Quantum Mechanics: Potential Well Problems
Ozcan, Ozgur; Didis, Nilufer; Tasar, Mehmet Fatih
2009-01-01
In this study, students' conceptual difficulties about some basic concepts in quantum mechanics like one-dimensional potential well problems and probability density of tunneling particles were identified. For this aim, a multiple choice instrument named Quantum Mechanics Conceptual Test has been developed by one of the researchers of this study…
Relativistic many-body perturbation-theory calculations based on Dirac-Fock-Breit wave functions
International Nuclear Information System (INIS)
Ishikawa, Y.; Quiney, H.M.
1993-01-01
A relativistic many-body perturbation theory based on the Dirac-Fock-Breit wave functions has been developed and implemented by employing analytic basis sets of Gaussian-type functions. The instantaneous Coulomb and low-frequency Breit interactions are treated using a unified formalism in both the construction of the Dirac-Fock-Breit self-consistent-field atomic potential and in the evaluation of many-body perturbation-theory diagrams. The relativistic many-body perturbation-theory calculations have been performed on the helium atom and ions of the helium isoelectronic sequence up to Z=50. The contribution of the low-frequency Breit interaction to the relativistic correlation energy is examined for the helium isoelectronic sequence
Many-body calculations with deuteron based single-particle bases and their associated natural orbits
Puddu, G.
2018-06-01
We use the recently introduced single-particle states obtained from localized deuteron wave-functions as a basis for nuclear many-body calculations. We show that energies can be substantially lowered if the natural orbits (NOs) obtained from this basis are used. We use this modified basis for {}10{{B}}, {}16{{O}} and {}24{{Mg}} employing the bare NNLOopt nucleon–nucleon interaction. The lowering of the energies increases with the mass. Although in principle NOs require a full scale preliminary many-body calculation, we found that an approximate preliminary many-body calculation, with a marginal increase in the computational cost, is sufficient. The use of natural orbits based on an harmonic oscillator basis leads to a much smaller lowering of the energies for a comparable computational cost.
Generalized Hartree-Fock-Bogoliubov approach in the description of many-body systems
International Nuclear Information System (INIS)
Janssen, D.
1979-01-01
The quantum mechanical equation for a group of states connected by large probabilities of transitions to each other, i.e. possessing common internal structure, is found. No phenomenological assumptions about the vibrational or rotational character of these states have been used. The equations obtained here can be understood as a direct generalization of the Hartree-Fock-Bogoliubov equation, this scheme including not only the ground state, but some excited states as well. The question of normalization of the density matrix in the generalized space has been solved and the additional solutions of the problem have been excluded. (author)
Time dependent mean field approximation to the many-body S-matrix
International Nuclear Information System (INIS)
Alhassid, Y.; Koonin, S.E.
1980-01-01
Time-dependent Hartree-Fock (TDHF) calculations are a good description of some inclusive properties of deep inelastic heavy-ion collisions. The first steps toward a mean-field theory that approximates specific elements of the many-body S matrix are presented. A many-body system with pairwise interactions excited by an external, time-dependent one-body field is considered. The methods are used to solve the forced Lipkin model. The moduli of elastic and excitation amplitudes are plotted. 3 figures
Lectures on quantum mechanics with problems, exercises and their solutions
Basdevant, Jean-Louis
2016-01-01
The new edition of this remarkable text offers the reader a conceptually strong introduction to quantum mechanics, but goes beyond this to present a fascinating tour of modern theoretical physics. Beautifully illustrated and engagingly written, it starts with a brief overview of diverse topics across physics including nanotechnology, statistical physics, materials science, astrophysics, and cosmology. The core of the book covers both established and emerging aspects of quantum mechanics. A concise introduction to traditional quantum mechanics covers the Schrödinger equation, Hilbert space, the algebra of observables, hydrogen atom, spin and Pauli principle. Modern features of the field are presented by exploring entangled states, Bell's inequality, quantum cryptography, quantum teleportation and quantum mechanics in the universe. This new edition has been enchanced through the addition of numerous problems with detailed solutions, an introduction to the mathematical tools needed and expanded discussion of th...
Security problem on arbitrated quantum signature schemes
International Nuclear Information System (INIS)
Choi, Jeong Woon; Chang, Ku-Young; Hong, Dowon
2011-01-01
Many arbitrated quantum signature schemes implemented with the help of a trusted third party have been developed up to now. In order to guarantee unconditional security, most of them take advantage of the optimal quantum one-time encryption based on Pauli operators. However, in this paper we point out that the previous schemes provide security only against a total break attack and show in fact that there exists an existential forgery attack that can validly modify the transmitted pair of message and signature. In addition, we also provide a simple method to recover security against the proposed attack.
Security problem on arbitrated quantum signature schemes
Energy Technology Data Exchange (ETDEWEB)
Choi, Jeong Woon [Emerging Technology R and D Center, SK Telecom, Kyunggi 463-784 (Korea, Republic of); Chang, Ku-Young; Hong, Dowon [Cryptography Research Team, Electronics and Telecommunications Research Institute, Daejeon 305-700 (Korea, Republic of)
2011-12-15
Many arbitrated quantum signature schemes implemented with the help of a trusted third party have been developed up to now. In order to guarantee unconditional security, most of them take advantage of the optimal quantum one-time encryption based on Pauli operators. However, in this paper we point out that the previous schemes provide security only against a total break attack and show in fact that there exists an existential forgery attack that can validly modify the transmitted pair of message and signature. In addition, we also provide a simple method to recover security against the proposed attack.
Quantum elastic net and the traveling salesman problem
International Nuclear Information System (INIS)
Kostenko, B.F.; Pribis, J.; Yur'ev, M.Z.
2009-01-01
Theory of computer calculations strongly depends on the nature of elements the computer is made of. Quantum interference allows one to formulate the Shor factorization algorithm turned out to be more effective than any one written for classical computers. Similarly, quantum wave packet reduction allows one to devise the Grover search algorithm which outperforms any classical one. In the present paper we argue that the quantum incoherent tunneling can be used for elaboration of new algorithms able to solve some NP-hard problems, such as the traveling Salesman Problem, considered to be intractable in the classical theory of computer computations
Modelling the many-body dynamics of heavy ion collisions. Present status and future perspective
International Nuclear Information System (INIS)
Hartnack, Ch.; Puri, R.K.; Aichelin, J.; Konopka, J.; Bass, S.A.; Stoecker, H.; Greiner, W.
1996-01-01
Basic problems of the semiclassical microscopic modelling of strongly interacting systems are discussed within the framework of Quantum Molecular Dynamics (QMD). It is shown that the same predictions can be obtained with several - numerically completely different and independently written -programs as far as the same model parameters are employed and the same basic approximations are made. Some of the physical results, however, depend also on rather technical parameters like the preparation of the initial configuration in phase space. This crucial problem is connected with the description of the ground state of single nuclei, which differs among the various approaches. An outlook to an improved molecular dynamics scheme for heavy ion collisions is given. (author)
Modelling the many-body dynamics of heavy ion collisions. Present status and future perspective
Energy Technology Data Exchange (ETDEWEB)
Hartnack, Ch.; Puri, R.K.; Aichelin, J. [Centre National de la Recherche Scientifique, 44 - Nantes (France). Lab. de Physique Subatomique et des Technologies Associees; Konopka, J.; Bass, S.A.; Stoecker, H.; Greiner, W. [Johann Wolfgang Goethe Univ., Frankfurt am Main (Germany). Inst. fuer Theoretische Physik
1996-12-31
Basic problems of the semiclassical microscopic modelling of strongly interacting systems are discussed within the framework of Quantum Molecular Dynamics (QMD). It is shown that the same predictions can be obtained with several - numerically completely different and independently written -programs as far as the same model parameters are employed and the same basic approximations are made. Some of the physical results, however, depend also on rather technical parameters like the preparation of the initial configuration in phase space. This crucial problem is connected with the description of the ground state of single nuclei, which differs among the various approaches. An outlook to an improved molecular dynamics scheme for heavy ion collisions is given. (author). 86 refs.
Efficient molecular dynamics simulations with many-body potentials on graphics processing units
Fan, Zheyong; Chen, Wei; Vierimaa, Ville; Harju, Ari
2017-09-01
Graphics processing units have been extensively used to accelerate classical molecular dynamics simulations. However, there is much less progress on the acceleration of force evaluations for many-body potentials compared to pairwise ones. In the conventional force evaluation algorithm for many-body potentials, the force, virial stress, and heat current for a given atom are accumulated within different loops, which could result in write conflict between different threads in a CUDA kernel. In this work, we provide a new force evaluation algorithm, which is based on an explicit pairwise force expression for many-body potentials derived recently (Fan et al., 2015). In our algorithm, the force, virial stress, and heat current for a given atom can be accumulated within a single thread and is free of write conflicts. We discuss the formulations and algorithms and evaluate their performance. A new open-source code, GPUMD, is developed based on the proposed formulations. For the Tersoff many-body potential, the double precision performance of GPUMD using a Tesla K40 card is equivalent to that of the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics code running with about 100 CPU cores (Intel Xeon CPU X5670 @ 2.93 GHz).
N=2 superconformal Newton-Hooke algebra and many-body mechanics
International Nuclear Information System (INIS)
Galajinsky, Anton
2009-01-01
A representation of the conformal Newton-Hooke algebra on a phase space of n particles in arbitrary dimension which interact with one another via a generic conformal potential and experience a universal cosmological repulsion or attraction is constructed. The minimal N=2 superconformal extension of the Newton-Hooke algebra and its dynamical realization in many-body mechanics are studied.
On the many-body foundation of the nuclear field theory
International Nuclear Information System (INIS)
Bes, D.R.; Dussel, G.G.; Liotta, R.J.; Perazzo, R.P.J.; Broglia, R.A.
1976-01-01
The equivalence between the description of the many-body finite nuclear system in terms of Feynman diagrams involving only the fermion degrees of freedom and of Feynman diagrams involving fermion and phonon degrees of freedom is proved for intermediate states in the case of a general two-body residual interaction. (Auth.)
Moores, Brad A.; Sletten, Lucas R.; Viennot, Jeremie; Lehnert, K. W.
Man-made systems of interacting qubits are a promising and powerful way of exploring many-body spin physics beyond classical computation. Although transmon qubits are perhaps the most advanced quantum computing technology, building a system of such qubits designed to emulate a system of many interacting spins is hindered by the mismatch of scales between the transmons and the electromagnetic modes that couple them. We propose a strategy to overcome this mismatch by using surface acoustic waves, which couple to qubits piezoelectrically and have micron wavelengths at GHz frequencies. In this talk, we will present characterizations of transmon qubits fabricated on a piezoelectric material, and show that their coherence properties are sufficient to explore acoustically mediated qubit interactions.
Quantum speedup in solving the maximal-clique problem
Chang, Weng-Long; Yu, Qi; Li, Zhaokai; Chen, Jiahui; Peng, Xinhua; Feng, Mang
2018-03-01
The maximal-clique problem, to find the maximally sized clique in a given graph, is classically an NP-complete computational problem, which has potential applications ranging from electrical engineering, computational chemistry, and bioinformatics to social networks. Here we develop a quantum algorithm to solve the maximal-clique problem for any graph G with n vertices with quadratic speedup over its classical counterparts, where the time and spatial complexities are reduced to, respectively, O (√{2n}) and O (n2) . With respect to oracle-related quantum algorithms for the NP-complete problems, we identify our algorithm as optimal. To justify the feasibility of the proposed quantum algorithm, we successfully solve a typical clique problem for a graph G with two vertices and one edge by carrying out a nuclear magnetic resonance experiment involving four qubits.
Universal many-body response of heavy impurities coupled to a Fermi sea: a review of recent progress
Schmidt, Richard; Knap, Michael; Ivanov, Dmitri A.; You, Jhih-Shih; Cetina, Marko; Demler, Eugene
2018-02-01
In this report we discuss the dynamical response of heavy quantum impurities immersed in a Fermi gas at zero and at finite temperature. Studying both the frequency and the time domain allows one to identify interaction regimes that are characterized by distinct many-body dynamics. From this theoretical study a picture emerges in which impurity dynamics is universal on essentially all time scales, and where the high-frequency few-body response is related to the long-time dynamics of the Anderson orthogonality catastrophe by Tan relations. Our theoretical description relies on different and complementary approaches: functional determinants give an exact numerical solution for time- and frequency-resolved responses, bosonization provides accurate analytical expressions at low temperatures, and the theory of Toeplitz determinants allows one to analytically predict response up to high temperatures. Using these approaches we predict the thermal decoherence rate of the fermionic system and prove that within the considered model the fastest rate of long-time decoherence is given by γ=π k_BT/4 . We show that Feshbach resonances in cold atomic systems give access to new interaction regimes where quantum effects can prevail even in the thermal regime of many-body dynamics. The key signature of this phenomenon is a crossover between different exponential decay rates of the real-time Ramsey signal. It is shown that the physics of the orthogonality catastrophe is experimentally observable up to temperatures T/T_F≲ 0.2 where it leaves its fingerprint in a power-law temperature dependence of thermal spectral weight and we review how this phenomenon is related to the physics of heavy ions in liquid {\\hspace{0pt}}3 He and the formation of Fermi polarons. The presented results are in excellent agreement with recent experiments on LiK mixtures, and we predict several new phenomena that can be tested using currently available experimental technology.
