Energy Technology Data Exchange (ETDEWEB)
Rivasseau, Vincent [Paris-Sud Univ. Orsay (France). Laboratoire de Physique Theorique; Seiringer, Robert [McGill Univ., Montreal, QC (Canada). Dept. of Mathematics and Statistics; Solovej, Jan Philip [Copenhagen Univ. (Denmark). Dept. of Mathematics; Spencer, Thomas [Institute for Advanced Study, Princeton, NJ (United States). School of Mathematics
2012-11-01
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.
Non-relativistic Quantum Mechanics versus Quantum Field Theories
Pineda, Antonio
2007-01-01
We briefly review the derivation of a non-relativistic quantum mechanics description of a weakly bound non-relativistic system from the underlying quantum field theory. We highlight the main techniques used.
Quantum scaling in many-body systems
Continentino, Mucio A
2001-01-01
This book on quantum phase transitions has been written by one of the pioneers in the application of scaling ideas to many-body systems - a new and exciting subject that has relevance to many areas of condensed matter and theoretical physics. One of the few books on the subject, it emphasizes strongly correlated electronic systems. Although dealing with complex problems in statistical mechanics, it does not lose sight of the experiments and the actual physical systems which motivate the theoretical work. The book starts by presenting the scaling theory of quantum critical phenomena. Critical e
Many-body quantum interference on hypercubes
Dittel, Christoph; Keil, Robert; Weihs, Gregor
2017-03-01
Beyond the regime of distinguishable particles, many-body quantum interferences influence quantum transport in an intricate manner. However, symmetries of the single-particle transformation matrix alleviate this complexity and even allow the analytic formulation of suppression laws, which predict final states to occur with a vanishing probability due to total destructive interference. Here we investigate the symmetries of hypercube graphs and their generalisations with arbitrary identical subgraphs on all vertices. We find that initial many-particle states, which are invariant under self-inverse symmetries of the hypercube, lead to a large number of suppressed final states. The condition for suppression is determined solely by the initial symmetry, while the fraction of suppressed states is given by the number of independent symmetries of the initial state. Our findings reveal new insights into particle statistics for ensembles of indistinguishable bosons and fermions and may represent a first step towards many-particle quantum protocols in higher-dimensional structures.
Non-relativistic quantum mechanics
Puri, Ravinder R.
2017-01-01
This book develops and simplifies the concept of quantum mechanics based on the postulates of quantum mechanics. The text discusses the technique of disentangling the exponential of a sum of operators, closed under the operation of commutation, as the product of exponentials to simplify calculations of harmonic oscillator and angular momentum. Based on its singularity structure, the Schrödinger equation for various continuous potentials is solved in terms of the hypergeometric or the confluent hypergeometric functions. The forms of the potentials for which the one-dimensional Schrödinger equation is exactly solvable are derived in detail. The problem of identifying the states of two-level systems which have no classical analogy is addressed by going beyond Bell-like inequalities and separability. The measures of quantumness of mutual information in two two-level systems is also covered in detail. Offers a new approach to learning quantum mechanics based on the history of quantum mechanics and its postu...
Understanding quantum work in a quantum many-body system.
Wang, Qian; Quan, H T
2017-03-01
Based on previous studies in a single-particle system in both the integrable [Jarzynski, Quan, and Rahav, Phys. Rev. X 5, 031038 (2015)2160-330810.1103/PhysRevX.5.031038] and the chaotic systems [Zhu, Gong, Wu, and Quan, Phys. Rev. E 93, 062108 (2016)1539-375510.1103/PhysRevE.93.062108], we study the the correspondence principle between quantum and classical work distributions in a quantum many-body system. Even though the interaction and the indistinguishability of identical particles increase the complexity of the system, we find that for a quantum many-body system the quantum work distribution still converges to its classical counterpart in the semiclassical limit. Our results imply that there exists a correspondence principle between quantum and classical work distributions in an interacting quantum many-body system, especially in the large particle number limit, and further justify the definition of quantum work via two-point energy measurements in quantum many-body systems.
Symmetry and Covariance of Non-relativistic Quantum Mechanics
Omote, Minoru; kamefuchi, Susumu
2000-01-01
On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.
Measuring entanglement entropy in a quantum many-body system.
Islam, Rajibul; Ma, Ruichao; Preiss, Philipp M; Tai, M Eric; Lukin, Alexander; Rispoli, Matthew; Greiner, Markus
2015-12-01
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
Ultracold atoms for simulation of many body quantum systems
Hutchinson, David A. W.
2017-01-01
Feynman famously proposed simulating quantum physics using other, better controlled, quantum systems. This vision is now a reality within the realm of ultracold atomic physics. We discuss how these systems can be used to simulate many body physics, concentrating the Berezinskii-Kosterlitz-Thouless transition in 2D physics and the role of disorder.
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...
Computational Nuclear Quantum Many-Body Problem: The UNEDF Project
Bogner, Scott; 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; Nazarewicz, Witold; Ng, Esmond G; Nobre, Gustavo P A; Ormand, Erich; Papenbrock, Thomas; Pei, Junchen; Pieper, Steven C; Quaglioni, Sofia; Roche, Kenneth J; Sarich, Jason; Schunck, Nicolas; Sosonkina, Masha; Terasaki, Jun; Thompson, Ian J; Vary, James P; Wild, Stefan M
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.
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.
Experimental quantum simulation of entanglement in many-body systems.
Zhang, Jingfu; Wei, Tzu-Chieh; Laflamme, Raymond
2011-07-01
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudoentanglement. The observed pseudoentanglement for a small-size system already displays a singularity, a signature which is qualitatively similar to that in the thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.
Experimental Quantum Simulation of Entanglement in Many-body Systems
Zhang, Jingfu; Laflamme, Raymond
2011-01-01
We employ a nuclear magnetic resonance (NMR) quantum information processor to simulate the ground state of an XXZ spin chain and measure its NMR analog of entanglement, or pseudo-entanglement. The observed pseudo-entanglement for a small system size already displays singularity, a signature which is qualitatively similar to that in thermodynamical limit across quantum phase transitions, including an infinite-order critical point. The experimental results illustrate a successful approach to investigate quantum correlations in many-body systems using quantum simulators.
Measuring entanglement entropy in a quantum many-body system
Rispoli, Matthew; Preiss, Philipp; Tai, Eric; Lukin, Alex; Schittko, Robert; Kaufman, Adam; Ma, Ruichao; Islam, Rajibul; Greiner, Markus
2016-05-01
The presence of large-scale entanglement is a defining characteristic of exotic quantum phases of matter. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. However, measuring entanglement remains a challenge. This is especially true in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. We demonstrate a novel approach to the measurement of entanglement entropy of any bosonic system, using a quantum gas microscope with tailored potential landscapes. This protocol enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. In general, these experiments exemplify a method enabling the measurement and characterization of quantum phase transitions and in particular would be apt for studying systems such as magnetic ordering within the quantum Ising model.
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.)
Periodically driven ergodic and many-body localized quantum systems
Energy Technology Data Exchange (ETDEWEB)
Ponte, Pedro [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Department of Physics and Astronomy, University of Waterloo, ON N2L 3G1 (Canada); Chandran, Anushya [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Papić, Z., E-mail: zpapic@perimeterinstitute.ca [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Institute for Quantum Computing, Waterloo, ON N2L 3G1 (Canada); Abanin, Dmitry A. [Perimeter Institute for Theoretical Physics, Waterloo, ON N2L 2Y5 (Canada); Institute for Quantum Computing, Waterloo, ON N2L 3G1 (Canada)
2015-02-15
We study dynamics of isolated quantum many-body systems whose Hamiltonian is switched between two different operators periodically in time. The eigenvalue problem of the associated Floquet operator maps onto an effective hopping problem. Using the effective model, we establish conditions on the spectral properties of the two Hamiltonians for the system to localize in energy space. We find that ergodic systems always delocalize in energy space and heat up to infinite temperature, for both local and global driving. In contrast, many-body localized systems with quenched disorder remain localized at finite energy. We support our conclusions by numerical simulations of disordered spin chains. We argue that our results hold for general driving protocols, and discuss their experimental implications.
Scattering approach to quantum transport and many body effects
Pichard, Jean-Louis; Freyn, Axel
2010-12-01
We review a series of works discussing how the scattering approach to quantum transport developed by Landauer and Buttiker for one body elastic scatterers can be extended to the case where electron-electron interactions act inside the scattering region and give rise to many body scattering. Firstly, we give an exact numerical result showing that at zero temperature a many body scatterer behaves as an effective one body scatterer, with an interaction dependent transmission. Secondly, we underline that this effective scatterer depends on the presence of external scatterers put in its vicinity. The implications of this non local scattering are illustrated studying the conductance of a quantum point contact where electrons interact with a scanning gate microscope. Thirdly, using the numerical renormalization group developed by Wilson for the Kondo problem, we study a double dot spinless model with an inter-dot interaction U and inter-dot hopping td, coupled to leads by hopping terms tc. We show that the quantum conductance as a function of td is given by a universal function, independently of the values of U and tc, if one measures td in units of a characteristic scale τ(U,tc). Mapping the double dot system without spin onto a single dot Anderson model with spin and magnetic field, we show that τ(U,tc) = 2TK, where TK is the Kondo temperature of the Anderson model.
Quantum power functional theory for many-body dynamics
Energy Technology Data Exchange (ETDEWEB)
Schmidt, Matthias, E-mail: Matthias.Schmidt@uni-bayreuth.de [Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth (Germany)
2015-11-07
We construct a one-body variational theory for the time evolution of nonrelativistic quantum many-body systems. The position- and time-dependent one-body density, particle current, and time derivative of the current act as three variational fields. The generating (power rate) functional is minimized by the true current time derivative. The corresponding Euler-Lagrange equation, together with the continuity equation for the density, forms a closed set of one-body equations of motion. Space- and time-nonlocal one-body forces are generated by the superadiabatic contribution to the functional. The theory applies to many-electron systems.
Prediction of quantum many-body chaos in protactinium atom
Viatkina, A V; Flambaum, V V
2016-01-01
Energy level spectrum of protactinium atom (Pa, Z=91) is simulated with a CI calculation. Levels belonging to the separate manifolds of a given total angular momentum and parity $J^\\pi$ exhibit distinct properties of many-body quantum chaos. Moreover, an extremely strong enhancement of small perturbations takes place. As an example, effective three-electron interaction is investigated and found to play a significant role in the system. Chaotic properties of the eigenstates allow one to develop a statistical theory and predict probabilities of different processes in chaotic systems.
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 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.
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.
Classical simulation of quantum many-body systems
Huang, Yichen
Classical simulation of quantum many-body systems is in general a challenging problem for the simple reason that the dimension of the Hilbert space grows exponentially with the system size. In particular, merely encoding a generic quantum many-body state requires an exponential number of bits. However, condensed matter physicists are mostly interested in local Hamiltonians and especially their ground states, which are highly non-generic. Thus, we might hope that at least some physical systems allow efficient classical simulation. Starting with one-dimensional (1D) quantum systems (i.e., the simplest nontrivial case), the first basic question is: Which classes of states have efficient classical representations? It turns out that this question is quantitatively related to the amount of entanglement in the state, for states with "little entanglement'' are well approximated by matrix product states (a data structure that can be manipulated efficiently on a classical computer). At a technical level, the mathematical notion for "little entanglement'' is area law, which has been proved for unique ground states in 1D gapped systems. We establish an area law for constant-fold degenerate ground states in 1D gapped systems and thus explain the effectiveness of matrix-product-state methods in (e.g.) symmetry breaking phases. This result might not be intuitively trivial as degenerate ground states in gapped systems can be long-range correlated. Suppose an efficient classical representation exists. How can one find it efficiently? The density matrix renormalization group is the leading numerical method for computing ground states in 1D quantum systems. However, it is a heuristic algorithm and the possibility that it may fail in some cases cannot be completely ruled out. Recently, a provably efficient variant of the density matrix renormalization group has been developed for frustration-free 1D gapped systems. We generalize this algorithm to all (i.e., possibly frustrated) 1D
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...