The challenge of quantum computer simulations of physical phenomena
International Nuclear Information System (INIS)
Ortiz, G.; Knill, E.; Gubernatis, J.E.
2002-01-01
The goal of physics simulation using controllable quantum systems ('physics imitation') is to exploit quantum laws to advantage, and thus accomplish efficient simulation of physical phenomena. In this Note, we discuss the fundamental concepts behind this paradigm of information processing, such as the connection between models of computation and physical systems. The experimental simulation of a toy quantum many-body problem is described
Classical limit of the quantum inverse scattering problem
International Nuclear Information System (INIS)
Bogdanov, I.V.
1986-01-01
This paper studies the passage to the limit of classical mechanics which is realized in the formalism of Marchenko's method for a spherically symmetric inverse problem of quantum scattering for fixed angular momentum. The limit is considered for the general case of partial waves with arbitrary values of the orbital number 1>0 in the lowest order of perturbation theory. It is shown how in the limit h→0 in the quantum inverse problem the integral Able transformation characteristic of classical inverse problems arises. The classical inversion formula with delay time is derived from the Marchenko equation
Quantum entanglement, indistinguishability, and the absent-minded driver's problem
International Nuclear Information System (INIS)
Cabello, Adan; Calsamiglia, John
2005-01-01
The absent-minded driver's problem illustrates that probabilistic strategies can give higher pay-offs than deterministic ones. We show that there are strategies using quantum entangled states that give even higher pay-offs, both for the original problem and for the generalized version with an arbitrary number of intersections and any possible set of pay-offs
Connes' embedding problem and winning strategies for quantum XOR games
Harris, Samuel J.
2017-12-01
We consider quantum XOR games, defined in the work of Regev and Vidick [ACM Trans. Comput. Theory 7, 43 (2015)], from the perspective of unitary correlations defined in the work of Harris and Paulsen [Integr. Equations Oper. Theory 89, 125 (2017)]. We show that the winning bias of a quantum XOR game in the tensor product model (respectively, the commuting model) is equal to the norm of its associated linear functional on the unitary correlation set from the appropriate model. We show that Connes' embedding problem has a positive answer if and only if every quantum XOR game has entanglement bias equal to the commuting bias. In particular, the embedding problem is equivalent to determining whether every quantum XOR game G with a winning strategy in the commuting model also has a winning strategy in the approximate finite-dimensional model.
Approximability of optimization problems through adiabatic quantum computation
Cruz-Santos, William
2014-01-01
The adiabatic quantum computation (AQC) is based on the adiabatic theorem to approximate solutions of the Schrödinger equation. The design of an AQC algorithm involves the construction of a Hamiltonian that describes the behavior of the quantum system. This Hamiltonian is expressed as a linear interpolation of an initial Hamiltonian whose ground state is easy to compute, and a final Hamiltonian whose ground state corresponds to the solution of a given combinatorial optimization problem. The adiabatic theorem asserts that if the time evolution of a quantum system described by a Hamiltonian is l
How should we understand non-equilibrium many-body steady states?
Maghrebi, Mohammad; Gorshkov, Alexey
: Many-body systems with both coherent dynamics and dissipation constitute a rich class of models which are nevertheless much less explored than their dissipationless counterparts. The advent of numerous experimental platforms that simulate such dynamics poses an immediate challenge to systematically understand and classify these models. In particular, nontrivial many-body states emerge as steady states under non-equilibrium dynamics. In this talk, I use a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in such models. I show that an effective temperature generically emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is described by a thermodynamic universality class. In the end, I will also discuss possibilities that go beyond the paradigm of an effective thermodynamic behavior.
Auger recombination in Dirac materials: A tangle of many-body effects
Alymov, Georgy; Vyurkov, Vladimir; Ryzhii, Victor; Satou, Akira; Svintsov, Dmitry
2018-05-01
The peculiar electron dispersion in Dirac materials makes lowest-order Auger processes prohibited or marginally prohibited by energy and momentum conservation laws. Thus, Auger recombination (AR) in these materials is very sensitive to many-body effects. We incorporate them at the level of the G W approximation into the nonequilibrium Green's functions approach to AR and study the role of dynamic screening, spectrum broadening, and renormalization in the case of weakly pumped undoped graphene. We find that incorrect treatment of many-body effects can lead to an order-of-magnitude error in the recombination rate. We show that the AR time depends weakly (sublinearly) on the background dielectric constant, which limits the possibility to control recombination by the choice of substrate. However, the AR time can be considerably prolonged by placing graphene under a metal gate or by introducing a band gap. With carrier cooling taken into account, our results comply with experiments on photoexcited graphene.
Bell Correlations in a Many-Body System with Finite Statistics
Wagner, Sebastian; Schmied, Roman; Fadel, Matteo; Treutlein, Philipp; Sangouard, Nicolas; Bancal, Jean-Daniel
2017-10-01
A recent experiment reported the first violation of a Bell correlation witness in a many-body system [Science 352, 441 (2016)]. Following discussions in this Letter, we address here the question of the statistics required to witness Bell correlated states, i.e., states violating a Bell inequality, in such experiments. We start by deriving multipartite Bell inequalities involving an arbitrary number of measurement settings, two outcomes per party and one- and two-body correlators only. Based on these inequalities, we then build up improved witnesses able to detect Bell correlated states in many-body systems using two collective measurements only. These witnesses can potentially detect Bell correlations in states with an arbitrarily low amount of spin squeezing. We then establish an upper bound on the statistics needed to convincingly conclude that a measured state is Bell correlated.
Coupled-channel equations and off-shell transformations in many-body scattering
International Nuclear Information System (INIS)
Cattapan, G.; Vanzani, V.
1977-01-01
The general structure and the basic features of several many-body coupled-channel integral equations, obtained by means of the channel coupling array device, are studied in a systematic way. Particular attention is paid to the employment of symmetric transition operators. The connection between different formulations has been clarified and the role played by some off-shell transformations for many-body transition operators has been discussed. Specific choices of the coupling scheme are considered and the corresponding coupled equations are compared with similar equations previously derived. Several sets of linear relations between transition operators have also been presented and used in a three-body context to derive uncoupled integral equations with connected kernel
Morphology of Laplacian growth processes and statistics of equivalent many-body systems
International Nuclear Information System (INIS)
Blumenfeld, R.
1994-01-01
The authors proposes a theory for the nonlinear evolution of two dimensional interfaces in Laplacian fields. The growing region is conformally mapped onto the unit disk, generating an equivalent many-body system whose dynamics and statistics are studied. The process is shown to be Hamiltonian, with the Hamiltonian being the imaginary part of the complex electrostatic potential. Surface effects are introduced through the Hamiltonian as an external field. An extension to a continuous density of particles is presented. The results are used to study the morphology of the interface using statistical mechanics for the many-body system. The distribution of the curvature and the moments of the growth probability along the interface are calculated exactly from the distribution of the particles. In the dilute limit, the distribution of the curvature is shown to develop algebraic tails, which may, for the first time, explain the origin of fractality in diffusion controlled processes
The closed time-path Green function formalism in many-body theory
International Nuclear Information System (INIS)
Guang-zhao Zhou; Zhao-bin Su; Bai-lin Hao; Lu Yu.
1983-09-01
The closed time-path Green function formalism, developed by our group during recent years, is briefly reviewed. The generating functional technique, the coupled equations for the order parameter and the elementary excitations as well as the systematic loop expansion are outlined. The applications to critical dynamics, quenched random systems, nonlinear response theory, superconductivity, laser system and quasi-one-dimensional conductors are described. The theoretical approach developed can be applied to both equilibrium and non-equilibrium many-body systems. (author)
Many-body theory of charge transfer in hyperthermal atomic scattering
International Nuclear Information System (INIS)
Marston, J.B.; Andersson, D.R.; Behringer, E.R.; Cooper, B.H.; DiRubio, C.A.; Kimmel, G.A.; Richardson, C.
1993-01-01
We use the Newns-Anderson Hamiltonian to describe many-body electronic processes that occur when hyperthermal alkali atoms scatter off metallic surfaces. Following Brako and Newns, we expand the electronic many-body wave function in the number of particle-hole pairs (we keep terms up to and including a single particle-hole pair). We extend their earlier work by including level crossings, excited neutrals, and negative ions. The full set of equations of motion is integrated numerically, without further approximations, to obtain the many-body amplitudes as a function of time. The velocity and work-function dependence of final-state quantities such as the distribution of ion charges and excited atomic occupancies are compared with experiment. In particular, experiments that scatter alkali ions off clean Cu(001) surfaces in the energy range 5--1600 eV constrain the theory quantitatively. The neutralization probability of Na + ions shows a minimum at intermediate velocity in agreement with the theory. This behavior contrasts with that of K + , which shows virtually no neutralization, and with Li + , which exhibits a monotonically increasing neutral fraction with decreasing velocity. Particle-hole excitations are left behind in the metal during a fraction of the collision events; this dissipated energy is predicted to be quite small (on the order of tenths of an electron volt). Indeed, classical trajectory simulations of the surface dynamics account well for the observed energy loss, and thus provide some justification for our truncation of the equations of motion at the single particle-hole pair level. Li + scattering experiments off low work-function surfaces provide qualitative information on the importance of many-body effects. At sufficiently low work function, the negative ions predicted to occur are in fact observed
One-dimensional classical many-body system having a normal thermal conductivity
International Nuclear Information System (INIS)
Casati, G.; Ford, J.; Vivaldi, F.; Visscher, W.M.
1984-01-01
By numerically computing orbits for a chaotic, one-dimensional, many-body system placed between two thermal reservoirs, we verify directly that its energy transport obeys the Fourier heat law and we determine its thermal conductivity K. The same value of K is independently obtained by use of the Green-Kubo formalism. These numerical studies verify that chaos is the essential ingredient of diffusive energy transport, and they validate the Green-Kubo formalism
Experimental quantum annealing: case study involving the graph isomorphism problem.
Zick, Kenneth M; Shehab, Omar; French, Matthew
2015-06-08
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical pre- and post-processing; at this early stage, little is known about how to partition and optimize the processing. This article presents an experimental case study of quantum annealing and some of the factors involved in real-world solvers, using a 504-qubit D-Wave Two machine and the graph isomorphism problem. To illustrate the role of classical pre-processing, a compact Hamiltonian is presented that enables a reduced Ising model for each problem instance. On random N-vertex graphs, the median number of variables is reduced from N(2) to fewer than N log2 N and solvable graph sizes increase from N = 5 to N = 13. Additionally, error correction via classical post-processing majority voting is evaluated. While the solution times are not competitive with classical approaches to graph isomorphism, the enhanced solver ultimately classified correctly every problem that was mapped to the processor and demonstrated clear advantages over the baseline approach. The results shed some light on the nature of real-world quantum annealing and the associated hybrid classical-quantum solvers.
Spin-dependent electron many-body effects in GaAs
Nemec, P.; Kerachian, Y.; van Driel, H. M.; Smirl, Arthur L.
2005-12-01
Time- and polarization-resolved differential transmission measurements employing same and oppositely circularly polarized 150fs optical pulses are used to investigate spin characteristics of conduction band electrons in bulk GaAs at 295K . Electrons and holes with densities in the 2×1016cm-3-1018cm-3 range are generated and probed with pulses whose center wavelength is between 865 and 775nm . The transmissivity results can be explained in terms of the spin sensitivity of both phase-space filling and many-body effects (band-gap renormalization and screening of the Coulomb enhancement factor). For excitation and probing at 865nm , just above the band-gap edge, the transmissivity changes mainly reflect spin-dependent phase-space filling which is dominated by the electron Fermi factors. However, for 775nm probing, the influence of many-body effects on the induced transmission change are comparable with those from reduced phase space filling, exposing the spin dependence of the many-body effects. If one does not take account of these spin-dependent effects one can misinterpret both the magnitude and time evolution of the electron spin polarization. For suitable measurements we find that the electron spin relaxation time is 130ps .
Many-body localization dynamics from a one-particle perspective
Energy Technology Data Exchange (ETDEWEB)
Lezama Mergold Love, Talia; Bera, Soumya; Bardarson, Jens Hjorleifur [Max Planck Institute for the Physics of Complex Systems, Dresden (Germany)
2016-07-01
Systems exhibiting many-body localization (Anderson insulators in the presence of interactions) present a novel class of nonergodic phases of matter. The study of entanglement, in terms of both exact eigenstates and its time evolution after quenches, has been useful to reveal the salient signatures of these systems. Similarly to the entanglement entropy of exact eigenstates, the one-particle density matrix can be used as a tool to characterize the many-body localization transition with its eigenvalues showing a Fermi-liquid like step discontinuity in the localized phase. However, this analysis distinguishes the Fock-space structure of the eigenstates from the real space. Here, we present numerical evidence for dynamical signatures of the many-body localized phase for a closed fermionic system, using the one-particle density matrix and its time evolution after a global quench. We discuss and compare our results with the well-known logarithmic spreading of entanglement (a dynamical signature of this phase, absent in the Anderson insulator).