Levy distribution in many-body quantum systems
Energy Technology Data Exchange (ETDEWEB)
Denisov, Sergey; Ponomarev, Alexey V.; Hanggi, Peter [Institute of Physics, University of Augsburg (Germany)
2010-07-01
Levy distribution is known to describe a whole range of complex phenomena: classical chaotic transport, processes of subrecoil laser cooling, fluctuations of stock market indices, time series of single molecule blinking events, bursting activity of small neuronal networks, to name a few. The appearance of Levy distribution in a system output is a strong indicator of a long-range correlation ''skeleton'' which conducts system intrinsic dynamics. Using two complimentary approaches, the canonical and the grand-canonical formalisms, we discovered that the momentum distribution of N strongly interacting (hard-core) bosons at finite temperatures confined on a one-dimensional optical lattice obeys the Levy distribution. The tunable Levy spline reproduces momentum distributions up to one recoil momentum. Our finding allows for calibration of complex quantum many-body states by using a unique scaling exponent.
Measurement of many-body chaos using a quantum clock
Zhu, Guanyu; Hafezi, Mohammad; Grover, Tarun
2016-12-01
There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time dependence of out-of-time-ordered (OTO) correlation functions such as is a faithful measure of quantum chaos. Experimentally, these correlators are challenging to access since they apparently require access to both forward and backward time evolution with the system Hamiltonian. Here we propose a protocol to measure such OTO correlators using an ancilla that controls the direction of time. Specifically, by coupling the state of the ancilla to the system Hamiltonian of interest, we can emulate the forward and backward time propagation, where the ancilla plays the role of a quantum clock. Within this scheme, the continuous evolution of the entire system (the system of interest and the ancilla) is governed by a time-independent Hamiltonian. We discuss the implementation of our protocol with current circuit-QED technology for a class of interacting Hamiltonians. Our protocol is immune to errors that could occur when the direction of time evolution is externally controlled by a classical switch.
Measurement of many-body chaos using a quantum clock
Zhu, Guanyu; Grover, Tarun
2016-01-01
There has been recent progress in understanding chaotic features in many-body quantum systems. Motivated by the scrambling of information in black holes, it has been suggested that the time dependence of out-of-time-ordered (OTO) correlation functions such as $\\langle O_2(t) O_1(0) O_2(t) O_1(0) \\rangle $ is a faithful measure of quantum chaos. Experimentally, these correlators are challenging to access since they apparently require access to both forward and backward time evolution with the system Hamiltonian. Here, we propose a protocol to measure such OTO correlators using an ancilla which controls the direction of time. Specifically, by coupling the state of ancilla to the system Hamiltonian of interest, we can emulate the forward and backward time propagation, where the ancilla plays the role of a 'quantum clock'. Within this scheme, the continuous evolution of the entire system (the system of interest and the ancilla) is governed by a time-independent Hamiltonian. Our protocol is immune to errors that c...
A Signed Particle Formulation of Non-Relativistic Quantum Mechanics
Sellier, Jean Michel
2015-01-01
A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schroedinger time-dependent wave-function. Its classical limit is discussed and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the val...
Effective approach to non-relativistic quantum mechanics
Jacobs, David M
2015-01-01
Boundary conditions on non-relativistic wavefunctions are generally not completely constrained by the basic precepts of quantum mechanics, so understanding the set of possible self-adjoint extensions of the Hamiltonian is required. For real physical systems, non-trivial self-adjoint extensions have been used to model contact potentials when those interactions are expected a priori. However, they must be incorporated into the effective description of any quantum mechanical system in order to capture possible short-distance physics that does not decouple in the low energy limit. Here, an approach is described wherein an artificial boundary is inserted at an intermediate scale on which boundary conditions may encode short-distance effects that are hidden behind the boundary. Using this approach, an analysis is performed of the free particle, harmonic oscillator, and Coulomb potential in three dimensions. Requiring measurable quantities, such as spectra and cross sections, to be independent of this artificial bou...
Geometric methods for nonlinear many-body quantum systems
Lewin, Mathieu
2010-01-01
Geometric techniques have played an important role in the seventies, for the study of the spectrum of many-body Schr\\"odinger operators. In this paper we provide a formalism which also allows to study nonlinear systems. We start by defining a weak topology on many-body states, which appropriately describes the physical behavior of the system in the case of lack of compactness, that is when some particles are lost at infinity. We provide several important properties of this topology and use them to provide a simple proof of the famous HVZ theorem in the repulsive case. In a second step we recall the method of geometric localization in Fock space as proposed by Derezi\\'nski and G\\'erard, and we relate this tool to our weak topology. We then provide several applications. We start by studying the so-called finite-rank approximation which consists in imposing that the many-body wavefunction can be expanded using finitely many one-body functions. We thereby emphasize geometric properties of Hartree-Fock states and ...
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.
General coordinate invariance in quantum many-body systems
Brauner, Tomas; Monin, Alexander; Penco, Riccardo
2014-01-01
We extend the notion of general coordinate invariance to many-body, not necessarily relativistic, systems. As an application, we investigate nonrelativistic general covariance in Galilei-invariant systems. The peculiar transformation rules for the background metric and gauge fields, first introduced by Son and Wingate in 2005 and refined in subsequent works, follow naturally from our framework. Our approach makes it clear that Galilei or Poincare symmetry is by no means a necessary prerequisite for making the theory invariant under coordinate diffeomorphisms. General covariance merely expresses the freedom to choose spacetime coordinates at will, whereas the true, physical symmetries of the system can be separately implemented as "internal" symmetries within the vielbein formalism. A systematic way to implement such symmetries is provided by the coset construction. We illustrate this point by applying our formalism to nonrelativistic s-wave superfluids.
Virial Theorem for Non-relativistic Quantum Fields in D Spatial Dimensions
Lin, Chris L
2015-01-01
The virial theorem for non-relativistic complex fields in $D$ spatial dimensions and with arbitrary many-body potential is derived, using path-integral methods and scaling arguments recently developed to analyze quantum anomalies in lower-dimensional systems. The potential appearance of a Jacobian $J$ due to a change of variables in the path-integral expression for the partition function of the system is pointed out, although in order to make contact with the literature most of the analysis deals with the $J=1$ case. The virial theorem is recast into a form that displays the effect of microscopic scales on the thermodynamics of the system. From the point of view of this paper the case usually considered, $J=1$, is not natural, and the generalization to the case $J\
Preparation of many-body states for quantum simulation
Ward, Nicholas J.; Kassal, Ivan; Aspuru-Guzik, Alán
2009-05-01
While quantum computers are capable of simulating many quantum systems efficiently, the simulation algorithms must begin with the preparation of an appropriate initial state. We present a method for generating physically relevant quantum states on a lattice in real space. In particular, the present algorithm is able to prepare general pure and mixed many-particle states of any number of particles. It relies on a procedure for converting from a second-quantized state to its first-quantized counterpart. The algorithm is efficient in that it operates in time that is polynomial in all the essential descriptors of the system, the number of particles, the resolution of the lattice, and the inverse of the maximum final error. This scaling holds under the assumption that the wave function to be prepared is bounded or its indefinite integral is known and that the Fock operator of the system is efficiently simulatable.
Quantum optical feedback control for creating strong correlations in many-body systems
Mazzucchi, Gabriel; Ivanov, Denis A; Mekhov, Igor B
2016-01-01
Light enables manipulating many-body states of matter, and atoms trapped in optical lattices is a prominent example. However, quantum properties of light are completely neglected in all quantum gas experiments. Extending methods of quantum optics to many-body physics will enable phenomena unobtainable in classical optical setups. We show how using the quantum optical feedback creates strong correlations in bosonic and fermionic systems. It balances two competing processes, originating from different fields: quantum backaction of weak optical measurement and many-body dynamics, resulting in stabilized density waves, antiferromagnetic and NOON states. Our approach is extendable to other systems promising for quantum technologies.
Dissipative effects in dipolar, quantum many-body systems
Safavi-Naini, Arghavan; Capogrosso-Sansone, Barbara; Rey, Ana Maria
2015-03-01
We use Quantum Monte Carlo simulations, by the Worm algorithm, to study the ground state phase diagram of two-dimensional, dipolar lattice bosons where each site is coupled, via density operators, to an external reservoir. A recent related study of the XXZ model with ohmic coupling to an external reservoir reported the existence of a bath-induced Bose metal phase in the ground state phase diagram away from half filling, and a Luttinger liquid and a charge density wave at half-filling. Our work extends this methodology to higher dimensional systems with long-range interactions. In the case of hard-core bosons, our method can be applied to experimental systems featuring dipolar fermionic molecules in the presence of losses. This work utilized the Janus supercomputer, which is supported by the NSF (award number CNS-0821794) and the University of Colorado Boulder, and is a joint effort with the University of Colorado Denver and the National Center for Atmospheric Research, as well as OU Supercomputing Center for Education and Research (OSCER) at the University of Oklahoma. NIST, JILA-NSF-PFC-1125844, NSF-PIF-1211914, NSF-PHY11-25915, ARO, ARO-DARPA-OLE, AFOSR, AFOSR-MURI.
Quantum effects in many-body gravitating systems
Golovko, V A
2015-01-01
A hierarchy of equations for equilibrium reduced density matrices obtained earlier is used to consider systems of spinless bosons bound by forces of gravity alone. The systems are assumed to be at absolute zero of temperature under conditions of Bose condensation. In this case, a peculiar interplay of quantum effects and of very weak gravitational interaction between microparticles occurs. As a result, there can form spatially-bounded equilibrium structures macroscopic in size, both immobile and rotating. The size of a structure is inversely related to the number of particles in the structure. When the number of particles is relatively small the size can be enormous, whereas if this numbder equals Avogadro's number the radius of the structure is about 30 cm in the case that the structure consists of hydrogen atoms. The rotating objects have the form of rings and exhibit superfluidity. An atmosphere that can be captured by tiny celestial bodies from the ambient medium is considered too. The thickness of the at...
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.
Estimates on Functional Integrals of Quantum Mechanics and Non-relativistic Quantum Field Theory
Bley, Gonzalo A.; Thomas, Lawrence E.
2017-01-01
We provide a unified method for obtaining upper bounds for certain functional integrals appearing in quantum mechanics and non-relativistic quantum field theory, functionals of the form {E[{exp}(A_T)]} , the (effective) action {A_T} being a function of particle trajectories up to time T. The estimates in turn yield rigorous lower bounds for ground state energies, via the Feynman-Kac formula. The upper bounds are obtained by writing the action for these functional integrals in terms of stochastic integrals. The method is illustrated in familiar quantum mechanical settings: for the hydrogen atom, for a Schrödinger operator with {1/|x|^2} potential with small coupling, and, with a modest adaptation of the method, for the harmonic oscillator. We then present our principal applications of the method, in the settings of non-relativistic quantum field theories for particles moving in a quantized Bose field, including the optical polaron and Nelson models.
Quantum statistical gravity: time dilation due to local information in many-body quantum systems
Sels, Dries; Wouters, Michiel
2017-08-01
We propose a generic mechanism for the emergence of a gravitational potential that acts on all classical objects in a quantum system. Our conjecture is based on the analysis of mutual information in many-body quantum systems. Since measurements in quantum systems affect the surroundings through entanglement, a measurement at one position reduces the entropy in its neighbourhood. This reduction in entropy can be described by a local temperature, that is directly related to the gravitational potential. A crucial ingredient in our argument is that ideal classical mechanical motion occurs at constant probability. This definition is motivated by the analysis of entropic forces in classical systems.