Calculation of the hyperfine interaction using an effective-operator form of many-body theory
International Nuclear Information System (INIS)
Garpman, S.; Lindgren, I.; Lindgren, J.; Morrison, J.
1975-01-01
The effective-operator form of many-body theory is reviewed and applied to the calculation of the hyperfine structure. Numerical results are given for the 2p, 3p, and 4p excited states of Li and the 3p state of Na. This is the first complete calculation of the hyperfine structure using an effective-operator form of perturbation theory. As in the Brueckner-Goldstone form of many-body theory, the various terms in the perturbation expansion are represented by Feynman diagrams which correspond to basic physical processes. The angular part of the perturbation diagrams are evaluated by taking advantage of the formal analogy between the Feynman diagrams and the angular-momentum diagrams, introduced by Jucys et al. The radial part of the diagrams is calculated by solving one- and two-particle equations for the particular linear combination of excited states that contribute to the Feynman diagrams. In this way all second- and third-order effects are accurately evaluated without explicitly constructing the excited orbitals. For the 2p state of Li our results are in agreement with the calculations of Nesbet and of Hameed and Foley. However, our quadrupole calculation disagrees with the work of Das and co-workers. The many-body results for Li and Na are compared with semiempirical methods for evaluating the quadrupole moment from the hyperfine interaction, and a new quadrupole moment of 23 Na is given
Energy Technology Data Exchange (ETDEWEB)
Millis, Andrew [Columbia Univ., New York, NY (United States). Dept. of Physics
2016-11-17
Understanding the behavior of interacting electrons in molecules and solids so that one can predict new superconductors, catalysts, light harvesters, energy and battery materials and optimize existing ones is the ``quantum many-body problem’’. This is one of the scientific grand challenges of the 21^{st} century. A complete solution to the problem has been proven to be exponentially hard, meaning that straightforward numerical approaches fail. New insights and new methods are needed to provide accurate yet feasible approximate solutions. This CMSCN project brought together chemists and physicists to combine insights from the two disciplines to develop innovative new approaches. Outcomes included the Density Matrix Embedding method, a new, computationally inexpensive and extremely accurate approach that may enable first principles treatment of superconducting and magnetic properties of strongly correlated materials, new techniques for existing methods including an Adaptively Truncated Hilbert Space approach that will vastly expand the capabilities of the dynamical mean field method, a self-energy embedding theory and a new memory-function based approach to the calculations of the behavior of driven systems. The methods developed under this project are now being applied to improve our understanding of superconductivity, to calculate novel topological properties of materials and to characterize and improve the properties of nanoscale devices.
Unary probabilistic and quantum automata on promise problems
Gainutdinova, Aida; Yakaryilmaz, Abuzer
2015-01-01
We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs ...
The problems of mapping in quantum systems
International Nuclear Information System (INIS)
Xu Gongou; Wang Wenge; Yang Yadian; Fu Deji
1992-01-01
The mapping from the state of Hamiltonian H(0) to that of H(λ) = H(0) + λ(H-H(0)) is established by means of Wigner-Brillion perturbation formula. An iterative perturbation calculation can be carried out to find the stable points set and to show that under what condition the iterative calculation is divergent(non convergent). Avoided crossing point is really a singularity-point showed clearly in such procedure. The topological invariant subspace endowed by corresponding Hamiltonian H(0) is destroyed after such avoided crossing point. It is similar to the classical invariant tori destruction. A quantum KAM theorem can be established in this manner. Numerical results of certain schematic systems are given as illustration
Solution of certain problems in quantum mechanics
Bolotin, A; Raudeliunas, A
2018-01-01
Intended for advanced undergraduates and graduate students in mathematics, physics, and chemistry, this concise treatment demonstrates the theory of special functions' use and application to problems in atomic and molecular physics. 2017 edition.
Strategies in a symmetric quantum Kolkata restaurant problem
Sharif, Puya; Heydari, Hoshang
2012-12-01
The Quantum Kolkata restaurant problem is a multiple-choice version of the quantum minority game, where a set of n non-communicating players have to chose between one of m choices. A payoff is granted to the players that make a unique choice. It has previously been shown that shared entanglement and quantum operations can aid the players to coordinate their actions and acquire higher payoffs than is possible with classical randomization. In this paper the initial quantum state is expanded to a family of GHZ-type states and strategies are discussed in terms of possible final outcomes. It is shown that the players individually seek outcomes that maximize the collective good.
Many-body forces and stability of the alkaline-earth tetramers
International Nuclear Information System (INIS)
Diaz-Torrejon, C.C.; Kaplan, Ilya G.
2011-01-01
Graphical abstract: Many-body forces effect. In a three-particle system, the two-body interaction energies depend upon coordinates of all three particles. The comparative study of the interaction energy and its many-body decomposition for alkaline-earths tetramers Be 4 , Mg 4 , and Ca 4 at the all-electron CCSD(T)/aug-cc-pVQZ level is performed. For study of dependence of the binding energy and the orbital population on the cluster size the corresponding dimers and trimers were also calculated at the same level of theory. In comparison with weakly bound dimers, the binding energy in trimers and, especially, in tetramers drastically increases; e.g., E b /N in Be 3 is 7 times larger and in Be 4 is 18.4 times larger than in Be 2 . This sharp increase is explained as a manifestation of many-body forces. The trimers and tetramers are stabilized by the three-body forces, whereas the two- and four-body forces are repulsive. The attractive contribution to the three-body forces has a three-atom electron exchange origin. The natural bond orbital (NBO) population analysis reveals a relatively large np-population in trimers and tetramers. The population of the valence np-orbitals leads to the sp-hybridization providing the covalent bonding. Research highlights: → The alkaline-earths trimers and tetramers are stabilized by the three-body forces. → Two- and four-body forces are repulsive for trimers and tetramers. → The attractive contribution to the three-body forces has a three-atom electron exchange origin. → The population of the np-orbitals leads to the sp-hybridization providing the covalent bonding. - Abstract: The comparative study of the interaction energy and its many-body decomposition for Be 4 , Mg 4 , and Ca 4 at the all-electron CCSD(T)/aug-cc-pVQZ level is performed. For study of dependence of the binding energy and the orbital population on the cluster size the corresponding dimers and trimers were also calculated at the same level of theory. In
Self-consistent RPA based on a many-body vacuum
International Nuclear Information System (INIS)
Jemaï, M.; Schuck, P.
2011-01-01
Self-Consistent RPA is extended in a way so that it is compatible with a variational ansatz for the ground-state wave function as a fermionic many-body vacuum. Employing the usual equation-of-motion technique, we arrive at extended RPA equations of the Self-Consistent RPA structure. In principle the Pauli principle is, therefore, fully respected. However, the correlation functions entering the RPA matrix can only be obtained from a systematic expansion in powers of some combinations of RPA amplitudes. We demonstrate for a model case that this expansion may converge rapidly.
The Lanczos algorithm for extensive many-body systems in the thermodynamic limit
International Nuclear Information System (INIS)
Witte, N.S.; Bessis, D.
1999-01-01
We establish rigorously the scaling properties of the Lanczos process applied to an arbitrary extensive Many-Body System which is carried to convergence n → ∞ and the thermodynamic limit N → ∞ taken. In this limit the solution for the limiting Lanczos coefficients are found exactly and generally through two equivalent sets of equations, given initial knowledge of the exact cumulant generating function. The measure and the Orthogonal Polynomial System associated with the Lanczos process in this regime are also given explicitly. Some important representations of these Lanczos functions are provided, including Taylor series expansions, and the theorems controlling their general properties are proven. (authors)
Energy Distributions from Three-Body Decaying Many-Body Resonances
International Nuclear Information System (INIS)
Alvarez-Rodriguez, R.; Jensen, A. S.; Fedorov, D. V.; Fynbo, H. O. U.; Garrido, E.
2007-01-01
We compute energy distributions of three particles emerging from decaying many-body resonances. We reproduce the measured energy distributions from decays of two archetypal states chosen as the lowest 0 + and 1 + resonances in 12 C populated in β decays. These states are dominated by sequential, through the 8 Be ground state, and direct decays, respectively. These decay mechanisms are reflected in the ''dynamic'' evolution from small, cluster or shell-model states, to large distances, where the coordinate or momentum space continuum wave functions are accurately computed
Exploring excited eigenstates of many-body systems using the functional renormalization group
Klöckner, Christian; Kennes, Dante Marvin; Karrasch, Christoph
2018-05-01
We introduce approximate, functional renormalization group based schemes to obtain correlation functions in pure excited eigenstates of large fermionic many-body systems at arbitrary energies. The algorithms are thoroughly benchmarked and their strengths and shortcomings are documented using a one-dimensional interacting tight-binding chain as a prototypical testbed. We study two "toy applications" from the world of Luttinger liquid physics: the survival of power laws in lowly excited states as well as the spectral function of high-energy "block" excitations, which feature several single-particle Fermi edges.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation.
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-05-13
We propose an alternative formulation of many-body perturbation theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, which leads to excellent optical absorption and energy-loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-dependent density-functional theory. Numerical results for the band gap of bulk silicon and solid argon illustrate corrections beyond the GW approximation for the self-energy.
Many-body perturbation theory using the density-functional concept: beyond the GW approximation
Bruneval, Fabien; Sottile, Francesco; Olevano, Valerio; Del Sole, Rodolfo; Reining, Lucia
2005-01-01
We propose an alternative formulation of Many-Body Perturbation Theory that uses the density-functional concept. Instead of the usual four-point integral equation for the polarizability, we obtain a two-point one, that leads to excellent optical absorption and energy loss spectra. The corresponding three-point vertex function and self-energy are then simply calculated via an integration, for any level of approximation. Moreover, we show the direct impact of this formulation on the time-depend...
Proceedings of the fifth symposium on simulation of hadronic many-body system
Energy Technology Data Exchange (ETDEWEB)
Chiba, Satoshi; Maruyama, Toshiki [eds.
1998-07-01
The fifth symposium on Simulation of Hadronic Many-Body System, organized by the Research Group for Hadron Transport Theory, Advanced Science Research Center, was held at Tokai Research Establishment of JAERI on March 3 and 4, 1998. The symposium was devoted for discussion and presentation of research results on light- and heavy-ion induced nuclear reactions in terms of microscopic simulation method, while wide variety of other topics were also presented such as nuclear structure, properties of nuclear matter and high-energy multi-fragmentation experiments. The 17 of the presented papers are indexed individually. (J.P.N.)
On nonequilibrium many-body systems. 1: The nonequilibrium statistical operator method
International Nuclear Information System (INIS)
Algarte, A.C.S.; Vasconcellos, A.R.; Luzzi, R.; Sampaio, A.J.C.
1985-01-01
The theoretical aspects involved in the treatment of many-body systems strongly departed from equilibrium are discussed. The nonequilibrium statistical operator (NSO) method is considered in detail. Using Jaynes' maximum entropy formalism complemented with an ad hoc hypothesis a nonequilibrium statistical operator is obtained. This approach introduces irreversibility from the outset and we recover statistical operators like those of Green-Mori and Zubarev as particular cases. The connection with Generalized Thermodynamics and the construction of nonlinear transport equations are briefly described. (Author) [pt
Continuous-time quantum algorithms for unstructured problems
International Nuclear Information System (INIS)
Hen, Itay
2014-01-01
We consider a family of unstructured optimization problems, for which we propose a method for constructing analogue, continuous-time (not necessarily adiabatic) quantum algorithms that are faster than their classical counterparts. In this family of problems, which we refer to as ‘scrambled input’ problems, one has to find a minimum-cost configuration of a given integer-valued n-bit black-box function whose input values have been scrambled in some unknown way. Special cases within this set of problems are Grover’s search problem of finding a marked item in an unstructured database, certain random energy models, and the functions of the Deutsch–Josza problem. We consider a couple of examples in detail. In the first, we provide an O(1) deterministic analogue quantum algorithm to solve the seminal problem of Deutsch and Josza, in which one has to determine whether an n-bit boolean function is constant (gives 0 on all inputs or 1 on all inputs) or balanced (returns 0 on half the input states and 1 on the other half). We also study one variant of the random energy model, and show that, as one might expect, its minimum energy configuration can be found quadratically faster with a quantum adiabatic algorithm than with classical algorithms. (paper)
Two-body quantum mechanical problem on spheres
Shchepetilov, Alexey V.
2005-01-01
The quantum mechanical two-body problem with a central interaction on the sphere ${\\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several interactive potentials these energy levels are calculated in explicit form.