Artificial quantum thermal bath: Engineering temperature for a many-body quantum system
Shabani, Alireza; Neven, Hartmut
2016-11-01
Temperature determines the relative probability of observing a physical system in an energy state when that system is energetically in equilibrium with its environment. In this paper we present a theory for engineering the temperature of a quantum system different from its ambient temperature. We define criteria for an engineered quantum bath that, when coupled to a quantum system with Hamiltonian H , drives the system to the equilibrium state e/-H/TTr (e-H /T) with a tunable parameter T . This is basically an analog counterpart of the digital quantum metropolis algorithm. For a system of superconducting qubits, we propose a circuit-QED approximate realization of such an engineered thermal bath consisting of driven lossy resonators. Our proposal opens the path to simulate thermodynamical properties of many-body quantum systems of size not accessible to classical simulations. Also we discuss how an artificial thermal bath can serve as a temperature knob for a hybrid quantum-thermal annealer.
A quantum many-body spin system in an optical lattice clock
Martin, M J; Swallows, M D; Zhang, X; Benko, C; von-Stecher, J; Gorshkov, A V; Rey, A M; Ye, Jun
2013-01-01
Strongly interacting quantum many-body systems are fundamentally compelling and ubiquitous in science. However, their complexity generally prevents exact solutions of their dynamics. Precisely engineered ultracold atomic gases are emerging as a powerful tool to unravel these challenging physical problems. Here we present a new laboratory for the study of many-body effects: strongly interacting two-level systems formed by the clock states in ${}^{87}$Sr, which are used to realize a neutral atom optical clock that performs at the highest level of optical-atomic coherence and with precision near the limit set by quantum fluctuations. Our measurements of the collective spin evolution reveal signatures of many-body dynamics, including beyond-mean-field effects. We derive a many-body Hamiltonian that describes the experimental observation of severely distorted lineshapes, atomic spin coherence decay, density-dependent frequency shifts, and correlated quantum spin noise. These investigations open the door to explori...
Observation of entanglement propagation in a quantum many-body system
Jurcevic, P; Hauke, P; Hempel, C; Zoller, P; Blatt, R; Roos, C F
2014-01-01
The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture that is ...
Positive Tensor Network Approach for Simulating Open Quantum Many-Body Systems
Werner, A. H.; Jaschke, D.; Silvi, P.; Kliesch, M.; Calarco, T.; Eisert, J.; Montangero, S.
2016-06-01
Open quantum many-body systems play an important role in quantum optics and condensed matter physics, and capture phenomena like transport, the interplay between Hamiltonian and incoherent dynamics, and topological order generated by dissipation. We introduce a versatile and practical method to numerically simulate one-dimensional open quantum many-body dynamics using tensor networks. It is based on representing mixed quantum states in a locally purified form, which guarantees that positivity is preserved at all times. Moreover, the approximation error is controlled with respect to the trace norm. Hence, this scheme overcomes various obstacles of the known numerical open-system evolution schemes. To exemplify the functioning of the approach, we study both stationary states and transient dissipative behavior, for various open quantum systems ranging from few to many bodies.
Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
Lee, Sung-Sik; Ryu, Shinsei
2007-01-01
We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson-loop of the SU(2) Berry gauge field, which is quantized due to the time-reversal symmetry.
Many-Body Generalization of the Z2 Topological Invariant for the Quantum Spin Hall Effect
Lee, Sung-Sik; Ryu, Shinsei
2008-05-01
We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson loop of the SU(2) Berry gauge field, which is quantized due to time-reversal symmetry.
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
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
Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths
Yang, Wen; Ma, Wen-Long; Liu, Ren-Bao
2017-01-01
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.
Quantum many-body theory for electron spin decoherence in nanoscale nuclear spin baths.
Yang, Wen; Ma, Wen-Long; Liu, Ren-Bao
2017-01-01
Decoherence of electron spins in nanoscale systems is important to quantum technologies such as quantum information processing and magnetometry. It is also an ideal model problem for studying the crossover between quantum and classical phenomena. At low temperatures or in light-element materials where the spin-orbit coupling is weak, the phonon scattering in nanostructures is less important and the fluctuations of nuclear spins become the dominant decoherence mechanism for electron spins. Since the 1950s, semi-classical noise theories have been developed for understanding electron spin decoherence. In spin-based solid-state quantum technologies, the relevant systems are in the nanometer scale and nuclear spin baths are quantum objects which require a quantum description. Recently, quantum pictures have been established to understand the decoherence and quantum many-body theories have been developed to quantitatively describe this phenomenon. Anomalous quantum effects have been predicted and some have been experimentally confirmed. A systematically truncated cluster-correlation expansion theory has been developed to account for the many-body correlations in nanoscale nuclear spin baths that are built up during electron spin decoherence. The theory has successfully predicted and explained a number of experimental results in a wide range of physical systems. In this review, we will cover this recent progress. The limitations of the present quantum many-body theories and possible directions for future development will also be discussed.
Many-Body Quantum Electrodynamics Networks: Non-Equilibrium Condensed Matter Physics with Light
Hur, Karyn Le; Henriet, Loïc; Petrescu, Alexandru; Plekhanov, Kirill; Roux, Guillaume; Schiró, Marco
2015-01-01
We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and of driving the system. We mention theoretical and experimental efforts to characterize these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect i...
Quantum thermalization through entanglement in an isolated many-body system
Kaufman, Adam M; Lukin, Alexander; Rispoli, Matthew; Schittko, Robert; Preiss, Philipp M; Greiner, Markus
2016-01-01
The concept of entropy is fundamental to thermalization, yet appears at odds with basic principles in quantum mechanics. While statistical mechanics relies on the maximization of entropy for a system at thermal equilibrium, an isolated many-body system undergoing Schr\\"{o}dinger dynamics has zero entropy because, at any given time, it is described by a single quantum state. The underlying role of quantum mechanics in many-body physics is then seemingly antithetical to the success of statistical mechanics in a large variety of systems. Here we observe experimentally how this conflict is resolved: we perform microscopy on an evolving quantum state, and we see thermalization occur on a local scale, while we measure that the full quantum state remains pure. We directly measure entanglement entropy and observe how it assumes the role of the thermal entropy in thermalization. Although the full state has zero entropy, entanglement creates local entropy that validates the use of statistical physics for local observab...
Measuring entanglement entropy of a generic many-body system with a quantum switch.
Abanin, Dmitry A; Demler, Eugene
2012-07-13
Entanglement entropy has become an important theoretical concept in condensed matter physics because it provides a unique tool for characterizing quantum mechanical many-body phases and new kinds of quantum order. However, the experimental measurement of entanglement entropy in a many-body system is widely believed to be unfeasible, owing to the nonlocal character of this quantity. Here, we propose a general method to measure the entanglement entropy. The method is based on a quantum switch (a two-level system) coupled to a composite system consisting of several copies of the original many-body system. The state of the switch controls how different parts of the composite system connect to each other. We show that, by studying the dynamics of the quantum switch only, the Rényi entanglement entropy of the many-body system can be extracted. We propose a possible design of the quantum switch, which can be realized in cold atomic systems. Our work provides a route towards testing the scaling of entanglement in critical systems as well as a method for a direct experimental detection of topological order.
Partial and quasi dynamical symmetries in quantum many-body systems
Leviatan, A
2014-01-01
We introduce the notions of partial dynamical symmetry (PDS) and quasi dynamical symmetry (QDS) and demonstrate their relevance to nuclear spectroscopy, to quantum phase transitions and to mixed systems with regularity and chaos. The analysis serves to highlight the potential role of PDS and QDS towards understanding the emergent "simplicity out of complexity" exhibited by complex many-body systems.
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.
Many-Body Effect in Spin Dephasing in n-Type GaAs Quantum Wells
Institute of Scientific and Technical Information of China (English)
WENG Ming-Qi; WU Ming-Wei
2005-01-01
@@ By constructing and numerically solving the kinetic Bloch equations we perform a many-body study of the spin dephasing due to the D'yakonov-Perel' effect in n-type GaAs (100) quantum wells for high temperatures.
Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties
Torres-Herrera, Eduardo; Karp, Jonathan; Távora, Marco; Santos, Lea
2016-10-01
We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems.
Realistic Many-Body Quantum Systems vs. Full Random Matrices: Static and Dynamical Properties
Directory of Open Access Journals (Sweden)
Eduardo Jonathan Torres-Herrera
2016-10-01
Full Text Available We study the static and dynamical properties of isolated many-body quantum systems and compare them with the results for full random matrices. In doing so, we link concepts from quantum information theory with those from quantum chaos. In particular, we relate the von Neumann entanglement entropy with the Shannon information entropy and discuss their relevance for the analysis of the degree of complexity of the eigenstates, the behavior of the system at different time scales and the conditions for thermalization. A main advantage of full random matrices is that they enable the derivation of analytical expressions that agree extremely well with the numerics and provide bounds for realistic many-body quantum systems.
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
Quantum many-body simulation using monolayer exciton-polaritons in coupled-cavities.
Wang, Hai-Xiao; Zhan, Alan; Xu, Yadong; Chen, Huanyang; You, Wen-Long; Majumdar, Arka; Jiang, JianHua
2017-08-30
Quantum simulation is a promising approach to understand complex strongly correlated many-body systems using relatively simple and tractable systems. Photon-based quantum simulators have great advantages due to the possibility of direct measurements of multi-particle correlations and ease of simulating non-equilibrium physics. However, interparticle interaction in existing photonic systems is often too weak limiting the potential of quantum simulation. Here we propose an approach to enhance the interparticle interaction using exciton-polaritons in MoS$_2$ monolayer quantum-dots embedded in 2D photonic crystal microcavities. Realistic calculation yields optimal repulsive interaction in the range of $1$-$10$~meV --- more than an order of magnitude greater than the state-of-art value. Such strong repulsive interaction is found to emerge neither in the photon-blockade regime for small quantum dot nor in the polariton-blockade regime for large quantum dot, but in the crossover between the two regimes with a moderate quantum-dot radius around 20~nm. The optimal repulsive interaction is found to be largest in MoS$_2$ among commonly used optoelectronic materials. Quantum simulation of strongly correlated many-body systems in a finite chain of coupled cavities and its experimental signature are studied via exact diagonalization of the many-body Hamiltonian. A method to simulate 1D superlattices for interacting exciton-polariton gases in serially coupled cavities is also proposed. Realistic considerations on experimental realizations reveal advantages of transition metal dichalcogenide monolayer quantum-dots over conventional semiconductor quantum-emitters. © 2017 IOP Publishing Ltd.
Solving the quantum many-body problem with artificial neural networks
Carleo, Giuseppe; Troyer, Matthias
2017-02-01
The challenge posed by the many-body problem in quantum physics originates from the difficulty of describing the nontrivial correlations encoded in the exponential complexity of the many-body wave function. Here we demonstrate that systematic machine learning of the wave function can reduce this complexity to a tractable computational form for some notable cases of physical interest. We introduce a variational representation of quantum states based on artificial neural networks with a variable number of hidden neurons. A reinforcement-learning scheme we demonstrate is capable of both finding the ground state and describing the unitary time evolution of complex interacting quantum systems. Our approach achieves high accuracy in describing prototypical interacting spins models in one and two dimensions.
Scaling approach to quantum non-equilibrium dynamics of many-body systems
Energy Technology Data Exchange (ETDEWEB)
Gritsev, Vladimir; Barmettler, Peter [Physics Department, University of Fribourg, Chemin du Musee 3, 1700 Fribourg (Switzerland); Demler, Eugene, E-mail: vladimir.gritsev@unifr.c [Lyman Laboratory of Physics, Physics Department, Harvard University, 17 Oxford Street, Cambridge, MA 02138 (United States)
2010-11-15
Understanding the non-equilibrium quantum dynamics of many-body systems is one of the most challenging problems in modern theoretical physics. While numerous approximate and exact solutions exist for systems in equilibrium, examples of non-equilibrium dynamics of many-body systems that allow reliable theoretical analysis are few and far between. In this paper, we discuss a broad class of time-dependent interacting systems subject to external linear and parabolic potentials, for which the many-body Schroedinger equation can be solved using a scaling transformation. We demonstrate that scaling solutions exist for both local and non-local interactions, and derive appropriate self-consistency equations. We apply this approach to several specific experimentally relevant examples of interacting bosons in one and two dimensions. As an intriguing result, we find that weakly and strongly interacting Bose gases expanding from a parabolic trap can exhibit very similar dynamics.
Blocking transport resonances via Kondo many-body entanglement in quantum dots
Niklas, Michael; Smirnov, Sergey; Mantelli, Davide; Margańska, Magdalena; Nguyen, Ngoc-Viet; Wernsdorfer, Wolfgang; Cleuziou, Jean-Pierre; Grifoni, Milena
2016-08-01
Many-body entanglement is at the heart of the Kondo effect, which has its hallmark in quantum dots as a zero-bias conductance peak at low temperatures. It signals the emergence of a conducting singlet state formed by a localized dot degree of freedom and conduction electrons. Carbon nanotubes offer the possibility to study the emergence of the Kondo entanglement by tuning many-body correlations with a gate voltage. Here we show another side of Kondo correlations, which counterintuitively tend to block conduction channels: inelastic co-tunnelling lines in the magnetospectrum of a carbon nanotube strikingly disappear when tuning the gate voltage. Considering the global SU(2) \\xotime SU(2) symmetry of a nanotube coupled to leads, we find that only resonances involving flips of the Kramers pseudospins, associated to this symmetry, are observed at temperatures and voltages below the corresponding Kondo scale. Our results demonstrate the robust formation of entangled many-body states with no net pseudospin.
Many-body quantum dynamics of polarisation squeezing in optical fibre
Corney, J F; Heersink, J; Josse, V; Leuchs, G; Andersen, U L
2006-01-01
We report new experiments that test quantum dynamical predictions of polarization squeezing for ultrashort photonic pulses in a birefringent fibre, including all relevant dissipative effects. This exponentially complex many-body problem is solved by means of a stochastic phase-space method. The squeezing is calculated and compared to experimental data, resulting in excellent quantitative agreement. From the simulations, we identify the physical limits to quantum noise reduction in optical fibres. The research represents a significant experimental test of first-principles time-domain quantum dynamics in a one-dimensional interacting Bose gas coupled to dissipative reservoirs.
Many-body quantum chaos: Recent developments and applications to nuclei
Energy Technology Data Exchange (ETDEWEB)
Gomez, J.M.G. [Grupo de Fisica Nuclear, Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, E-28040 Madrid (Spain); Kar, K. [Theory Division, Saha Institute of Nuclear Physics, Calcutta 700 064 (India); Kota, V.K.B. [Physical Research Laboratory, Ahmedabad 380 009 (India); Molina, R.A. [Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid (Spain); Relano, A. [Grupo de Fisica Nuclear, Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, E-28040 Madrid (Spain); Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid (Spain); Retamosa, J., E-mail: iokin@nuc3.fis.ucm.e [Grupo de Fisica Nuclear, Departamento de Fisica Atomica, Molecular y Nuclear, Universidad Complutense de Madrid, E-28040 Madrid (Spain)
2011-03-15
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.
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.
Remanent Magnetization: Signature of Many-Body Localization in Quantum Antiferromagnets
Ros, V.; Müller, M.
2017-06-01
We study the remanent magnetization in antiferromagnetic, many-body localized quantum spin chains, initialized in a fully magnetized state. Its long time limit is an order parameter for the localization transition, which is readily accessible by standard experimental probes in magnets. We analytically calculate its value in the strong-disorder regime exploiting the explicit construction of quasilocal conserved quantities of the localized phase. We discuss analogies in cold atomic systems.
Equivalent dynamical complexity in a many-body quantum and collective human system
Directory of Open Access Journals (Sweden)
Neil F. Johnson
2011-03-01
Full Text Available Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i explains a mysterious recent finding of Fratini et al. concerning quantum many-body effects in cuprate superconductors (i.e. scale of 10−9 − 10−4 meters and 10−12 − 10−6 seconds, (ii explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism (i.e. scale of 103 − 106 meters and 104 − 108 seconds, (iii shows consistency with various established empirical facts for financial markets, neurons and human gangs and (iv makes microscopic sense for each application. Our findings also suggest that a potentially productive shift can be made in Complexity research toward the identification of equivalent many-body dynamics in both classical and quantum regimes.
Many-body physics and the capacity of quantum channels with memory
Energy Technology Data Exchange (ETDEWEB)
Plenio, M B; Virmani, S [QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom)], E-mail: s.virmani@imperial.ac.uk
2008-04-15
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.
Experimental characterization of a quantum many-body system via higher-order correlations.
Schweigler, Thomas; Kasper, Valentin; Erne, Sebastian; Mazets, Igor; Rauer, Bernhard; Cataldini, Federica; Langen, Tim; Gasenzer, Thomas; Berges, Jürgen; Schmiedmayer, Jörg
2017-05-17
Quantum systems can be characterized by their correlations. Higher-order (larger than second order) correlations, and the ways in which they can be decomposed into correlations of lower order, provide important information about the system, its structure, its interactions and its complexity. The measurement of such correlation functions is therefore an essential tool for reading, verifying and characterizing quantum simulations. Although higher-order correlation functions are frequently used in theoretical calculations, so far mainly correlations up to second order have been studied experimentally. Here we study a pair of tunnel-coupled one-dimensional atomic superfluids and characterize the corresponding quantum many-body problem by measuring correlation functions. We extract phase correlation functions up to tenth order from interference patterns and analyse whether, and under what conditions, these functions factorize into correlations of lower order. This analysis characterizes the essential features of our system, the relevant quasiparticles, their interactions and topologically distinct vacua. From our data we conclude that in thermal equilibrium our system can be seen as a quantum simulator of the sine-Gordon model, relevant for diverse disciplines ranging from particle physics to condensed matter. The measurement and evaluation of higher-order correlation functions can easily be generalized to other systems and to study correlations of any other observable such as density, spin and magnetization. It therefore represents a general method for analysing quantum many-body systems from experimental data.
Area laws and efficient descriptions of quantum many-body states
Ge, Yimin; Eisert, Jens
2016-08-01
It is commonly believed that area laws for entanglement entropies imply that a quantum many-body state can be faithfully represented by efficient tensor network states—a conjecture frequently stated in the context of numerical simulations and analytical considerations. In this work, we show that this is in general not the case, except in one-dimension. We prove that the set of quantum many-body states that satisfy an area law for all Renyi entropies contains a subspace of exponential dimension. We then show that there are states satisfying area laws for all Renyi entropies but cannot be approximated by states with a classical description of small Kolmogorov complexity, including polynomial projected entangled pair states or states of multi-scale entanglement renormalisation. Not even a quantum computer with post-selection can efficiently prepare all quantum states fulfilling an area law, and we show that not all area law states can be eigenstates of local Hamiltonians. We also prove translationally and rotationally invariant instances of these results, and show a variation with decaying correlations using quantum error-correcting codes.
Non-relativistic Limit of Dirac Equations in Gravitational Field and Quantum Effects of Gravity
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Based on unified theory of electromagnetic interactions and gravitational interactions, the non-relativistic limit of the equation of motion of a charged Dirac particle in gravitational field is studied. From the Schrodinger equation obtained from this non-relativistic limit, we can see that the classical Newtonian gravitational potential appears as a part of the potential in the Schrodinger equation, which can explain the gravitational phase effects found in COW experiments.And because of this Newtonian gravitational potential, a quantum particle in the earth's gravitational field may form a gravitationally bound quantized state, which has already been detected in experiments. Three different kinds of phase effects related to gravitational interactions are studied in this paper, and these phase effects should be observable in some astrophysical processes. Besides, there exists direct coupling between gravitomagnetic field and quantum spin, and radiation caused by this coupling can be used to directly determine the gravitomagnetic field on the surface of a star.
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.
Editorial: Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems
Cazalilla, M. A.; Rigol, M.
2010-05-01
The dynamics and thermalization of classical systems have been extensively studied in the past. However, the corresponding quantum phenomena remain, to a large extent, uncharted territory. Recent experiments with ultracold quantum gases have at last allowed exploration of the coherent dynamics of isolated quantum systems, as well as observation of non-equilibrium phenomena that challenge our current understanding of the dynamics of quantum many-body systems. These experiments have also posed many new questions. How can we control the dynamics to engineer new states of matter? Given that quantum dynamics is unitary, under which conditions can we expect observables of the system to reach equilibrium values that can be predicted by conventional statistical mechanics? And, how do the observables dynamically approach their statistical equilibrium values? Could the approach to equilibrium be hampered if the system is trapped in long-lived metastable states characterized, for example, by a certain distribution of topological defects? How does the dynamics depend on the way the system is perturbed, such as changing, as a function of time and at a given rate, a parameter across a quantum critical point? What if, conversely, after relaxing to a steady state, the observables cannot be described by the standard equilibrium ensembles of statistical mechanics? How would they depend on the initial conditions in addition to the other properties of the system, such as the existence of conserved quantities? The search for answers to questions like these is fundamental to a new research field that is only beginning to be explored, and to which researchers with different backgrounds, such as nuclear, atomic, and condensed-matter physics, as well as quantum optics, can make, and are making, important contributions. This body of knowledge has an immediate application to experiments in the field of ultracold atomic gases, but can also fundamentally change the way we approach and
Many-body localization in a quantum simulator with programmable random disorder
Smith, Jacob; Richerme, Philip; Neyenhuis, Brian; Hess, Paul W; Hauke, Philipp; Heyl, Markus; Huse, David A; Monroe, Christopher
2015-01-01
When a system thermalizes it loses all local memory of its initial conditions. This is a general feature of open systems and is well described by equilibrium statistical mechanics. Even within a closed (or reversible) quantum system, where unitary time evolution retains all information about its initial state, subsystems can still thermalize using the rest of the system as an effective heat bath. Exceptions to quantum thermalization have been predicted and observed, but typically require inherent symmetries or noninteracting particles in the presence of static disorder. The prediction of many-body localization (MBL), in which disordered quantum systems can fail to thermalize in spite of strong interactions and high excitation energy, was therefore surprising and has attracted considerable theoretical attention. Here we experimentally generate MBL states by applying an Ising Hamiltonian with long-range interactions and programmably random disorder to ten spins initialized far from equilibrium. We observe the e...
Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light
Le Hur, Karyn; Henriet, Loïc; Petrescu, Alexandru; Plekhanov, Kirill; Roux, Guillaume; Schiró, Marco
2016-10-01
We review recent developments regarding the quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues, by analogy with atomic physics. We start with quantum impurity models addressing dissipative and driven systems. Both theorists and experimentalists are making efforts towards the characterization of these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect can be characterized by a renormalized light frequency and a peak in the Rayleigh elastic transmission of a photon. We also address the physics of hybrid systems comprising mesoscopic quantum dot devices coupled with an electromagnetic resonator. Then, we discuss extensions to Quantum Electrodynamics (QED) Networks allowing one to engineer the Jaynes-Cummings lattice and Rabi lattice models through the presence of superconducting qubits in the cavities. This opens the door to novel many-body physics with light out of equilibrium, in relation with the Mott-superfluid transition observed with ultra-cold atoms in optical lattices. Then, we summarize recent theoretical predictions for realizing topological phases with light. Synthetic gauge fields and spin-orbit couplings have been successfully implemented in quantum materials and with ultra-cold atoms in optical lattices - using time-dependent Floquet perturbations periodic in time, for example - as well as in photonic lattice systems. Finally, we discuss the Josephson effect related to Bose-Hubbard models in ladder and two-dimensional geometries, producing phase coherence and Meissner currents. The Bose-Hubbard model is related to the Jaynes-Cummings lattice model in the large detuning limit between light and matter (the superconducting qubits). In the presence of synthetic gauge fields, we show that Meissner currents subsist in an insulating Mott phase. xml:lang="fr"
Rahman Prize Talk: Pushing the frontier in the simulation of correlated quantum many body systems
Troyer, Matthias
Amazing progress in the simulation of correlated quantum many body systems has been achieved in the past two decades by combining significant advances in new algorithms with efficient implementations on ever faster supercomputers. This has enabled the accurate simulation of an increasing number of problems and helped settle many open questions. I will review a selection of results that my collaborators and I have worked on, from quantum phase transitions in quantum magnets, over supersolidity of bosons in lattice models and Helium-4 to recent simulations of correlated fermions and quantum gases. I will then provide an outlook to the future and discuss how in the short term analog quantum simulators can help tackle problems for which no efficient simulation algorithms exist and how in the longer term quantum computers can be used to solve many of the still open questions in the field. I will finally connect to the topic of the remainder of this symposium by touching on how the design of new topological materials will help in the construction of these quantum computers.