Quantum particle swarm approaches applied to combinatorial problems
Energy Technology Data Exchange (ETDEWEB)
Nicolau, Andressa dos S.; Schirru, Roberto; Lima, Alan M.M. de, E-mail: andressa@lmp.ufrj.br [Universidade Federal do Rio de Janeiro (UFRJ), RJ (Brazil). Programa de Engenharia Nuclear
2017-07-01
Quantum Particle Swarm Optimization (QPSO) is a global convergence algorithm that combines the classical PSO philosophy and quantum mechanics to improve performance of PSO. Different from PSO it only has the 'measurement' of the position equation for all particles. The process of 'measurement' in quantum mechanics, obey classic laws while the particle itself follows the quantum rules. QPSO works like PSO in search ability but has fewer parameters control. In order to improve the QPSO performance, some strategies have been proposed in the literature. Weighted QPSO (WQPSO) is a version of QPSO, where weight parameter is insert in the calculation of the balance between the global and local searching of the algorithm. It has been shown to perform well in finding the optimal solutions for many optimization problems. In this article random confinement was introduced in WQPSO. The WQPSO with random confinement was tested in two combinatorial problems. First, we execute the model on Travelling Salesman Problem (TSP) to find the parameters' values resulting in good solutions in general. Finally, the model was tested on Nuclear Reactor Reload Problem, and the performance was compared with QPSO standard. (author)
Impedance model for quantum-mechanical barrier problems
International Nuclear Information System (INIS)
Nelin, Evgenii A
2007-01-01
Application of the impedance model to typical quantum-mechanical barrier problems, including those for structures with resonant electron tunneling, is discussed. The efficiency of the approach is illustrated. The physical transparency and compactness of the model and its potential as a teaching and learning tool are discussed. (methodological notes)
Quantum particle swarm approaches applied to combinatorial problems
International Nuclear Information System (INIS)
Nicolau, Andressa dos S.; Schirru, Roberto; Lima, Alan M.M. de
2017-01-01
Quantum Particle Swarm Optimization (QPSO) is a global convergence algorithm that combines the classical PSO philosophy and quantum mechanics to improve performance of PSO. Different from PSO it only has the 'measurement' of the position equation for all particles. The process of 'measurement' in quantum mechanics, obey classic laws while the particle itself follows the quantum rules. QPSO works like PSO in search ability but has fewer parameters control. In order to improve the QPSO performance, some strategies have been proposed in the literature. Weighted QPSO (WQPSO) is a version of QPSO, where weight parameter is insert in the calculation of the balance between the global and local searching of the algorithm. It has been shown to perform well in finding the optimal solutions for many optimization problems. In this article random confinement was introduced in WQPSO. The WQPSO with random confinement was tested in two combinatorial problems. First, we execute the model on Travelling Salesman Problem (TSP) to find the parameters' values resulting in good solutions in general. Finally, the model was tested on Nuclear Reactor Reload Problem, and the performance was compared with QPSO standard. (author)
Uniqueness of inverse scattering problem in local quantum physics
Energy Technology Data Exchange (ETDEWEB)
Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: schroer@cbpf.br
2001-06-01
It is shown that the a Bisognano-Wichmann-Unruh inspired formulation of local quantum physics which starts from wedge-localized algebras, leads to a uniqueness proof for the scattering problem. The important mathematical tool is the thermal KMS aspect of localization and its strengthening by the requirement of crossing symmetry for generalized formfactors. (author)
Model many-body Stoner Hamiltonian for binary FeCr alloys
Nguyen-Manh, D.; Dudarev, S. L.
2009-09-01
We derive a model tight-binding many-body d -electron Stoner Hamiltonian for FeCr binary alloys and investigate the sensitivity of its mean-field solutions to the choice of hopping integrals and the Stoner exchange parameters. By applying the local charge-neutrality condition within a self-consistent treatment we show that the negative enthalpy-of-mixing anomaly characterizing the alloy in the low chromium concentration limit is due entirely to the presence of the on-site exchange Stoner terms and that the occurrence of this anomaly is not specifically related to the choice of hopping integrals describing conventional chemical bonding between atoms in the alloy. The Bain transformation pathway computed, using the proposed model Hamiltonian, for the Fe15Cr alloy configuration is in excellent agreement with ab initio total-energy calculations. Our investigation also shows how the parameters of a tight-binding many-body model Hamiltonian for a magnetic alloy can be derived from the comparison of its mean-field solutions with other, more accurate, mean-field approximations (e.g., density-functional calculations), hence stimulating the development of large-scale computational algorithms for modeling radiation damage effects in magnetic alloys and steels.
Dynamics of many-body localization in the presence of particle loss
van Nieuwenburg, EPL; Yago Malo, J.; Daley, AJ; Fischer, MH
2018-01-01
At long times, residual couplings to the environment become relevant even in the most isolated experiments, a crucial difficulty for the study of fundamental aspects of many-body dynamics. A particular example is many-body localization in a cold-atom setting, where incoherent photon scattering introduces both dephasing and particle loss. Whereas dephasing has been studied in detail and is known to destroy localization already on the level of non-interacting particles, the effect of particle loss is less well understood. A difficulty arises due to the ‘non-local’ nature of the loss process, complicating standard numerical tools using matrix product decomposition. Utilizing symmetries of the Lindbladian dynamics, we investigate the particle loss on both the dynamics of observables, as well as the structure of the density matrix and the individual states. We find that particle loss in the presence of interactions leads to dissipation and a strong suppression of the (operator space) entanglement entropy. Our approach allows for the study of the interplay of dephasing and loss for pure and mixed initial states to long times, which is important for future experiments using controlled coupling of the environment.
Many-Body Effects on the Thermodynamics of Fluids, Mixtures, and Nanoconfined Fluids.
Desgranges, Caroline; Delhommelle, Jerome
2015-11-10
Using expanded Wang-Landau simulations, we show that taking into account the many-body interactions results in sharp changes in the grand-canonical partition functions of single-component systems, binary mixtures, and nanoconfined fluids. The many-body contribution, modeled with a 3-body Axilrod-Teller-Muto term, results in shifts toward higher chemical potentials of the phase transitions from low-density phases to high-density phases and accounts for deviations of more than, e.g., 20% of the value of the partition function for a single-component liquid. Using the statistical mechanics formalism, we analyze how this contribution has a strong impact on some properties (e.g., pressure, coexisting densities, and enthalpy) and a moderate impact on others (e.g., Gibbs or Helmholtz free energies). We also characterize the effect of the 3-body terms on adsorption isotherms and adsorption thermodynamic properties, thereby providing a full picture of the effect of the 3-body contribution on the thermodynamics of nanoconfined fluids.
Testing quantum contextuality. The problem of compatibility
International Nuclear Information System (INIS)
Szangolies, Jochen
2015-01-01
Jochen Szangolies contributes a novel way of dealing with the problem of the experimental testability of the Kochen-Specker theorem posed by realistic, that is, noisy, measurements. Such noise spoils perfect compatibility between successive measurements, which however is a necessary requirement to test the notion of contextuality in usual approaches. To overcome this difficulty, a new, extended notion of contextuality that reduces to Kochen-Specker contextuality in the limit of perfect measurement implementations is proposed by the author, together with a scheme to test this notion experimentally. Furthermore, the behaviour of these tests under realistic noise conditions is investigated.
Numerical and analytical solutions for problems relevant for quantum computers
International Nuclear Information System (INIS)
Spoerl, Andreas
2008-01-01
Quantum computers are one of the next technological steps in modern computer science. Some of the relevant questions that arise when it comes to the implementation of quantum operations (as building blocks in a quantum algorithm) or the simulation of quantum systems are studied. Numerical results are gathered for variety of systems, e.g. NMR systems, Josephson junctions and others. To study quantum operations (e.g. the quantum fourier transform, swap operations or multiply-controlled NOT operations) on systems containing many qubits, a parallel C++ code was developed and optimised. In addition to performing high quality operations, a closer look was given to the minimal times required to implement certain quantum operations. These times represent an interesting quantity for the experimenter as well as for the mathematician. The former tries to fight dissipative effects with fast implementations, while the latter draws conclusions in the form of analytical solutions. Dissipative effects can even be included in the optimisation. The resulting solutions are relaxation and time optimised. For systems containing 3 linearly coupled spin (1)/(2) qubits, analytical solutions are known for several problems, e.g. indirect Ising couplings and trilinear operations. A further study was made to investigate whether there exists a sufficient set of criteria to identify systems with dynamics which are invertible under local operations. Finally, a full quantum algorithm to distinguish between two knots was implemented on a spin(1)/(2) system. All operations for this experiment were calculated analytically. The experimental results coincide with the theoretical expectations. (orig.)
International Nuclear Information System (INIS)
Gambini, Rodolfo; Porto, Rafael A; Pullin, Jorge
2004-01-01
The use of a relational time in quantum mechanics is a framework in which one promotes to quantum operators all variables in a system, and later chooses one of the variables to operate like a 'clock'. Conditional probabilities are computed for variables of the system to take certain values when the 'clock' specifies a certain time. This framework is attractive in contexts where the assumption of usual quantum mechanics of the existence of an external, perfectly classical clock, appears unnatural, as in quantum cosmology. Until recently, there were problems with such constructions in ordinary quantum mechanics with additional difficulties in the context of constrained theories like general relativity. A scheme we recently introduced to consistently discretize general relativity removed such obstacles. Since the clock is now an object subject to quantum fluctuations, the resulting evolution in time is not exactly unitary and pure states decohere into mixed states. Here we work out in detail the type of decoherence generated, and we find it to be of Lindblad type. This is attractive since it implies that one can have loss of coherence without violating the conservation of energy. We apply the framework to a simple cosmological model to illustrate how a quantitative estimate of the effect could be computed. For most quantum systems it appears to be too small to be observed, although certain macroscopic quantum systems could in the future provide a testing ground for experimental observation
Team decision problems with classical and quantum signals.
Brandenburger, Adam; La Mura, Pierfrancesco
2016-01-13
We study team decision problems where communication is not possible, but coordination among team members can be realized via signals in a shared environment. We consider a variety of decision problems that differ in what team members know about one another's actions and knowledge. For each type of decision problem, we investigate how different assumptions on the available signals affect team performance. Specifically, we consider the cases of perfectly correlated, i.i.d., and exchangeable classical signals, as well as the case of quantum signals. We find that, whereas in perfect-recall trees (Kuhn 1950 Proc. Natl Acad. Sci. USA 36, 570-576; Kuhn 1953 In Contributions to the theory of games, vol. II (eds H Kuhn, A Tucker), pp. 193-216) no type of signal improves performance, in imperfect-recall trees quantum signals may bring an improvement. Isbell (Isbell 1957 In Contributions to the theory of games, vol. III (eds M Drescher, A Tucker, P Wolfe), pp. 79-96) proved that, in non-Kuhn trees, classical i.i.d. signals may improve performance. We show that further improvement may be possible by use of classical exchangeable or quantum signals. We include an example of the effect of quantum signals in the context of high-frequency trading. © 2015 The Authors.
Three-player quantum Kolkata restaurant problem under decoherence
Ramzan, M.
2013-01-01
Effect of quantum decoherence in a three-player quantum Kolkata restaurant problem is investigated using tripartite entangled qutrit states. Different qutrit channels such as, amplitude damping, depolarizing, phase damping, trit-phase flip and phase flip channels are considered to analyze the behaviour of players payoffs. It is seen that Alice's payoff is heavily influenced by the amplitude damping channel as compared to the depolarizing and flipping channels. However, for higher level of decoherence, Alice's payoff is strongly affected by depolarizing noise. Whereas the behaviour of phase damping channel is symmetrical around 50% decoherence. It is also seen that for maximum decoherence ( p = 1), the influence of amplitude damping channel dominates over depolarizing and flipping channels. Whereas, phase damping channel has no effect on the Alice's payoff. Therefore, the problem becomes noiseless at maximum decoherence in case of phase damping channel. Furthermore, the Nash equilibrium of the problem does not change under decoherence.
Solved Problems in Quantum and Statistical Mechanics
Cini, Michele; Sbragaglia, Mauro
2012-01-01
This work arises from our teaching this subject during many years. The vast majority of these exercises are the exams we gave to our students in this period. We carefully selected the subjects of the exercises to cover all the material which is most needed and which is treated in the most well known texts on these subjects. Each exercise is carefully solved in full details, explaining the theory behind the solution with particular care for those issues that, from our experience, are found most difficult from the average student. Indeed, several exercises are designed to throw light on aspects of the theory that, for one reason or another, are usually neglected with the result to make the students feel uneasy about them. In fact most students get acquainted just with the more common manipulations, which are illustrated by many examples in textbooks. Our exercises never require extensive calculations but tend to be somewhat unusual and force the solver to think about the problem starting from the ...
Many-body formation and dissociation of a dipolar chain crystal
International Nuclear Information System (INIS)
You, Jhih-Shih; Wang, Daw-Wei
2014-01-01
We propose an experimental scheme to effectively assemble chains of dipolar gases with a uniform length in a multi-layer system. The obtained dipolar chains can form a chain crystal with the system temperature easily controlled by the initial lattice potential and the external field strength during processing. When the density of chains increases, we further observe a second order quantum phase transition for the chain crystal to be dissociated toward layers of 2D crystal, where the quantum fluctuation dominates the classical energy and the compressibility diverges at the phase boundary. The experimental implication of such a dipolar chain crystal and its quantum phase transition is also discussed. (paper)
Evidence of tensor correlations in the nuclear many-body system using a modern NN potential
International Nuclear Information System (INIS)
Fiase, J.O.; Nkoma, J.S.; Sharmaand, L.K.; Hosaka, A.
2003-01-01
In this paper we show evidence of the importance of tensor correlations in the nuclear many-body system by calculating the effective two-body nuclear matrix elements in the frame work of the Lowest-Order Constrained Variational (LOCV) technique with two-body correlation functions using the Reid93 potential. We have achieved this by switching on and off the strength of the tensor correlations, α k . We have found that in order to obtain reasonable agreement with earlier calculations based on the G-matrix theory, we must turn on the strength of the tensor correlations especially in the triplet even (TE) and tensor even (TNE) channels to take the value of approximately, 0.05. As an application, we have estimated the value of the Landau - Migdal parameter, g' NN which we found to be g' NN = 0.65. This compares favorably with the G-matrix calculated value of g' NN = 0.54. (author)
Towards predictive many-body calculations of phonon-limited carrier mobilities in semiconductors
Poncé, Samuel; Margine, Elena R.; Giustino, Feliciano
2018-03-01
We probe the accuracy limit of ab initio calculations of carrier mobilities in semiconductors, within the framework of the Boltzmann transport equation. By focusing on the paradigmatic case of silicon, we show that fully predictive calculations of electron and hole mobilities require many-body quasiparticle corrections to band structures and electron-phonon matrix elements, the inclusion of spin-orbit coupling, and an extremely fine sampling of inelastic scattering processes in momentum space. By considering all these factors we obtain excellent agreement with experiment, and we identify the band effective masses as the most critical parameters to achieve predictive accuracy. Our findings set a blueprint for future calculations of carrier mobilities, and pave the way to engineering transport properties in semiconductors by design.
The electronic structure of molecules by a many-body approach. Pt. 1
International Nuclear Information System (INIS)
Niessen, W. von; Cederbaum, L.S.; Kraemer, W.P.
1976-01-01
The ionization potentials of benzene are studied by an ab initio many-body approach which includes the effects of electron correlation and reorganization beyond the one-particle approximation. The calculations confirm the assignment of the photoelectron spectrum experimentally proposed by Jonsson and Lindholm: 1esub(1g)(π), 2esub(2g), 1asub(2u)(π), 2esub(1u), 1bsub(2u), 1bsub(1u), 2asub(1g), 1esub(2g) in order of increasing binding energy. To definitely establish the ordering of the ionization potentials in the second band, which has been very controversial, the corresponding vibrational structure has been calculated. A number of one-electron properties are calculated in the one-particle approximation and compared to experimental work and other theoretical calculations. (orig.) [de
Probing the electronic structure of liquid water with many-body perturbation theory
Pham, Tuan Anh; Zhang, Cui; Schwegler, Eric; Galli, Giulia
2014-03-01
We present a first-principles investigation of the electronic structure of liquid water based on many-body perturbation theory (MBPT), within the G0W0 approximation. The liquid quasiparticle band gap and the position of its valence band maximum and conduction band minimum with respect to vacuum were computed and it is shown that the use of MBPT is crucial to obtain results that are in good agreement with experiment. We found that the level of theory chosen to generate molecular dynamics trajectories may substantially affect the electronic structure of the liquid, in particular, the relative position of its band edges and redox potentials. Our results represent an essential step in establishing a predictive framework for computing the relative position of water redox potentials and the band edges of semiconductors and insulators. Work supported by DOE/BES (Grant No. DE-SC0008938). Work at LLNL was performed under Contract DE-AC52-07NA27344.
New formalism for determining excitation spectra of many-body systems
International Nuclear Information System (INIS)
Saito, S.; Zhang, S.B.; Louie, S.G.; Cohen, M.L.
1990-01-01
We present a new general formalism for determining the excitation spectrum of interacting many-body systems. The basic assumption is that the number of the excitations is equal to the number of sites. Within this approximation, it is shown that the density-density response functions with two different pure-imaginary energies determine the excitation spectrum. The method is applied to the valence electrons of sodium clusters of differing sizes in the time-dependent local-density approximation (TDLDA). A jellium-sphere background model is used for the ion cores. The excitation spectra obtained in this way represent well the excitation spectra given by the full TDLDA calculation along the real energy axis. Important collective modes are reproduced very well
Ab Initio Many-Body Calculations Of Nucleon-Nucleus Scattering
Energy Technology Data Exchange (ETDEWEB)
Quaglioni, S; Navratil, P
2008-12-17
We develop a new ab initio many-body approach capable of describing simultaneously both bound and scattering states in light nuclei, by combining the resonating-group method with the use of realistic interactions, and a microscopic and consistent description of the nucleon clusters. This approach preserves translational symmetry and Pauli principle. We outline technical details and present phase shift results for neutron scattering on {sup 3}H, {sup 4}He and {sup 10}Be and proton scattering on {sup 3,4}He, using realistic nucleon-nucleon (NN) potentials. Our A = 4 scattering results are compared to earlier ab initio calculations. We find that the CD-Bonn NN potential in particular provides an excellent description of nucleon-{sup 4}He S-wave phase shifts. We demonstrate that a proper treatment of the coupling to the n-{sup 10}Be continuum is successful in explaining the parity-inverted ground state in {sup 11}Be.
Excitons and Cooper pairs two composite bosons in many-body physics
Combescot, Monique
2015-01-01
This book bridges a gap between two major communities of Condensed Matter Physics, Semiconductors and Superconductors, that have thrived independently. Through an original perspective that their key particles, excitons and Cooper pairs, are composite bosons, the authors raise fundamental questions of current interest: how does the Pauli exclusion principle wield its power on the fermionic components of bosonic particles at a microscopic level and how this affects the macroscopic physics? What can we learn from Wannier and Frenkel excitons and from Cooper pairs that helps us understand "bosonic condensation" of composite bosons and its difference from Bose-Einstein condensation of elementary bosons? The authors start from solid mathematical and physical foundation to derive excitons and Cooper pairs. They further introduce Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange - a novel mechanism not visualized by standard Feynman diagrams. Advanced undergraduate or grad...
Collective many-body dynamics in the vicinity of nuclear driplines
International Nuclear Information System (INIS)
Volya, Alexander; Zelevinsky, Vladimir
2007-01-01
The Continuum Shell Model is a powerful theoretical tool for analysis of many-body dynamics embedded in the continuum. Here we formulate the method and use an example of a realistic shell model calculation for oxygen isotopes to demonstrate the seamless transition from bound states to resonances and cross sections in continuum within the same framework. The coupled dynamics of intrinsic states and continuum is traced further to the regime of continuum dominance that implies the decay width collectivization and onset of super-radiance. The coexistence and interplay of internal collective motion, such as giant resonances, and decay are of particular interest. Schematic and realistic calculations illustrate changes in the strength distribution and the natural appearance of the so-called pygmy mode
Lee, Tsung-Han
Strongly correlated materials are a class of materials that cannot be properly described by the Density Functional Theory (DFT), which is a single-particle approximation to the original many-body electronic Hamiltonian. These systems contain d or f orbital electrons, i.e., transition metals, actinides, and lanthanides compounds, for which the electron-electron interaction (correlation) effects are too strong to be described by the single-particle approximation of DFT. Therefore, complementary many-body methods have been developed, at the model Hamiltonians level, to describe these strong correlation effects. Dynamical Mean Field Theory (DMFT) and Rotationally Invariant Slave-Boson (RISB) approaches are two successful methods that can capture the correlation effects for a broad interaction strength. However, these many-body methods, as applied to model Hamiltonians, treat the electronic structure of realistic materials in a phenomenological fashion, which only allow to describe their properties qualitatively. Consequently, the combination of DFT and many body methods, e.g., Local Density Approximation augmented by RISB and DMFT (LDA+RISB and LDA+DMFT), have been recently proposed to combine the advantages of both methods into a quantitative tool to analyze strongly correlated systems. In this dissertation, we studied the possible improvements of these approaches, and tested their accuracy on realistic materials. This dissertation is separated into two parts. In the first part, we studied the extension of DMFT and RISB in three directions. First, we extended DMFT framework to investigate the behavior of the domain wall structure in metal-Mott insulator coexistence regime by studying the unstable solution describing the domain wall. We found that this solution, differing qualitatively from both the metallic and the insulating solutions, displays an insulating-like behavior in resistivity while carrying a weak metallic character in its electronic structure. Second, we
On the acceleration of convergence of many-body perturbation theory. Pt. 2
International Nuclear Information System (INIS)
Dietz, K.; Schmidt, C.; Warken, M.; Hess, B.A.
1992-07-01
We employ the method developed in a previous paper to small systems-Be, LiH, H 2 -where full CI-calculations are available for monitoring convergence of many-body perturbation theory. It is shown that divergent series, in particular for excited states, can be transformed into fast converging ones. In essence our method consists in performing infinite subsummations of perturbation series in order to improve convergence: coupling constants are redefined such that singularities are incorporated in a non-perturbative manner and remaining correlations can be expanded in a larger domain of the complex coupling constant plane. It is in this way that the notion of 'improved convergence' has a well defined meaning. (orig.)
Regimes of heating and dynamical response in driven many-body localized systems
Gopalakrishnan, Sarang; Knap, Michael; Demler, Eugene
2016-09-01
We explore the response of many-body localized (MBL) systems to periodic driving of arbitrary amplitude, focusing on the rate at which they exchange energy with the drive. To this end, we introduce an infinite-temperature generalization of the effective "heating rate" in terms of the spread of a random walk in energy space. We compute this heating rate numerically and estimate it analytically in various regimes. When the drive amplitude is much smaller than the frequency, this effective heating rate is given by linear response theory with a coefficient that is proportional to the optical conductivity; in the opposite limit, the response is nonlinear and the heating rate is a nontrivial power law of time. We discuss the mechanisms underlying this crossover in the MBL phase. We comment on implications for the subdiffusive thermal phase near the MBL transition, and for response in imperfectly isolated MBL systems.
Graphene-induced band gap renormalization in polythiophene: a many-body perturbation study
Marsusi, F.; Fedorov, I. A.; Gerivani, S.
2018-01-01
Density functional theory and many-body perturbation theory at the G0W0 level are employed to study the electronic properties of polythiophene (PT) adsorbed on the graphene surface. Analysis of the charge density difference shows that substrate-adsorbate interaction leads to a strong physisorption and interfacial electric dipole moment formation. The electrostatic potential displays a -0.19 eV shift in the graphene work function from its initial value of 4.53 eV, as the result of the interaction. The LDA band gap of the polymer does not show any change. However, the band structure exhibits weak orbital hybridizations resulting from slight overlapping between the polymer and graphene states wave functions. The interfacial polarization effects on the band gap and levels alignment are investigated at the G0W0 level and show a notable reduction of PT band gap compared to that of the isolated chain.
Coefficient of reversibility and two particular cases of deterministic many body systems
International Nuclear Information System (INIS)
Grossu, Ioan Valeriu; Besliu, Calin; Jipa, Alexandru
2004-01-01
We discuss the importance of a new measure of chaos in study of nonlinear dynamic systems, the - coefficient of reversibility-. This is defined as the probability of returning in the same point of phasic space. Is very interesting to compare this coefficient with other measures like fractal dimension or Liapunov exponent. We have also studied two very interesting many body systems, both having any number of particles but a deterministic evolution. One system is composed by n particles initially at rest, having the same mass and interacting through harmonic bi-particle forces, other is composed by two types of particles (with mass m 1 and mass m 2 ) initially at rest and interacting too through harmonic bi-particle forces
Electronic and optical properties of phosphorene-like arsenic phosphorus: a many-body study
Shu, Huabing; Guo, Jiyuan
2018-03-01
By employing density functional and many-body perturbation theories, we explore the geometrics, quasiparticle band structure, and optical response of two-dimensional arsenic phosphorus (α-AsxP1-x). Calculations indicate that the α-AsxP1-x exhibits excellent stability at high temperature. The quasi-particle bandgap of α-AsxP1-x is highly tunable in a broad range of 1.54-2.14 eV depending on the composition. The optical absorption of α-AsxP1-x can cover the visible and ultraviolet regions, and is highly anisotropic. More interestingly, it is tunable to optical absorption of α-AsxP1-x when the composition continuously increased. Also, they have sizable exciton binding energies. These findings suggest that α-AsxP1-x holds great potentials for applications in high-performance electronics and optoelectronics.
From optics to superconductivity. Many body effects in transition metal dichalcogenides
Energy Technology Data Exchange (ETDEWEB)
Roesner, Malte; Schoenhoff, Gunnar; Wehling, Tim [Institute for Theoretical Physics, University of Bremen (Germany); Bremen Center for Computational Material Sciences, University of Bremen (Germany); Steinhoff, Alexander; Jahnke, Frank; Gies, Christopher [Institute for Theoretical Physics, University of Bremen (Germany); Haas, Stephan [Department of Physics and Astronomy, University of Southern California, Los Angeles, CA (United States)
2015-07-01
We discuss many body effects in MoS{sub 2} ranging from optical properties to the emergence superconductivity (SC) and charge density wave phases (CDW). Combining ab-initio theory and semiconductor Bloch equations we show that excited carriers cause a redshift of the excitonic ground-state absorption line, while higher excitonic lines disappear successively due to a huge Coulomb-induced band gap shrinkage of more than 500 meV and concomitant exciton binding-energy reductions. Upon strong charge doping, we observe a succession of semiconducting, metallic, SC, and CDW regimes. Both, the SC and the CDW instabilities trace back to a Kohn anomaly and related softening of Brillouin zone boundary phonons.