Particle number conservation in quantum many-body simulations with matrix product operators
Muth, Dominik
2011-01-01
Incorporating conservation laws explicitly into Matrix product states (MPS) has proven to make numerical simulations of quantum many-body systems much less resources consuming. We will discuss here, to what extent this concept can be used in matrix product operators (MPO). Quite counter-intuitively the expectation of gaining in speed by sacrificing information about all but a single symmetry sector is not in all cases fulfilled. It turns out that often the entanglement imposed by the global constraint of fixed particle number is the limiting factor in the canonical ensemble.
Prediction of quantum many-body chaos in the protactinium atom
Viatkina, A. V.; Kozlov, M. G.; Flambaum, V. V.
2017-02-01
The energy-level spectrum of the protactinium atom (Pa, Z =91 ) is simulated with a configuration interaction calculation. Levels belonging to the separate manifolds of a given total angular momentum and parity Jπ exhibit distinct properties of many-body quantum chaos. Moreover, an extremely strong enhancement of small perturbations takes place. As an example, effective three-electron interaction is investigated and found to play a significant role in the system. Chaotic properties of the eigenstates allow one to develop a statistical theory and predict probabilities of different processes in chaotic systems.
Engineering Many-Body Dynamics with Quantum Light Potentials and Measurements
Elliott, Thomas J
2015-01-01
Interactions between many-body atomic systems and light in cavities induce new atomic dynamics, which we show can be tailored by projective light measurement backaction, leading to collective effects such as density-density interactions, perfectly-correlated atomic tunneling, superexchange, and effective pair creation and annihilation. These can be long- and short-range, with tunable strengths, based on the optical setup. We show this provides a framework to enhance quantum simulations of novel physical phenomena, including reservoir models and dynamical gauge fields, beyond current methods.
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).
Topological order of mixed states in correlated quantum many-body systems
Grusdt, F.
2017-02-01
Topological order has become a new paradigm to distinguish ground states of interacting many-body systems without conventional long-range order. Here, we discuss possible extensions of this concept to density matrices describing statistical ensembles. For a large class of quasithermal states, which can be realized as thermal states of some quasilocal Hamiltonian, we generalize earlier definitions of density-matrix topology to generic many-body systems with strong correlations. We point out that the robustness of topological order, defined as a pattern of long-range entanglement, depends crucially on the perturbations under consideration. While it is intrinsically protected against local perturbations of arbitrary strength in an infinite closed quantum system, purely local perturbations can destroy topological order in open systems coupled to baths if the coupling is sufficiently strong. We discuss our classification scheme using the finite-temperature quantum Hall states and point out that the classical Hall effect can be understood as a finite-temperature topological phase.
Equivalent dynamical complexity in a many-body quantum and collective human system
Johnson, Neil F; Zhao, Zhenyuan; Quiroga, Luis
2010-01-01
Proponents of Complexity Science believe that the huge variety of emergent phenomena observed throughout nature, are generated by relatively few microscopic mechanisms [1-7]. Skeptics however point to the lack of concrete examples in which a single mechanistic model manages to capture relevant macroscopic and microscopic properties for two or more distinct systems operating across radically different length and time scales. Here we show how a single complexity model built around cluster coalescence and fragmentation, can cross the fundamental divide between many-body quantum physics and social science. It simultaneously (i) explains a mysterious recent finding concerning quantum many-body effects in cuprate superconductors [8,9] (i.e. scale of 10^{-9}-10^{-4} meters and 10^{-12}-10^{-6} seconds), (ii) explains the apparent universality of the casualty distributions in distinct human insurgencies and terrorism [10] (i.e. scale of 10^{3}-10^{6} meters and 10^{4}-10^{8} seconds), (iii) shows consistency with var...
Spin, angular momentum and spin-statistics for a relativistic quantum many body system
Horwitz, Lawrence
2012-01-01
The adaptation of Wigner's induced representation for a relativistic quantum theory making possible the construction of wavepackets and admitting covariant expectation values for the coordinate operator x^\\mu introduces a foliation on the Hilbert space of states. The spin-statistics relation for fermions and bosons implies the universality of the parametrization of orbits of the induced representation, implying that all particles within the identical particle sets transform under the same SU(2) subgroup of the Lorentz group, and therefore their spins and angular momentum states can be computed using the usual Clebsch-Gordon coefficients associated with angular momentum. Important consequences, such as entanglement for subsystems at unequal times, covariant statistical correlations in many body systems, and the construction of relativistic boson and fermion statistical ensembles, as well as implications for the foliation of the Fock space and for quantum field theory are discussed.
Cavity quantum electrodynamics with many-body states of a two-dimensional electron gas.
Smolka, Stephan; Wuester, Wolf; Haupt, Florian; Faelt, Stefan; Wegscheider, Werner; Imamoglu, Ataç
2014-10-17
Light-matter interaction has played a central role in understanding as well as engineering new states of matter. Reversible coupling of excitons and photons enabled groundbreaking results in condensation and superfluidity of nonequilibrium quasiparticles with a photonic component. We investigated such cavity-polaritons in the presence of a high-mobility two-dimensional electron gas, exhibiting strongly correlated phases. When the cavity was on resonance with the Fermi level, we observed previously unknown many-body physics associated with a dynamical hole-scattering potential. In finite magnetic fields, polaritons show distinct signatures of integer and fractional quantum Hall ground states. Our results lay the groundwork for probing nonequilibrium dynamics of quantum Hall states and exploiting the electron density dependence of polariton splitting so as to obtain ultrastrong optical nonlinearities.
Simulating open quantum systems: from many-body interactions to stabilizer pumping
Mueller, M; Zhou, Y L; Roos, C F; Zoller, P
2011-01-01
In a recent experiment, Barreiro et al. demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions [Nature 470, 486 (2011)]. Using up to five ions, single- and multi-qubit entangling gate operations were combined with optical pumping in stroboscopic sequences. This enabled the implementation of both coherent many-body dynamics as well as dissipative processes by controlling the coupling of the system to an artificial, suitably tailored environment. This engineering was illustrated by the dissipative preparation of entangled two- and four-qubit states, the simulation of coherent four-body spin interactions and the quantum non-demolition measurement of a multi-qubit stabilizer operator. In the present paper, we present the theoretical framework of this gate-based ("digital") simulation approach for open-system dynamics with trapped ions. In addition, we discuss how within this simulation approach minimal instances of spin models of interest in the context of topological q...
Postnikov, Sergey
2013-01-01
This work extends the seminal work of Gottfried on the two-body quantum physics of particles interacting through a delta-shell potential to many-body physics by studying a system of non-relativistic particles when the thermal De-Broglie wavelength of a particle is smaller than the range of the potential and the density is such that average distance between particles is smaller than the range. The ability of the delta-shell potential to reproduce some basic properties of the deuteron are examined. Relations for moments of bound states are derived. The virial expansion is used to calculate the first quantum correction to the ideal gas pressure in the form of the second virial coefficient. Additionally, all thermodynamic functions are calculated up to the first order quantum corrections. For small departures from equilibrium, the net flows of mass, energy and momentum, characterized by the coefficients of diffusion, thermal conductivity and shear viscosity, respectively, are calculated. Properties of the gas are...
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.
Directory of Open Access Journals (Sweden)
David Pekker
2014-03-01
Full Text Available We study a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. One example of such a transition is the recently proposed many-body localization-delocalization transition, in which transport coefficients vanish at a critical temperature with no singularities in thermodynamic observables. Describing this purely dynamical quantum criticality is technically challenging as understanding the finite-temperature dynamics necessarily requires averaging over a large number of matrix elements between many-body eigenstates. Here, we develop a real-space renormalization group method for excited states that allows us to overcome this challenge in a large class of models. We characterize a specific example: the 1 D disordered transverse-field Ising model with generic interactions. While thermodynamic phase transitions are generally forbidden in this model, using the real-space renormalization group method for excited states we find a finite-temperature dynamical transition between two localized phases. The transition is characterized by nonanalyticities in the low-frequency heat conductivity and in the long-time (dynamic spin correlation function. The latter is a consequence of an up-down spin symmetry that results in the appearance of an Edwards-Anderson-like order parameter in one of the localized phases.
Strongdeco: Expansion of analytical, strongly correlated quantum states into a many-body basis
Juliá-Díaz, Bruno; Graß, Tobias
2012-03-01
We provide a Mathematica code for decomposing strongly correlated quantum states described by a first-quantized, analytical wave function into many-body Fock states. Within them, the single-particle occupations refer to the subset of Fock-Darwin functions with no nodes. Such states, commonly appearing in two-dimensional systems subjected to gauge fields, were first discussed in the context of quantum Hall physics and are nowadays very relevant in the field of ultracold quantum gases. As important examples, we explicitly apply our decomposition scheme to the prominent Laughlin and Pfaffian states. This allows for easily calculating the overlap between arbitrary states with these highly correlated test states, and thus provides a useful tool to classify correlated quantum systems. Furthermore, we can directly read off the angular momentum distribution of a state from its decomposition. Finally we make use of our code to calculate the normalization factors for Laughlin's famous quasi-particle/quasi-hole excitations, from which we gain insight into the intriguing fractional behavior of these excitations. Program summaryProgram title: Strongdeco Catalogue identifier: AELA_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AELA_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 5475 No. of bytes in distributed program, including test data, etc.: 31 071 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer on which Mathematica can be installed Operating system: Linux, Windows, Mac Classification: 2.9 Nature of problem: Analysis of strongly correlated quantum states. Solution method: The program makes use of the tools developed in Mathematica to deal with multivariate polynomials to decompose analytical strongly correlated states of bosons
Quantum Mutual Information as a Probe for Many-Body Localization
De Tomasi, Giuseppe; Bera, Soumya; Bardarson, Jens H.; Pollmann, Frank
2017-01-01
We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal-insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from a MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.
Quantum phase transitions in the collective degrees of freedom: nuclei and other many-body systems
Cejnar, Pavel; Stránský, Pavel
2016-08-01
Quantum phase transitions (QPTs) represent a quickly developing subject of theoretical and experimental research. Nuclear physics contributed to the formation of the QPT concept in the 1970s and remains an area where new viewpoints and original approaches to criticality in many-body systems can be created. In this review, we present a comprehensible introduction to the subject, with an emphasis on the role of nuclear physics, and point out some specific features of QPTs in the systems that exhibit an effective separation of some collective degrees of freedom. The focus on collectivity, which stems from the nuclear context, is an essential ingredient of our treatise. It leads to some consequences that find application in nuclei as well as in a wide spectrum of non-nuclear systems.
The nonequilibrium quantum many-body problem as a paradigm for extreme data science
Freericks, J. K.; Nikolić, B. K.; Frieder, O.