A mesoscopic simulation of static and dynamic wetting using many-body dissipative particle dynamics
Ghorbani, Najmeh; Pishevar, Ahmadreza
2018-01-01
A many-body dissipative particle dynamics simulation is applied here to pave the way for investigating the behavior of mesoscale droplets after impact on horizontal solid substrates. First, hydrophobic and hydrophilic substrates are simulated through tuning the solid-liquid interfacial interaction parameters of an innovative conservative force model. The static contact angles are calculated on homogeneous and several patterned surfaces and compared with the predicted values by the Cassie's law in order to verify the model. The results properly evaluate the amount of increase in surface superhydrophobicity as a result of surface patterning. Then drop impact phenomenon is studied by calculating the spreading factor and dimensionless height versus dimensionless time and the comparisons made between the results and the experimental values for three different static contact angles. The results show the capability of the procedure in calculating the amount of maximum spreading factor, which is a significant concept in ink-jet printing and coating process.
Measure problem in slow roll inflation and loop quantum cosmology
International Nuclear Information System (INIS)
Corichi, Alejandro; Karami, Asieh
2011-01-01
We consider the measure problem in standard slow-roll inflationary models from the perspective of loop quantum cosmology (LQC). Following recent results by Ashtekar and Sloan, we study the probability of having enough e-foldings and focus on its dependence on the quantum gravity scale, including the transition of the theory to the limit where general relativity (GR) is recovered. Contrary to the standard expectation, the probability of having enough inflation, that is close to 1 in LQC, grows and tends to 1 as one approaches the GR limit. We study the origin of the tension between these results with those by Gibbons and Turok, and offer an explanation that brings these apparent contradictory results into a coherent picture. As we show, the conflicting results stem from different choices of initial conditions for the computation of probability. The singularity-free scenario of loop quantum cosmology offers a natural choice of initial conditions, and suggests that enough inflation is generic.
Quantum broadcasting problem in classical low-power signal processing
International Nuclear Information System (INIS)
Janzing, Dominik; Steudel, Bastian
2007-01-01
We prove a no-broadcasting theorem for the Holevo information of a noncommuting ensemble stating that no operation can generate a bipartite ensemble such that both copies have the same information as the original. We argue that upper bounds on the average information over both copies imply lower bounds on the quantum capacity required to send the ensemble without information loss. This is because a channel with zero quantum capacity has a unitary extension transferring at least as much information to its environment as it transfers to the output. For an ensemble being the time orbit of a pure state under a Hamiltonian evolution, we derive such a bound on the required quantum capacity in terms of properties of the input and output energy distribution. Moreover, we discuss relations between the broadcasting problem and entropy power inequalities. The broadcasting problem arises when a signal should be transmitted by a time-invariant device such that the outgoing signal has the same timing information as the incoming signal had. Based on previous results we argue that this establishes a link between quantum information theory and the theory of low power computing because the loss of timing information implies loss of free energy
Quantum N-body problem with a minimal length
International Nuclear Information System (INIS)
Buisseret, Fabien
2010-01-01
The quantum N-body problem is studied in the context of nonrelativistic quantum mechanics with a one-dimensional deformed Heisenberg algebra of the form [x,p]=i(1+βp 2 ), leading to the existence of a minimal observable length √(β). For a generic pairwise interaction potential, analytical formulas are obtained that allow estimation of the ground-state energy of the N-body system by finding the ground-state energy of a corresponding two-body problem. It is first shown that in the harmonic oscillator case, the β-dependent term grows faster with increasing N than the β-independent term. Then, it is argued that such a behavior should also be observed with generic potentials and for D-dimensional systems. Consequently, quantum N-body bound states might be interesting places to look at nontrivial manifestations of a minimal length, since the more particles that are present, the more the system deviates from standard quantum-mechanical predictions.
Test-state approach to the quantum search problem
International Nuclear Information System (INIS)
Sehrawat, Arun; Nguyen, Le Huy; Englert, Berthold-Georg
2011-01-01
The search for 'a quantum needle in a quantum haystack' is a metaphor for the problem of finding out which one of a permissible set of unitary mappings - the oracles - is implemented by a given black box. Grover's algorithm solves this problem with quadratic speedup as compared with the analogous search for 'a classical needle in a classical haystack'. Since the outcome of Grover's algorithm is probabilistic - it gives the correct answer with high probability, not with certainty - the answer requires verification. For this purpose we introduce specific test states, one for each oracle. These test states can also be used to realize 'a classical search for the quantum needle' which is deterministic - it always gives a definite answer after a finite number of steps - and 3.41 times as fast as the purely classical search. Since the test-state search and Grover's algorithm look for the same quantum needle, the average number of oracle queries of the test-state search is the classical benchmark for Grover's algorithm.
Bally, B.; Duguet, T.
2018-02-01
Background: State-of-the-art multi-reference energy density functional calculations require the computation of norm overlaps between different Bogoliubov quasiparticle many-body states. It is only recently that the efficient and unambiguous calculation of such norm kernels has become available under the form of Pfaffians [L. M. Robledo, Phys. Rev. C 79, 021302 (2009), 10.1103/PhysRevC.79.021302]. Recently developed particle-number-restored Bogoliubov coupled-cluster (PNR-BCC) and particle-number-restored Bogoliubov many-body perturbation (PNR-BMBPT) ab initio theories [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] make use of generalized norm kernels incorporating explicit many-body correlations. In PNR-BCC and PNR-BMBPT, the Bogoliubov states involved in the norm kernels differ specifically via a global gauge rotation. Purpose: The goal of this work is threefold. We wish (i) to propose and implement an alternative to the Pfaffian method to compute unambiguously the norm overlap between arbitrary Bogoliubov quasiparticle states, (ii) to extend the first point to explicitly correlated norm kernels, and (iii) to scrutinize the analytical content of the correlated norm kernels employed in PNR-BMBPT. Point (i) constitutes the purpose of the present paper while points (ii) and (iii) are addressed in a forthcoming paper. Methods: We generalize the method used in another work [T. Duguet and A. Signoracci, J. Phys. G 44, 015103 (2017), 10.1088/0954-3899/44/1/015103] in such a way that it is applicable to kernels involving arbitrary pairs of Bogoliubov states. The formalism is presently explicated in detail in the case of the uncorrelated overlap between arbitrary Bogoliubov states. The power of the method is numerically illustrated and benchmarked against known results on the basis of toy models of increasing complexity. Results: The norm overlap between arbitrary Bogoliubov product states is obtained under a closed
Quantum method of the inverse scattering problem. Pt. 1
International Nuclear Information System (INIS)
Sklyamin, E.K.; Takhtadzhyan, L.A.; Faddeev, L.D.
1978-12-01
In this work the authors use a formulation for the method of the inverse scattering problem for quantum-mechanical models of the field theory, that can be found in a quantization of these fully integrable systems. As the most important example serves the system (sinγ) 2 with the movement equation: γtt -γxx + m 2 /β sinβγ = 0 that is known under the specification Sine-Gordon-equation. (orig.) [de
Many-body and spin-orbit aspects of the alternating current phenomena
Glenn, Rachel M.
The thesis reports on research in the general field of light interaction with matter. According to the topics addressed, it can be naturally divided into two parts: Part I, many-body aspects of the Rabi oscillations which a two-level systems undergoes under a strong resonant drive; and Part II, absorption of the ac field between the spectrum branches of two-dimensional fermions that are split by the combined action of Zeeman and spin-orbit (SO) fields. The focus of Part I is the following many-body effects that modify the conventional Rabi oscillations: Chapter 1, coupling of a two-level system to a single vibrational mode of the environment. Chapter 2, correlated Rabi oscillations in two electron-hole systems coupled by tunneling with strong electron-hole attraction. In Chapter 1, a new effect of Rabi-vibronic resonance is uncovered. If the frequency of the Rabi oscillations, OR, is close to the frequency o0 of the vibrational mode, the oscillations acquire a collective character. It is demonstrated that the actual frequency of the collective oscillations exhibits a bistable behavior as a function of OR - o0. The main finding in Chapter 2 is, that the Fourier spectrum of the Rabi oscillations in two coupled electron-hole systems undergoes a strong transformation with increasing O R. For OR smaller than the tunneling frequency, the spectrum is dominated by a low-frequency (Rabi oscillations are restored only as OR exceeds the electron-hole attraction strength. The highlight of Part II is a finding that, while the spectrum of absorption between either Zeeman-split branches or SO-split branches is close to a delta-peak, in the presence of both, it transforms into a broad line with singular behavior at the edges. In particular, when the magnitudes of Zeeman and SO are equal, absorption of very low (much smaller than the splitting) frequencies become possible. The shape of the absorption spectrum is highly anisotropic with respect to the exciting field. This peculiar
Daily, Kevin Michael
Underlying the many-body effects of ultracold atomic gases are the few-body dynamics and interparticle interactions. Moreover, the study of few-body systems on their own has accelerated due to confining few atoms in each well of a deep optical lattice or in a single microtrap. This thesis studies the microscopic properties of few-body systems under external spherically symmetric harmonic confinement and how the few-body properties translate to the many-body system. Bosonic and fermionic few-body systems are considered and the dependence of the energetics and other quantities are investigated as functions of the s-wave scattering length, the mass ratio and the temperature. It is found that the condensate fraction of a weakly-interacting trapped Bose gas depletes quadratically with the s-wave scattering length. The next order term in the depletion depends not only, as might be expected naively, on the s-wave scattering length and the effective range but additionally on a two-body parameter that is not needed to reproduce the energy of weakly-interacting trapped Bose gases. This finding has important implications for effective field theory treatments of the system. Weakly-interacting atomic and molecular two-component Fermi gases with equal masses are described using perturbative approaches. The energy shifts are tabulated and interpreted, and a measure of the molecular condensate fraction is developed. We develop a measure of the molecular condensate fraction using the two-body density matrix and we develop a model of the spherical component of the momentum distribution that agrees well with stochastic variational calculations. We establish the existence of intersystem degeneracies for equal mass two-component Fermi gases with zero-range interactions, where the eigen energies of the spin-imbalanced system are degenerate with a subset of the eigen energies of the more spin-balanced system and the same total number of fermions. For unequal mass two-component Fermi
Rare events in many-body systems: reactive paths and reaction constants for structural transitions
International Nuclear Information System (INIS)
Picciani, M.
2012-01-01
This PhD thesis deals with the study of fundamental physics phenomena, with applications to nuclear materials of interest. We have developed methods for the study of rare events related to thermally activated structural transitions in many body systems. The first method involves the numerical simulation of the probability current associated with reactive paths. After deriving the evolution equations for the probability current, a Diffusion Monte Carlo algorithm is implemented in order to sample this current. This technique, called Transition Current Sampling was applied to the study of structural transitions in a cluster of 38 atoms with Lennard-Jones potential (LJ-38). A second algorithm, called Transition Path Sampling with local Lyapunov bias (LyTPS), was then developed. LyTPS calculates reaction rates at finite temperature by following the transition state theory. A statistical bias based on the maximum local Lyapunov exponents is introduced to accelerate the sampling of reactive trajectories. To extract the value of the equilibrium reaction constants obtained from LyTPS, we use the Multistate Bennett Acceptance Ratio. We again validate this method on the LJ-38 cluster. LyTPS is then used to calculate migration constants for vacancies and divacancies in the α-Iron, and the associated migration entropy. These constants are used as input parameter for codes modeling the kinetic evolution after irradiation (First Passage Kinetic Monte Carlo) to reproduce numerically resistivity recovery experiments in α-Iron. (author) [fr
Many-body localization in disorder-free systems: The importance of finite-size constraints
Energy Technology Data Exchange (ETDEWEB)
Papić, Z., E-mail: zpapic@perimeterinstitute.ca [School of Physics and Astronomy, University of Leeds, Leeds, LS2 9JT (United Kingdom); Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Stoudenmire, E. Miles [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Abanin, Dmitry A. [Department of Theoretical Physics, University of Geneva, 24 quai Ernest-Ansermet, 1211 Geneva (Switzerland); Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada)
2015-11-15
Recently it has been suggested that many-body localization (MBL) can occur in translation-invariant systems, and candidate 1D models have been proposed. We find that such models, in contrast to MBL systems with quenched disorder, typically exhibit much more severe finite-size effects due to the presence of two or more vastly different energy scales. In a finite system, this can artificially split the density of states (DOS) into bands separated by large gaps. We argue for such models to faithfully represent the thermodynamic limit behavior, the ratio of relevant coupling must exceed a certain system-size depedent cutoff, chosen such that various bands in the DOS overlap one another. Setting the parameters this way to minimize finite-size effects, we study several translation-invariant MBL candidate models using exact diagonalization. Based on diagnostics including entanglement and local observables, we observe thermal (ergodic), rather than MBL-like behavior. Our results suggest that MBL in translation-invariant systems with two or more very different energy scales is less robust than perturbative arguments suggest, possibly pointing to the importance of non-perturbative effects which induce delocalization in the thermodynamic limit.
Many-body excitations and deexcitations in trapped ultracold bosonic clouds
Theisen, Marcus; Streltsov, Alexej I.
2016-11-01
We employ the multiconfigurational time-dependent Hartree for bosons (MCTDHB) method to study excited states of interacting Bose-Einstein condensates confined by harmonic and double-well trap potentials. Two approaches to access excitations, one static and the other dynamic, are investigated and contrasted. In static simulations the low-lying excitations are computed by utilizing a linear-response theory constructed on top of a static MCTDHB solution (LR-MCTDHB). Complimentarily, we propose two dynamic protocols that address excitations by propagating the MCTDHB wave function. In particular, we investigate dipolelike oscillations induced by shifting the origin of the confining potential and breathinglike excitations by quenching the frequency of a parabolic part of the trap. To contrast static predictions and dynamic results we compute the time evolution and regard the respective Fourier transform of several local and nonlocal observables. Namely, we study the expectation value of the position operator , its variance Var [x (t )] , and a local density computed at selected positions. We find that the variance is the most sensitive and informative quantity: Along with excitations it contains information about deexcitations even in a linear regime of the induced dynamics. The dynamic protocols are found to access the many-body excitations predicted by the static LR-MCTDHB approach.
Relativistic many-body calculations of magnetic dipole transitions in Be-like ions
International Nuclear Information System (INIS)
Safronova, U.I.; Johnson, W.R.; Derevianko, A.
1999-01-01
Reduced matrix elements and transition rates are calculated for all magnetic dipole (M1) transitions within 2l2l' configurations and for some 2l3l'-2l2l' transitions in Be-like ions with nuclear charges ranging from Z = 4 to 100. Many-body perturbation theory (MBPT), including the Breit interaction, is used to evaluate retarded M1 matrix elements. The calculations start with a (1s) 2 Dirac-Fock potential and include all possible n = 2 configurations, leading to 4 odd-parity and 6 even-parity states, and some n = 3 configurations. First-order perturbation theory is used to obtain intermediate coupling coefficients. Second-order MBPT is used to determine the matrix elements, which are evaluated for all 11 M1 transitions within 2l2l' configurations and for 35 M1 transitions between 2l3l' and 2l2l' states. The transition energies used in the calculation of oscillator strengths and transition rates are obtained from second-order MBPT. The importance of negative-energy contributions to M1 transition amplitudes is discussed. (orig.)
Many-body dynamics of holes in a driven, dissipative spin chain of Rydberg superatoms
Letscher, Fabian; Petrosyan, David; Fleischhauer, Michael
2017-11-01
Strong, long-range interactions between atoms in high-lying Rydberg states can suppress multiple Rydberg excitations within a micron-sized trapping volume and yield sizable Rydberg level shifts at larger distances. Ensembles of atoms in optical microtraps then form Rydberg superatoms with collectively enhanced transition rates to the singly excited state. These superatoms can represent mesoscopic, strongly interacting spins. We study a regular array of such effective spins driven by a laser field tuned to compensate the interaction-induced level shifts between neighboring superatoms. During the initial transient, a few excited superatoms seed a cascade of resonantly facilitated excitation of large clusters of superatoms. Due to spontaneous decay, the system then relaxes to the steady state having nearly universal Rydberg excitation density {ρ }{{R}}=2/3. This state is characterized by highly non-trivial equilibrium dynamics of quasi-particles—excitation holes in the lattice of Rydberg excited superatoms. We derive an effective many-body model that accounts for hole mobility as well as continuous creation and annihilation of holes upon collisions with each other. We find that holes exhibit a nearly incompressible liquid phase with highly sub-Poissonian number statistics and finite-range density-density correlations.
Evidence for many-body interactions in the structure of molten alkali chlorides
International Nuclear Information System (INIS)
Malescio, G.P.; Tosi, M.P.
1985-02-01
An inversion of the measured partial structure factors of molten sodium chloride is attempted in order to assess some qualitative features of interionic forces in the melt. We start from a calculation of liquid structure and thermodynamic properties by means of a refined theory based on interionic pair potentials determined from properties of the solid phase. This yields very good agreement with the measured values of the internal energy and the compressibility of the liquid, whereas discrepancies with the observed structure are mainly localized in the region of interionic distances outside the minimum of the cation-anion potential. These discrepancies, when interpreted in terms of effective pair potentials in the melt through inversion of the structural data, strongly suggest the presence of many-body effects, insofar as such effective pair potentials oscillate with the local liquid structure and are inconsistent with the measured thermodynamic quantities. A similar analysis of data on molten rubidium and cesium chloride, though harder to carry out quantitatively, supports the above conclusion. (author)
Comparison of many bodied and binary collision cascade models up to 1 keV
International Nuclear Information System (INIS)
Schwartz, D.M.; Schiffgens, J.D.; Doran, D.G.; Odette, G.R.; Ariyasu, R.G.
1976-01-01
A quasi-dynamical code ADDES has been developed to model displacement cascades in copper for primary knockon atom energies up to several keV. ADDES is like a dynamical code in that it employs a many body treatment, yet similar to a binary collision code in that it incorporates the basic assumption that energy transfers below several eV can be ignored in describing cascade evolution. This paper is primarily concerned with (1) a continuing effort to validate the assumptions and specific parameters in the code by the comparison of ADDES results with experiment and with results from a dynamical code, and (2) comparisons of ADDES results with those from a binary collision code. The directional dependence of the displacement threshold is in reasonable agreement with the measurements of Jung et al. The behavior of focused replacement sequences is very similar to that obtained with the dynamical codes GRAPE and COMENT. Qualitative agreement was found between ADDES and COMENT for a higher energy (500 eV) defocused event while differences, still under study, are apparent in a 250 eV high index event. Comparisons of ADDES with the binary collision code MARLOWE show surprisingly good agreement in the 250 to 1000 eV range for both number and separation of Frenkel pairs. A preliminary observation, perhaps significant to displacement calculations utilizing the concept of a mean displacement energy, is the dissipation of 300 to 400 eV in a replacement sequence producing a single interstitial
Hartree–Fock many-body perturbation theory for nuclear ground-states
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Alexander Tichai
2016-05-01
Full Text Available We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree–Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.
Hartree–Fock many-body perturbation theory for nuclear ground-states
Energy Technology Data Exchange (ETDEWEB)
Tichai, Alexander, E-mail: alexander.tichai@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); Langhammer, Joachim [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany); Binder, Sven [Department of Physics and Astronomy, University of Tennessee, Knoxville, TN 37996 (United States); Physics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831 (United States); Roth, Robert, E-mail: robert.roth@physik.tu-darmstadt.de [Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt (Germany)
2016-05-10
We investigate the order-by-order convergence behavior of many-body perturbation theory (MBPT) as a simple and efficient tool to approximate the ground-state energy of closed-shell nuclei. To address the convergence properties directly, we explore perturbative corrections up to 30th order and highlight the role of the partitioning for convergence. The use of a simple Hartree–Fock solution for the unperturbed basis leads to a convergent MBPT series for soft interactions, in contrast to the divergent MBPT series obtained with a harmonic oscillator basis. For larger model spaces and heavier nuclei, where a direct high-order MBPT calculation is not feasible, we perform third-order calculations and compare to advanced ab initio coupled-cluster results for the same interactions and model spaces. We demonstrate that third-order MBPT provides ground-state energies for nuclei up into the tin isotopic chain in excellent agreement with the best available coupled-cluster calculations at a fraction of the computational cost.
Density functional approach to many-body effects in the optical response of atoms
International Nuclear Information System (INIS)
Zangwill, A.
1981-01-01
The purpose of this work is to present a new method for calculating the optical response of finite electronic system which is accurate, computationally simple, and lends itself to a ready physical interpretation of the results. This work is concerned with the so-called many-body effects which render an independent particle calculation inappropriate for comparison with experimental photoabsorption and photoemission cross sections. Polarization effects are included which describe the response of the system to an external probe and self-energy effects, which describe the dynamics and decay of a single particle state. This work, which essentially reintroduces the residual Coulomb interactions among the electrons, is confined to atoms. The method is a time-dependent local density approximation (TDLDA) and represents a natural generalization of the usual local density approximation to the ground state properties of a many electron system. Using standard first-order time-dependent perturbation theory, a self-consistent mean field theory is derived for an effective field which replaces the external field in the dipole matrix elements of the Golden Rule for photoabsorption. This effective field includes a contribution from an induced classical Coulomb field as well as an induced exchange-correlation field. This work successfully demonstrates the applicability of time-dependent generalization of the local density approximation to the practical calculation of the photo-response of atoms. For the rare gases, barium, cerium and copper are obtained cross sections in quantitative agreement with recent experiments
International Nuclear Information System (INIS)
Hansen, Katja; Biegler, Franziska; Ramakrishnan, Raghunathan; Pronobis, Wiktor; Lilienfeld, O. Anatole von; Müller, Klaus-Robert; Tkatchenko, Alexandre
2015-01-01
Simultaneously accurate and efficient prediction of molecular properties throughout chemical compound space is a critical ingredient toward rational compound design in chemical and pharmaceutical industries. Aiming toward this goal, we develop and apply a systematic hierarchy of efficient empirical methods to estimate atomization and total energies of molecules. These methods range from a simple sum over atoms, to addition of bond energies, to pairwise interatomic force fields, reaching to the more sophisticated machine learning approaches that are capable of describing collective interactions between many atoms or bonds. In the case of equilibrium molecular geometries, even simple pairwise force fields demonstrate prediction accuracy comparable to benchmark energies calculated using density functional theory with hybrid exchange-correlation functionals; however, accounting for the collective many-body interactions proves to be essential for approaching the 'holy grail' of chemical accuracy of 1 kcal/mol for both equilibrium and out-of-equilibrium geometries. This remarkable accuracy is achieved by a vectorized representation of molecules (so-called Bag of Bonds model) that exhibits strong nonlocality in chemical space. The same representation allows us to predict accurate electronic properties of molecules, such as their polarizability and molecular frontier orbital energies
Wzgarda-Raj, Kinga; Rybarczyk-Pirek, Agnieszka J; Wojtulewski, Sławomir; Palusiak, Marcin
2018-02-01
Pentachloropyridine N-oxide, C 5 Cl 5 NO, crystallizes in the monoclinic space group P2 1 /c. In the crystal structure, molecules are linked by C-Cl...Cl halogen bonds into infinite ribbons extending along the crystallographic [100] direction. These molecular aggregates are further stabilized by very short intermolecular N-oxide-N-oxide interactions into herringbone motifs. Computations based on quantum chemistry methods allowed for a more detailed description of the N-oxide-N-oxide interactions and Cl...Cl halogen bonds. For this purpose, Hirshfeld surface analysis and the many-body approach to interaction energy were applied.
Energy Technology Data Exchange (ETDEWEB)
Issaoui, Noureddine, E-mail: issaoui-noureddine@yahoo.fr; Abdessalem, Kawther; Ghalla, Houcine [Faculty of Sciences, Quantum Physics Laboratory, University of Monastir, Monastir 5079 (Tunisia); Yaghmour, Saud Jamil [Faculty of Science, King Abdul-Aziz University, Jeddah (Saudi Arabia); Calvo, Florent [University of Grenoble Alpes, LIPHY, F-38000 Grenoble, France and CNRS, LIPHY, F-38000 Grenoble (France); Oujia, Brahim [Faculty of Sciences, Quantum Physics Laboratory, University of Monastir, Monastir 5079 (Tunisia); Faculty of Science, King Abdul-Aziz University, Jeddah (Saudi Arabia)
2014-11-07
The solvation of the Na{sup +} ion in helium clusters has been studied theoretically using optimization methods. A many-body empirical potential was developed to account for Na{sup +}–He and polarization interactions, and the most stable structures of Na{sup +}He{sub n} clusters were determined using the basin-hopping method. Vibrational delocalization was accounted for using zero-point energy corrections at the harmonic or anharmonic levels, the latter being evaluated from quantum Monte Carlo simulations for spinless particles. From the static perspective, many-body effects are found to play a minor role, and the structures obtained reflect homogeneous covering up to n = 10, followed by polyicosahedral packing above this size, the cluster obtained at n = 12 appearing particularly stable. The cationic impurity binds the closest helium atoms sufficiently to negate vibrational delocalization at small sizes. However, this snowball effect is obliterated earlier than shell completion, the nuclear wavefunctions of {sup 4}He{sub n}Na{sup +} with n = 5–7, and n > 10 already exhibiting multiple inherent structures. The decrease in the snowball size due to many-body effects is consistent with recent mass spectrometry measurements.
Scaling the robustness of the solutions for quantum controllable problems
International Nuclear Information System (INIS)
Kallush, S.; Kosloff, R.