2014-12-01
Generating big data pervades much of physics. But some problems, which we call extreme data problems, are too large to be treated within big data science. The nonequilibrium quantum many-body problem on a lattice is just such a problem, where the Hilbert space grows exponentially with system size and rapidly becomes too large to fit on any computer (and can be effectively thought of as an infinite-sized data set). Nevertheless, much progress has been made with computational methods on this problem, which serve as a paradigm for how one can approach and attack extreme data problems. In addition, viewing these physics problems from a computer-science perspective leads to new approaches that can be tried to solve more accurately and for longer times. We review a number of these different ideas here.
Liu, Wenyuan; Wang, Chao; Li, Yanbin; Lao, Yuyang; Han, Yongjian; Guo, Guang-Can; Zhao, Yong-Hua; He, Lixin
2015-03-01
Tensor network states (TNS) methods combined with the Monte Carlo (MC) technique have been proven a powerful algorithm for simulating quantum many-body systems. However, because the ground state energy is a highly non-linear function of the tensors, it is easy to get stuck in local minima when optimizing the TNS of the simulated physical systems. To overcome this difficulty, we introduce a replica-exchange molecular dynamics optimization algorithm to obtain the TNS ground state, based on the MC sampling technique, by mapping the energy function of the TNS to that of a classical mechanical system. The method is expected to effectively avoid local minima. We make benchmark tests on a 1D Hubbard model based on matrix product states (MPS) and a Heisenberg J1-J2 model on square lattice based on string bond states (SBS). The results show that the optimization method is robust and efficient compared to the existing results.
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.
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.
Desgranges, C.; Anderson, P. W.; Delhommelle, J.
2017-02-01
Using molecular simulation, we determine the critical properties of Si as well as the loci for several remarkable thermodynamic contours spanning the supercritical region of the phase diagram. We consider a classical three-body potential as well as a quantum (tight-binding) many-body model, and determine the loci for the ideality contours, including the Zeno line and the H line of ideal enthalpy. The two strategies (classical or quantum) lead to strongly asymmetric binodals and to critical properties in good agreement with each other. The Zeno and H lines are found to remain linear over a wide temperature interval, despite the changes in electronic structure undergone by the fluid along these contours. We also show that the classical and quantum model yield markedly different results for the parameters defining the H line, the exponents for the power-laws underlying the line of minima for the isothermal enthalpy and for the density required to achieve ideal behavior, most notably for the enthalpy.
DEFF Research Database (Denmark)
Houmark-Nielsen, Jakob; Nielsen, Torben Roland; Mørk, Jesper;
2009-01-01
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...
Preparing ground States of quantum many-body systems on a quantum computer.
Poulin, David; Wocjan, Pawel
2009-04-03
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to determine the one with lowest energy, requiring a running time proportional to N. A quantum computer, if it could be built, could solve this problem in time sqrt[N]. Here, we present a powerful extension of this result to the case of interacting quantum particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems.
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
Spectrum of Quantum Transfer Matrices via Classical Many-Body Systems
Gorsky, A; Zotov, A
2014-01-01
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 ${\\mathfrak g}{\\mathfrak l}_n$-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 eige...
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
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.
Dynamics of isolated quantum systems: many-body localization and thermalization
Torres-Herrera, E. Jonathan; Tavora, Marco; Santos, Lea F.
2016-05-01
We show that the transition to a many-body localized phase and the onset of thermalization can be inferred from the analysis of the dynamics of isolated quantum systems taken out of equilibrium abruptly. The systems considered are described by one-dimensional spin-1/2 models with static random magnetic fields and by power-law band random matrices. We find that the short-time decay of the survival probability of the initial state is faster than exponential for sufficiently strong perturbations. This initial evolution does not depend on whether the system is integrable or chaotic, disordered or clean. At long-times, the dynamics necessarily slows down and shows a power-law behavior. The value of the power-law exponent indicates whether the system will reach thermal equilibrium or not. We present how the properties of the spectrum, structure of the initial state, and number of particles that interact simultaneously affect the value of the power-law exponent. We also compare the results for the survival probability with those for few-body observables. EJTH aknowledges financial support from PRODEP-SEP and VIEP-BUAP, Mexico.
Manifestation of many-body interactions in the integer quantum Hall effect regime
Oswald, Josef; Römer, Rudolf A.
2017-09-01
We use the self-consistent Hartree-Fock approximation for numerically addressing the integer quantum Hall (IQH) regime in terms of many-body physics at higher Landau levels (LL). The results exhibit a strong tendency to avoid the simultaneous existence of partly filled spin-up and spin-down LLs. Partly filled LLs appear as a mixture of coexisting regions of full and empty LLs. We obtain edge stripes with approximately constant filling factor ν close to half-odd filling at the boundaries between the regions of full and empty LLs, which we explain in terms of the g -factor enhancement as a function of a locally varying ν across the compressible stripes. The many-particle interactions follow a behavior as it would result from applying Hund's rule for the occupation of the spin split LLs. The screening of the disorder and edge potential appears significantly reduced as compared to screening based on a Thomas-Fermi approximation. For addressing carrier transport, we use a nonequilibrium network model (NNM) that handles the lateral distribution of the experimentally injected nonequilibrium chemical potentials μ .
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.
Velocity operator and velocity field for spinning particles in (non-relativistic) quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Recami, E. [Bergamo Univ. (Italy). Facolta` di Ingegneria]|[INFN, Milan (Italy)]|[Campinas State Univ., SP (Brazil). Dept. of Applied Math.; Salesi, G. [Catania Univ. (Italy). Dip. di Fisica
1995-06-01
Starting from the formal expressions of the hydrodynamical (or local) quantities employed in the applications of Clifford Algebras to quantum mechanics, the paper introduces - in terms of the ordinary tensorial framework - a new definition for the field of a generic quantity. By translating from Clifford into tensor algebra, a new (non-relativistic) velocity operator for a spin 1/2 particle is also proposed. This operator is the sum of the ordinary part p/m describing the mean motion (the motion of the center-of-mass), and of a second part associated with the so-called Zitterbewegung, which is the spin internal motion observed in the center-of- mass frame. This spin component of the velocity operator is non-zero not only in the Pauli theoretical framework, i.e. in presence of external magnetic fields and spin precession, but also in the Schroedinger case, when the wave-function is a spin eigenstate. In the latter case, one gets a decomposition of the velocity field for the Madelueng fluid into two distinct parts: which the constitutes the non-relativistic analogue of the Gordon decomposition for the Dirac current.
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
Wachter, H
2007-01-01
This is the second part of a paper about a q-deformed analog of non-relativistic Schroedinger theory. It applies the general ideas of part I and tries to give a description of one-particle states on q-deformed quantum spaces like the braided line or the q-deformed Euclidean space in three dimensions. Hamiltonian operators for the free q-deformed particle in one as well as three dimensions are introduced. Plane waves as solutions to the corresponding Schroedinger equations are considered. Their completeness and orthonormality relations are written down. Expectation values of position and momentum observables are taken with respect to one-particle states and their time-dependence is discussed. A potential is added to the free-particle Hamiltonians and q-analogs of the Ehrenfest theorem are derived from the Heisenberg equations of motion. The conservation of probability is proved.
A many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
Lee, Sung-Sik; Ryu, Shinsei
2008-03-01
We propose a many-body generalization of the Z2 topological invariant for the quantum spin Hall insulator, which does not rely on single-particle band structures. The invariant is derived as a topological obstruction that distinguishes topologically distinct many-body ground states on a torus. It is also expressed as a Wilson-loop of the SU(2) Berry gauge field, which is quantized due to the time-reversal symmetry.
Generalized Lagrangian-Path Representation of Non-Relativistic Quantum Mechanics
Tessarotto, Massimo; Cremaschini, Claudio
2016-08-01
In this paper a new trajectory-based representation to non-relativistic quantum mechanics is formulated. This is ahieved by generalizing the notion of Lagrangian path (LP) which lies at the heart of the deBroglie-Bohm " pilot-wave" interpretation. In particular, it is shown that each LP can be replaced with a statistical ensemble formed by an infinite family of stochastic curves, referred to as generalized Lagrangian paths (GLP). This permits the introduction of a new parametric representation of the Schrödinger equation, denoted as GLP-parametrization, and of the associated quantum hydrodynamic equations. The remarkable aspect of the GLP approach presented here is that it realizes at the same time also a new solution method for the N-body Schrödinger equation. As an application, Gaussian-like particular solutions for the quantum probability density function (PDF) are considered, which are proved to be dynamically consistent. For them, the Schrödinger equation is reduced to a single Hamilton-Jacobi evolution equation. Particular solutions of this type are explicitly constructed, which include the case of free particles occurring in 1- or N-body quantum systems as well as the dynamics in the presence of suitable potential forces. In all these cases the initial Gaussian PDFs are shown to be free of the spreading behavior usually ascribed to quantum wave-packets, in that they exhibit the characteristic feature of remaining at all times spatially-localized.
Non-relativistic Schroedinger theory on q-deformed quantum spaces III, Scattering theory
Wachter, H
2007-01-01
This is the third part of a paper about non-relativistic Schroedinger theory on q-deformed quantum spaces like the braided line or the three-dimensional q-deformed Euclidean space. Propagators for the free q-deformed particle are derived and their basic properties are discussed. A time-dependent formulation of scattering is proposed. In this respect, q-analogs of the Lippmann-Schwinger equation are given. Expressions for their iterative solutions are written down. It is shown how to calculate S-matrices and transition probabilities. Furthermore, attention is focused on the question what becomes of unitarity of S-matrices in a q-deformed setting. The examinations are concluded by a discussion of the interaction picture and its relation to scattering processes.
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
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
Many-body localization transition in random quantum spin chains with long-range interactions
Moure, N.; Haas, S.; Kettemann, S.
2015-07-01
While there are well-established methods to study delocalization transitions of single particles in random systems, it remains a challenging problem how to characterize many-body delocalization transitions. Here, we use a generalized real-space renormalization group technique to study the anisotropic Heisenberg model with long-range interactions, decaying with a power α, which are generated by placing spins at random positions along the chain. This method permits a large-scale finite-size scaling analysis. We examine the full distribution function of the excitation energy gap from the ground state and observe a crossover with decreasing α. At αc the full distribution coincides with a critical function. Thereby, we find strong evidence for the existence of a many-body localization transition in disordered antiferromagnetic spin chains with long-range interactions.
Quantum Exact Non-Abelian Vortices in Non-relativistic Theories
Nitta, Muneto; Vinci, Walter
2014-01-01
Non-Abelian vortices arise when a non-Abelian global symmetry is exact in the ground state but spontaneously broken in the vicinity of their cores. In this case, there appear (non-Abelian) Nambu-Goldstone (NG) modes confined and propagating along the vortex. In relativistic theories, the Coleman-Mermin-Wagner theorem forbids the existence of a spontaneous symmetry breaking, or a long-range order, in 1+1 dimensions: quantum corrections restore the symmetry along the vortex and the NG modes acquire a mass gap. We show that in non-relativistic theories NG modes with quadratic dispersion relation confined on a vortex can remain gapless at quantum level. We provide a concrete and experimentally realizable example of a three-component Bose-Einstein condensate with U(1) x U(2) symmetry. We first show, at the classical level, the existence of S^3 = S^1 |x S^2 (S^1 fibered over S^2) NG modes associated to the breaking U(2) -> U(1) on vortices, where S^1 and S^2 correspond to type I and II NG modes, respectively. We th...
2016-01-01
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 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 co...
A transmon quantum annealer: decomposing many-body Ising constraints into pair interactions
Leib, Martin; Zoller, Peter; Lechner, Wolfgang
2016-12-01
Adiabatic quantum computing is an analogue quantum computing scheme with various applications in solving optimisation problems. In the parity picture of quantum optimization, the problem is encoded in local fields that act on qubits that are connected via local four-body terms We present an implementation of a parity annealer with Transmon qubits with a specifically tailored Ising interaction from Josephson ring modulators.