2011-01-01
The major task in quantum control theory is to find an external field that transforms the system from one state to another or executes a predetermined unitary transformation. We investigate the difficulty of computing the control field as the size of the Hilbert space is increased. In the models studied the controls form a small closed subalgebra of operators. Complete controllability is obtained by the commutators of the controls with the stationary Hamiltonian. We investigate the scaling of the computation effort required to converge a solution for the quantum control task with respect to the size of the Hilbert space. The models studied include the double-well Bose Hubbard model with the SU(2) control subalgebra and the Morse oscillator with the Heisenberg-Weil algebra. We find that for initial and target states that are classified as generalized coherent states (GCSs) of the control subalgebra the control field is easily found independent of the size of the Hilbert space. For such problems, a control field generated for a small system can serve as a pilot for finding the field for larger systems. Attempting to employ pilot fields that generate superpositions of GCSs or cat states failed. No relation was found between control solutions of different Hilbert space sizes. In addition the task of finding such a field scales unfavorably with Hilbert space sizes. We demonstrate the use of symmetry to obtain quantum transitions between states without phase information. Implications to quantum computing are discussed.
Many-body pairing in a two-dimensional Fermi gas
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Neidig, Mathias
2017-05-24
This thesis reports on experiments conducted in a single layer, quasi two-dimensional, two-component ultracold Fermi gas in the strongly interacting regime. Ultracold gases can be used to simulate key aspects of more complicated systems like for example cuprates which show high-T{sub c} superconductivity. The momentum distribution of a sample of bosonic dimers in a quasi-2D square lattice geometry was measured to obtain the coherence properties. For shallow lattices, sharp peaks in the momentum distribution, indicating coherence, were observed at zero momentum as well as at positive and negative lattice momenta along each axis. For deeper lattices, heating impeded the ability to prepare a Mott-insulator. A spatially resolved radio-frequency spectroscopy was employed for a quasi-2D Fermi gas in the normal phase throughout the BEC-BCS crossover. The interaction induced energy shifts were measured in the strongly interacting region where they can be on the order of the Fermi energy and thus the local resolution is crucial. Furthermore, the onset of pairing in the strongly interacting region was measured as a function of temperature and it was shown that the fraction of free atoms decreases faster than expected from thermal non-interacting theory. At last, the pairing gap was measured using an imbalanced sample. On the BEC side it was found to be in very good agreement with two-body physics as expected. In the strongly interacting regime, however, a deviation from two-body physics indicates that here many-body effects play a role and thus further studies are required.
Hallez, Yannick; Meireles, Martine
2016-10-11
Electrostatic interactions play a key role in hollow shell suspensions as they determine their structure, stability, thermodynamics, and rheology and also the loading capacity of small charged species for nanoreservoir applications. In this work, fast, reliable modeling strategies aimed at predicting the electrostatics of hollow shells for one, two, and many colloids are proposed and validated. The electrostatic potential inside and outside a hollow shell with a finite thickness and a specific permittivity is determined analytically in the Debye-Hückel (DH) limit. An expression for the interaction potential between two such hollow shells is then derived and validated numerically. It follows a classical Yukawa form with an effective charge depending on the shell geometry, permittivity, and inner and outer surface charge densities. The predictions of the Ornstein-Zernike (OZ) equation with this pair potential to determine equations of state are then evaluated by comparison to results obtained with a Brownian dynamics algorithm coupled to the resolution of the linearized Poisson-Boltzmann and Laplace equations (PB-BD simulations). The OZ equation based on the DLVO-like potential performs very well in the dilute regime as expected, but also quite well, and more surprisingly, in the concentrated regime in which full spheres exhibit significant many-body effects. These effects are shown to vanish for shells with small thickness and high permittivity. For highly charged hollow shells, we propose and validate a charge renormalization procedure. Finally, using PB-BD simulations, we show that the cell model predicts the ion distribution inside and outside hollow shells accurately in both electrostatically dilute and concentrated suspensions. We then determine the shell loading capacity as a function of salt concentration, volume fraction, and surface charge density for nanoreservoir applications such as drug delivery, sensing, or smart coatings.
Many-body calculation of the coincidence L3 photoelectron spectroscopy main line of Ni metal
International Nuclear Information System (INIS)
Ohno, Masahide
2008-01-01
The partial singles L 3 photoelectron spectroscopy (PES) main line of Ni metal correlated with Auger electrons emitted by the localized L 3 -VV Auger decay is calculated by a many-body theory. The partial singles L 3 PES main line of Ni metal almost coincides in both line shape and peak kinetic energy (KE) with the singles one. The former main line peak shows a KE shift of only 0.01 eV toward the lower KE and a very small asymmetric line shape change compared to the singles one. The asymmetric line shape change and the peak KE shift of the partial singles L 3 main line are very small. However, they are due to the variation with photoelectron KE in the branching ratio of the partial Auger decay width in the partial singles L 3 PES main line by the photoelectron KE dependent imaginary part of the shakeup self-energy. The L 3 PES main line of Ni metal measured in coincidence with the L 3 -VV ( 1 G) Auger electron spectroscopy (AES) main line peak is the partial singles one modulated by a spectral function R a of a fixed energy Auger electron analyzer so that it should show only a symmetric line narrowing by R a compared to the singles one. The L 3 PES main line peak of Ni metal measured in coincidence with the delocalized band-like L 3 -VV AES peak or not completely split-off (or not completely localized) L 3 -VV ( 3 F) AES peak, will show an asymmetric line narrowing and a KE shift compared to the singles one. Thus, the L 3 PES main line of Ni metal in coincidence with various parts of the L 3 -VV AES spectrum depends on which part of the L 3 -VV AES spectrum a fixed energy Auger electron analyzer is set. The experimental verification is in need
Time-dependent, many-body scattering theory and nuclear reaction applications
International Nuclear Information System (INIS)
Levin, F.S.
1977-01-01
The channel component state form of the channel coupling array theory of many-body scattering is briefly reviewed. These states obey a non-hermitian matrix equation whose exact solution yields the Schroedinger eigenstates, eigenvalues and scattering amplitudes. A time-dependent formulation of the theory is introduced in analogy to the time-dependent Schrodinger equation and several consequences of the development are noted. These include an interaction picture, a single (matrix) S operator, and the usual connection between the t = 0 time-dependent and the time-independent scattering states. Finally, the channel component states (psi/sub j/) are shown to have the useful property that only psi/sub j/ has (two-body) outgoing waves in channel j: psi/sub m/, m not equal to j, is asymptotically zero in two-body channel j. This formalism is then considered as a means for direct nuclear reaction analysis. Typical bound state approximations are introduced and it is shown that a DWBA amplitude occurs in only one channel. The non-time-reversal invariance of the approximate theory is noted. Results of calculations based on a realistic model for two sets of light-ion induced, one-particle transfer reactions are discussed and compared with the coupled reaction channel (CRC) results using the CRC procedure of Cotanch and Vincent. Angular distributions for the two calculational methods are found to be similar in shape and magnitude. Higher ordercorrections are small as are time-reversal non-invariant effects. Post- and prior-type CRC calculations are seen to differ; the latter are closer to the full CRC results
International Nuclear Information System (INIS)
Griffin, J.J.; Lichtner, P.C.; Dworzecka, M.; Kan, K.K.
1979-01-01
The restrictions implied for the time dependent many-body reaction theory by the (TDHF) single determinantal assumption are explored by constructive analysis. A restructured TD-S-HF reaction theory is modelled, not after the initial-value form of the Schroedinger reaction theory, but after the (fully equivalent) S-matrix form, under the conditions that only self-consistent TDHF solutions occur in the theory, every wave function obeys the fundamental statistical interpretation of quantum mechanics, and the theory reduces to the exact Schroedinger theory for exact solutions which are single determinantal. All of these conditions can be accomodated provided that the theory is interpreted on a time-averaged basis, i.e., physical constants of the Schroedinger theory which are time-dependent in the TDHF theory, are interpreted in TD-S-HF in terms of their time averaged values. The resulting reaction theory, although formulated heuristically, prescribes a well defined and unambiguous calculational program which, although somewhat more demanding technically than the conventional initial-value TDHF method, is nevertheless more consonant with first principles, structurally and mechanistically. For its physical predictions do not depend upon the precise location of the distant measuring apparatus, and are in no way influenced by the spurious cross channel correlations which arise whenever the description of many reaction channels is imposed upon one single-determinantal solution. For nuclear structure physics, the TDHF-eigenfunctions provide the first plausible description of exact eigenstates in the time-dependent framework; moreover, they are unencumbered by any restriction to small amplitudes. 14 references
On the problem of existence of quantum field theory
International Nuclear Information System (INIS)
Chaichian, M.; Hayashi, M.; Nelipa, N.F.; Pukhov, E.A.
1978-01-01
Existence of quantum field theory is considered for the four-dimensional phi 3 -model. The mathematical tool of contraction mapping principle is used to investigate the question of existence of solution for the infinite system of coupled equations for the Green functions of the theory in the Euclidean region. Formulation of the problem for this model with one divergent part is interesting in itself and provides the first attempt towards the study of other renormalizable quantum field theory models with infinite number of divergent graphs. For sufficiently small values of coupling constant, the theory has a unique solution for the truncated system of equations for the Green functions. However, for the complete, infinite set of equations, the Banach fixed point theorem admits a solution only when the coupling constant tends to zero. Possible reasons for such a result are discussed. (author)
Moment problems and the causal set approach to quantum gravity
International Nuclear Information System (INIS)
Ash, Avner; McDonald, Patrick
2003-01-01
We study a collection of discrete Markov chains related to the causal set approach to modeling discrete theories of quantum gravity. The transition probabilities of these chains satisfy a general covariance principle, a causality principle, and a renormalizability condition. The corresponding dynamics are completely determined by a sequence of non-negative real coupling constants. Using techniques related to the classical moment problem, we give a complete description of any such sequence of coupling constants. We prove a representation theorem: every discrete theory of quantum gravity arising from causal set dynamics satisfying covariance, causality, and renormalizability corresponds to a unique probability distribution function on the non-negative real numbers, with the coupling constants defining the theory given by the moments of the distribution
A Non-Perturbative Treatment of Quantum Impurity Problems in Real Lattices
Allerdt, Andrew C.
Historically, the RKKY or indirect exchange, interaction has been accepted as being able to be described by second order perturbation theory. A typical universal expression is usually given in this context. This approach, however, fails to incorporate many body effects, quantum fluctuations, and other important details. In Chapter 2, a novel numerical approach is developed to tackle these problems in a quasi-exact, non-perturbative manner. Behind the method lies the main concept of being able to exactly map an n-dimensional lattice problem onto a 1-dimensional chain. The density matrix renormalization group algorithm is then employed to solve the newly cast Hamiltonian. In the following chapters, it is demonstrated that conventional RKKY theory does not capture the crucial physics. It is found that the Kondo effect, i.e. the screening of an impurity spin, tends to dominate over a ferromagnetic interaction between impurity spins. Furthermore, it is found that the indirect exchange interaction does not decay algebraically. Instead, there is a crossover upon increasing JK, where impurities favor forming their own independent Kondo states after just a few lattice spacings. This is not a trivial result, as one may naively expect impurities to interact when their conventional Kondo clouds overlap. The spin structure around impurities coupled to the edge of a 2D topological insulator is investigated in Chapter 7. Modeled after materials such as silicine, germanene, and stanene, it is shown with spatial resolution of the lattice that the specific impurity placement plays a key role. Effects of spin-orbit interactions are also discussed. Finally, in the last chapter, transition metal complexes are studied. This really shows the power and versatility of the method developed throughout the work. The spin states of an iron atom in the molecule FeN4C 10 are calculated and compared to DFT, showing the importance of inter-orbital coulomb interactions. Using dynamical DMRG, the
The measurement problem in quantum mechanics: A phenomenological investigation
Hunter, Joel Brooks
2008-10-01
This dissertation is a phenomenological investigation of the measurement problem in quantum mechanics. The primary subject matter for description and analysis is scientific instruments and their use in experiments which elicit the measurement problem. A methodological critique is mounted against the ontological commitments taken for granted in the canonical interpretations of quantum theory and the scientific activity of measurement as the necessary interface between theoretical interest and perceptual results. I argue that an aesthetic dimension of reality functions as aproto-scientific establishment of sense-making that constantly operates to set integratively all other cognitively neat determinations, including scientifically rendered objects that are intrinsically non-visualizable. The way in which data "key in" to the original and originative register of the sensible in observation is clarified by examining prostheses, measuring apparatuses and instruments that are sense-conveying and -integrative with the human sensorium. Experiments, technology and instrumentation are examined in order to understand how knowing and that which is known is bonded by praxis-aisthesis. Quantum measurement is a praxic-dynamie activity and homologically structured and structur ing functional engagement in terms of instantiation, quantifiability, and spatiotemporal differentiation. The distinctions between a beauty-aesthetic and praxis-aisthesis are delineated. It is argued that a beauty-aesthetic is a construal of the economic dimension of scientific objects and work, and is not the primary manner in which the aesthetic dimension is disclosed. The economic dimension of abstractions reduces to an austere aesthetic of calculative economy. Nature itself, however, is not stingy; it is intrinsically capacious, extravagant, full of surprise, nuance, ambiguity and allusiveness. The capaciousness of Nature and the way in which we are integratively set within Nature in a materiality