Quantum Optical Lattices for Emergent Many-Body Phases of Ultracold Atoms
Caballero-Benitez, Santiago F.; Mekhov, Igor B.
2015-12-01
Confining ultracold gases in cavities creates a paradigm of quantum trapping potentials. We show that this allows us to bridge models with global collective and short-range interactions as novel quantum phases possess properties of both. Some phases appear solely due to quantum light-matter correlations. Because of a global, but spatially structured, interaction, the competition between quantum matter and light waves leads to multimode structures even in single-mode cavities, including delocalized dimers of matter-field coherences (bonds), beyond density orders as supersolids and density waves.
Generalized One-Dimensional Point Interaction in Relativistic and Non-relativistic Quantum Mechanics
Shigehara, T; Mishima, T; Cheon, T; Cheon, Taksu
1999-01-01
We first give the solution for the local approximation of a four parameter family of generalized one-dimensional point interactions within the framework of non-relativistic model with three neighboring $\\delta$ functions. We also discuss the problem within relativistic (Dirac) framework and give the solution for a three parameter family. It gives a physical interpretation for so-called high energy substantially differ between non-relativistic and relativistic cases.
Theoretical Methods in the Non-Equilibrium Quantum Mechanics of Many Bodies
2011-01-01
function in real time GR (t) = ∫ dω 2π e−iωtGR (ω) ≈ e−it(ξα+ΣR)+tΣI (2.19) From here we see that the inclusion of many-body interactions renormalizes the...equilibrium with a bath at zero temperature. Following [63], we write the total Hamiltonian as Ĥ = Ĥ0 + V̂ where Ĥ0 is a “ bare ” Hamiltonian for...averaged over the known ground state |φ0〉 of the bare Hamiltonian. Gα,α′ (t, t ′) = −i〈Tâ † α (t) âα′ (t ′) Ŝ (∞,−∞)〉0 〈φ0|TŜ (∞,−∞) |φ0〉 (4.8) In
Lavalle, Catia; Rigol, Marcos; Muramatsu, Alejandro
2005-08-01
The cover picture of the current issue, taken from the Feature Article [1], depicts the evolution of local density (a) and its quantum fluctuations (b) in trapped fermions on one-dimensional optical lattices. As the number of fermions in the trap is increased, figure (a) shows the formation of a Mott-insulating plateau (local density equal to one) whereas the quantum fluctuations - see figure (b) - are strongly suppressed, but nonzero. For a larger number of fermions new insulating plateaus appear (this time with local density equal to two), but no density fluctuations. Regions with non-constant density are metallic and exhibit large quantum fluctuations of the density.The first author Catia Lavalle is a Postdoc at the University of Stuttgart. She works in the field of strongly correlated quantum systems by means of Quantum Monte Carlo methods (QMC). While working on her PhD thesis at the University of Stuttgart, she developed a new QMC technique that allows to study dynamical properties of the t-J model.
Many-Body Quantum Optics with Decaying Atomic Spin States: ($\\gamma$, $\\kappa$) Dicke model
Gelhausen, Jan; Strack, Philipp
2016-01-01
We provide a theory for quantum-optical realizations of the open Dicke model with internal, atomic spin states subject to uncorrelated, single-site spontaneous emission with rate $\\gamma$. This introduces a second decay channel for excitations to irreversibly dissipate into the environment, in addition to the photon loss with rate $\\kappa$. We compute the mean-field non-equilibrium steady states for spin and photon observables in the long-time limit, $t\\rightarrow \\infty$. Although $\\gamma$ does not conserve the total angular momentum of the spin array, we argue that our solution is exact in the thermodynamic limit, for the number of atoms $N\\rightarrow \\infty$. In light of recent and upcoming experiments realizing superradiant phase transitions using internal atomic states with pinned atoms in optical lattices, our work lays the foundation for the pursuit of a new class of open quantum magnets coupled to quantum light.
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.
When cooler is not better: Stochastic Resonance Phenomena in Quantum Many-Body Systems
Huelga, S; Huelga, Susana; Plenio, Martin
2006-01-01
We discuss stochastic resonance (SR) effects in weakly driven coupled quantum systems. We show that both dynamical and information theoretic measures of the system's response can be introduced that exhibit a non-monotonic behaviour as a function of the noise strength. We analyze the relation between lack of monotonicity in the response and the presence of quantum correlations, showing that there are parameter regimes where the breakdown of a linear response can be associated to the presence of entanglement. We also show that a chain of coupled spin systems can exhibit an array-enhanced response, where the sensitivity of a single resonator to a weak driving signal is enhanced as a result of the nearest-neighbour coupling. These results enlarge the domain where SR effects exist and should be observable in state-of-the-art arrays of superconducting qubits.
Renormalization of myoglobin-ligand binding energetics by quantum many-body effects
Weber, Cedric; O'Regan, David D; Payne, Mike C
2014-01-01
We carry out a first-principles atomistic study of the electronic mechanisms of ligand binding and discrimination in the myoglobin protein. Electronic correlation effects are taken into account using one of the most advanced methods currently available, namely a linear-scaling density functional theory (DFT) approach wherein the treatment of localized iron 3d electrons is further refined using dynamical mean-field theory (DMFT). This combination of methods explicitly accounts for dynamical and multi-reference quantum physics, such as valence and spin fluctuations, of the 3d electrons, whilst treating a significant proportion of the protein (more than 1000 atoms) with density functional theory. The computed electronic structure of the myoglobin complexes and the nature of the Fe-O2 bonding are validated against experimental spectroscopic observables. We elucidate and solve a long standing problem related to the quantum-mechanical description of the respiration process, namely that DFT calculations predict a st...
Scrambling and thermalization in a diffusive quantum many-body system
Bohrdt, A.; Mendl, C. B.; Endres, M.; Knap, M.
2017-06-01
Out-of-time ordered (OTO) correlation functions describe scrambling of information in correlated quantum matter. They are of particular interest in incoherent quantum systems lacking well defined quasi-particles. Thus far, it is largely elusive how OTO correlators spread in incoherent systems with diffusive transport governed by a few globally conserved quantities. Here, we study the dynamical response of such a system using high-performance matrix-product-operator techniques. Specifically, we consider the non-integrable, one-dimensional Bose-Hubbard model in the incoherent high-temperature regime. Our system exhibits diffusive dynamics in time-ordered correlators of globally conserved quantities, whereas OTO correlators display a ballistic, light-cone spreading of quantum information. The slowest process in the global thermalization of the system is thus diffusive, yet information spreading is not inhibited by such slow dynamics. We furthermore develop an experimentally feasible protocol to overcome some challenges faced by existing proposals and to probe time-ordered and OTO correlation functions. Our study opens new avenues for both the theoretical and experimental exploration of thermalization and information scrambling dynamics.
Mazzucchi, Gabriel; Caballero-Benitez, Santiago F; Elliott, Thomas J; Mekhov, Igor B
2015-01-01
Trapping ultracold atoms in optical lattices enabled numerous breakthroughs uniting several disciplines. Although the light is a key ingredient in such systems, its quantum properties are typically neglected, reducing the role of light to a classical tool for atom manipulation. Here we show how elevating light to the quantum level leads to novel phenomena, inaccessible in setups based on classical optics. Interfacing a many-body atomic system with quantum light opens it to the environment in an essentially nonlocal way, where spatial coupling can be carefully designed. The competition between typical processes in strongly correlated systems (local tunnelling and interaction) with global measurement backaction leads to novel multimode dynamics and the appearance of long-range correlated tunnelling capable of entangling distant lattices sites, even when tunnelling between neighbouring sites is suppressed by the quantum Zeno effect. We demonstrate both the break-up and protection of strongly interacting fermion ...
Krajewski, Florian R.; Müser, Martin H.
2005-07-01
The spectral density of quantum mechanical Frenkel Kontorova chains moving in disordered, external potentials is investigated by means of path-integral molecular dynamics. If the second moment of the embedding potential is well defined (roughness exponent H=0), there is one regime in which the chain is pinned (large masses m of chain particles) and one in which it is unpinned (small m). If the embedding potential can be classified as a random walk on large length scales ( H=1/2), then the chain is always pinned irrespective of the value of m. For H=1/2, two phonon-like branches appear in the spectra.
Transport of quantum excitations coupled to spatially extended nonlinear many-body systems
Iubini, Stefano; Boada, Octavi; Omar, Yasser; Piazza, Francesco
2015-11-01
The role of noise in the transport properties of quantum excitations is a topic of great importance in many fields, from organic semiconductors for technological applications to light-harvesting complexes in photosynthesis. In this paper we study a semi-classical model where a tight-binding Hamiltonian is fully coupled to an underlying spatially extended nonlinear chain of atoms. We show that the transport properties of a quantum excitation are subtly modulated by (i) the specific type (local versus non-local) of exciton-phonon coupling and by (ii) nonlinear effects of the underlying lattice. We report a non-monotonic dependence of the exciton diffusion coefficient on temperature, in agreement with earlier predictions, as a direct consequence of the lattice-induced fluctuations in the hopping rates due to long-wavelength vibrational modes. A standard measure of transport efficiency confirms that both nonlinearity in the underlying lattice and off-diagonal exciton-phonon coupling promote transport efficiency at high temperatures, preventing the Zeno-like quench observed in other models lacking an explicit noise-providing dynamical system.
Dynamical scaling in infinitely correlated many-body systems through a quantum phase transition
Acevedo, Oscar Leonardo; Quiroga, Luis; Rodriguez, Ferney Javier; Johnson, Neil
2013-03-01
We assess dynamical scaling of many two-level systems (TLSs) infinitely correlated, either through a mediating radiation mode as in the Dicke Model, or through a direct interaction between TLSs as in the Lipkin-Meshkov-Glick model. Those models are characterized by the presence of a Quantum Phase Transition (QPT) in the thermodynamic limit, and they belong to the same universality class. The assessment is done by means of exact computational simulations of finite-size systems under linear rampings of the interaction parameter crossing the quantum critical point. Our results exhibit significant differences with respect to previous works on dynamical scaling across QPTs in the near-adiabatic regime, which have focused on spin-chain models where correlation lengths can be defined. We have confirmed that in infinitely correlated models an effective system size can play the role of the correlation length in traditional scaling arguments. However, due to the infinite correlation among TLSs, the standard Kibble-Zurek mechanism is not realized as the system cannot fully enter an adiabatic evolution during the ordered phase. Also, in the two-level approximation, a suitable deviation from the standard Landau-Zener protocol must be performed in order to obtain scaling collapse.
Exploring Few- and Many-Body Dipolar Quantum Phenomena with Ultracold Erbium Atoms
Ferlaino, Francesca
2016-05-01
Given their strong magnetic moment and exotic electronic configuration, rare-earth atoms disclose a plethora of intriguing phenomena in ultracold quantum physics with dipole-dipole interaction. Here, we report on the first degenerate Fermi gas of erbium atoms, based on direct cooling of identical fermions via dipolar collisions. We reveal universal scattering laws between identical dipolar fermions close to zero temperature, and we demonstrate the long-standing prediction of a deformed Fermi surface in dipolar gas. Finally, we present the first experimental study of an extended Bose-Hubbard model using bosonic Er atoms in a three-dimensional optical lattice and we report on the first observation of nearest-neighbor interactions.
Zhang, Tianyuan
2016-01-01
In this work we propose a novel approach to solve the Schr\\"{o}dinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased towards any determinant. Therefore, the PCI approach can equally well describe static an...
Many-body effects on graphene conductivity: Quantum Monte Carlo calculations
Boyda, D. L.; Braguta, V. V.; Katsnelson, M. I.; Ulybyshev, M. V.
2016-08-01
Optical conductivity of graphene is studied using quantum Monte Carlo calculations. We start from a Euclidean current-current correlator and extract σ (ω ) from Green-Kubo relations using the Backus-Gilbert method. Calculations were performed both for long-range interactions and taking into account only the contact term. In both cases we vary interaction strength and study its influence on optical conductivity. We compare our results with previous theoretical calculations choosing ω ≈κ , thus working in the region of the plateau in σ (ω ) which corresponds to optical conductivity of Dirac quasiparticles. No dependence of optical conductivity on interaction strength is observed unless we approach the antiferromagnetic phase transition in the case of an artificially enhanced contact term. Our results strongly support previous theoretical studies that claimed very weak regularization of graphene conductivity.
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.
Efficient Implementation of Many-body Quantum Chemical Methods on the Intel Xeon Phi Coprocessor
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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.
Many-body quantum chemistry for the electron gas: convergent perturbative theories
Shepherd, James J
2013-01-01
We investigate the accuracy of a number of wavefunction based methods at the heart of quantum chemistry for metallic systems. Using Hartree-Fock as a reference, perturbative (M{\\o}ller-Plesset, MP) and coupled cluster (CC) theories are used to study the uniform electron gas model. Our findings suggest that non-perturbative coupled cluster theories are acceptable for modelling electronic interactions in metals whilst perturbative coupled cluster theories are not. Using screened interactions, we propose a simple modification to the widely-used coupled-cluster singles and doubles plus perturbative triples method (CCSD(T)) that lifts the divergent behaviour and is shown to give very accurate correlation energies for the homogeneous electron gas.
Thermalization and out-of-equilibrium dynamics in open quantum many-body systems
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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
Stability and Clustering for Lattice Many-Body Quantum Hamiltonians with Multiparticle Potentials
Faria da Veiga, Paulo A.; O'Carroll, Michael
2015-11-01
We analyze a quantum system of N identical spinless particles of mass m, in the lattice Z^d, given by a Hamiltonian H_N=T_N+V_N, with kinetic energy T_N≥ 0 and potential V_N=V_{N,2}+V_{N,3} composed of attractive pair and repulsive 3-body contact-potentials. This Hamiltonian is motivated by the desire to understand the stability of quantum field theories, with massive single particles and bound states in the energy-momentum spectrum, in terms of an approximate Hamiltonian for their N-particle sector. We determine the role of the potentials V_{N,2} and V_{N,3} on the physical stability of the system, such as to avoid a collapse of the N particles. Mathematically speaking, stability is associated with an N-linear lower bound for the infimum of the H_N spectrum, \\underline{σ }(H_N)≥ -cN, for c>0 independent of N. For V_{N,3}=0, H_N is unstable, and the system collapses. If V_{N,3}not =0, H_N is stable and, for strong enough repulsion, we obtain \\underline{σ }(H_N)≥ -c' N, where c'N is the energy of ( N/2) isolated bound pairs. This result is physically expected. A much less trivial result is that, as N varies, we show [ \\underline{σ }(V_N)/N ] has qualitatively the same behavior as the well-known curve for minus the nuclear binding energy per nucleon. Moreover, it turns out that there exists a saturation value N_s of N at and above which the system presents a clustering: the N particles distributed in two fragments and, besides lattice translations of particle positions, there is an energy degeneracy of all two fragments with particle numbers N_r and N_s-N_r, with N_r=1,ldots ,N_s-1.
Bethe ansatz matrix elements as non-relativistic limits of form factors of quantum field theory
Kormos, M.; Mussardo, G.; Pozsgay, B.
2010-01-01
We show that the matrix elements of integrable models computed by the algebraic Bethe ansatz (BA) can be put in direct correspondence with the form factors of integrable relativistic field theories. This happens when the S-matrix of a Bethe ansatz model can be regarded as a suitable non-relativistic
Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Super-Geometry
Hasebe, Kazuki
2013-01-01
Recent vigorous investigations of topological order have not only discovered new topological states of matter but also shed new light to "already known" topological states. One established example with topological order is the valence bond solid (VBS) states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking but most typically manifest topological order known as hidden string order on 1D chain. Interestingly, the VBS models are based on mathematics analogous to fuzzy geometry. We review applications of the mathematics of fuzzy super-geometry in the construction of supersymmetric versions of VBS (SVBS) states, and give a pedagogical introduction of SVBS models and their properties [arXiv:0809.4885, 1105.3529, 1210.0299]. As concrete examples, we present detail analysis of supersymmetric versions of SU(2) and SO(5) VBS states, i.e. UOSp(N|2) and UOSp(N|4) SVBS states whose mathematics are closely related to fuzzy two- and four-superspheres. The SVBS sta...
Gauging Quantum States: From Global to Local Symmetries in Many-Body Systems
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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.
Hartono, Albert; Lu, Qingda; Henretty, Thomas; Krishnamoorthy, Sriram; Zhang, Huaijian; Baumgartner, Gerald; Bernholdt, David E; Nooijen, Marcel; Pitzer, Russell; Ramanujam, J; Sadayappan, P
2009-11-12
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.
Energy Technology Data Exchange (ETDEWEB)
Hartono, Albert; Lu, Qingda; henretty, thomas; Krishnamoorthy, Sriram; zhang, huaijian; Baumgartner, Gerald; Bernholdt, David E.; Nooijen, Marcel; Pitzer, Russell M.; Ramanujam, J.; Sadayappan, Ponnuswamy
2009-11-12
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.
Topological Many-Body States in Quantum Antiferromagnets via Fuzzy Supergeometry
Directory of Open Access Journals (Sweden)
Keisuke Totsuka
2013-04-01
Full Text Available Recent vigorous investigations of topological order have not only discovered new topological states of matter, but also shed new light on “already known” topological states. One established example with topological order is the valence bond solid (VBS states in quantum antiferromagnets. The VBS states are disordered spin liquids with no spontaneous symmetry breaking, but most typically manifest a topological order known as a hidden string order on the 1D chain. Interestingly, the VBS models are based on mathematics analogous to fuzzy geometry. We review applications of the mathematics of fuzzy supergeometry in the construction of supersymmetric versions of VBS (SVBS states and give a pedagogical introduction of SVBS models and their properties. As concrete examples, we present detailed analysis of supersymmetric versions of SU(2 and SO(5 VBS states, i.e., UOSp(N|2 and UOSp(N|4 SVBS states, whose mathematics are closely related to fuzzy two- and four-superspheres. The SVBS states are physically interpreted as hole-doped VBS states with a superconducting property that interpolates various VBS states, depending on the value of a hole-doping parameter. The parent Hamiltonians for SVBS states are explicitly constructed, and their gapped excitations are derived within the single-mode approximation on 1D SVBS chains. Prominent features of the SVBS chains are discussed in detail, such as a generalized string order parameter and entanglement spectra. It is realized that the entanglement spectra are at least doubly degenerate, regardless of the parity of bulk (superspins. The stability of the topological phase with supersymmetry is discussed, with emphasis on its relation to particular edge (superspin states.
Zhang, Tianyuan; Evangelista, Francesco A
2016-09-13
In this work we propose a novel approach to solve the Schrödinger equation which combines projection onto the ground state with a path-filtering truncation scheme. The resulting projector configuration interaction (PCI) approach realizes a deterministic version of the full configuration interaction quantum Monte Carlo (FCIQMC) method [Booth, G. H.; Thom, A. J. W.; Alavi, A. J. Chem. Phys. 2009, 131, 054106]. To improve upon the linearized imaginary-time propagator, we develop an optimal projector scheme based on an exponential Chebyshev expansion in the limit of an infinite imaginary time step. After writing the exact projector as a path integral in determinant space, we introduce a path filtering procedure that truncates the size of the determinantal basis and approximates the Hamiltonian. The path filtering procedure is controlled by one real threshold that determines the accuracy of the PCI energy and is not biased toward any determinant. Therefore, the PCI approach can equally well describe static and dynamic electron correlation effects. This point is illustrated in benchmark computations on N2 at both equilibrium and stretched geometries. In both cases, the PCI achieves chemical accuracy with wave functions that contain less than 0.5% determinants of full CI space. We also report computations on the ground state of C2 with up to quaduple-ζ basis sets and wave functions as large as 200 million determinants, which allow a direct comparison of the PCI, FCIQMC, and density matrix renormalization group (DMRG) methods. The size of the PCI wave function grows modestly with the number of unoccupied orbitals, and its accuracy may be tuned to match that of FCIQMC and DMRG.
Bienert, M; Kun, S Yu
2006-01-01
We estimate how accurate the phase relaxation time of quantum many-body systems can be determined from data on forward peaking of evaporating protons from a compound nucleus. The angular range and accuracy of the data needed for a reliable determination of the phase relaxation time are evaluated. The general method is applied to analyze the inelastic scattering of 18 MeV protons from Pt for which previously measured double differential cross sections for two angles in the evaporating domain of the spectra show a strong forward peaking. A new experiment for an improved determination of the phase relaxation time is proposed.
Eichler, C.; Mlynek, J.; Butscher, J.; Kurpiers, P.; Hammerer, K.; Osborne, T. J.; Wallraff, A.
2015-10-01
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.
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}.
Many-body effects and self-contained phase dynamics in an optically injected quantum-dot laser
Lingnau, Benjamin; Lüdge, Kathy; Chow, Weng W.; Schöll, Eckehard
2012-06-01
Quantum-dot (QD) lasers exhibit unique properties when subjected to optical injection, e.g. lower sensitivity and less complex dynamics when compared to conventional quantum-well (QW) lasers. These features can be explained by a lower phase-amplitude coupling and a higher damping of relaxation oscillations in QD laser devices. In this work, we investigate an optically injected QD laser and clarify the role of many-body effects. We model the QD laser device using a semi-classical approach based on the semiconductor-Bloch and Maxwell's equations. The QD optical transition is modeled with a finite spectral width, accounting for inhomogeneous broadening due to QD imperfections. Furthermore, many-body Coulomb interactions, leading to renormalizations of the single-particle energies, are taken into account assuming the screened Hartree-Fock approximation. Throughout the literature the phase dynamics of the electric field inside the laser cavity is implemented by assuming a constant α-factor. Our model accounts for the effects of α via a more rigorous treatment of light-semiconductor interaction. As a result the model allows to extract a value for the α-factor from the intrinsic phase dynamics of the system. The extracted α-factor is not a constant, but rather changes on the one hand dynamically throughout the simulations, and on the other hand with all operation conditions. Furthermore, the dynamical shift of the band-gap energy due to the Coulomb interactions gives rise to modifications in the locking behavior of the laser, that can not be explained with the simpler free-carrier models.
The coupled-cluster approach to quantum many-body problem in a three-Hilbert-space reinterpretation
Bishop, Raymond F
2013-01-01
The quantum many-body bound-state problem in its computationally successful coupled cluster method (CCM) representation is reconsidered. In conventional practice one factorizes the ground-state wave functions $|\\Psi\\rangle= e^S |\\Phi\\rangle$ which live in the "physical" Hilbert space ${\\cal H}^{(P)}$ using an elementary ansatz for $|\\Phi\\rangle$ plus a formal expansion of $S$ in an operator basis of multi-configurational creation operators. In our paper a reinterpretation of the method is proposed. Using parallels between the CCM and the so called quasi-Hermitian, alias three-Hilbert-space (THS), quantum mechanics, the CCM transition from the known microscopic Hamiltonian (denoted by usual symbol $H$), which is self-adjoint in ${\\cal H}^{(P)}$, to its effective lower-case isospectral avatar $\\hat{h}=e^{-S} H e^S$, is assigned a THS interpretation. In the opposite direction, a THS-prescribed, non-CCM, innovative reinstallation of Hermiticity is shown to be possible for the CCM effective Hamiltonian $\\hat{h}$, ...
Rai, Neeraj; Tiwari, Surya P; Maginn, Edward J
2012-09-06
Advances in computational algorithms and methodologies make it possible to use highly accurate quantum mechanical calculations to develop force fields (pair-wise additive intermolecular potentials) for condensed phase simulations. Despite these advances, this approach faces numerous hurdles for the case of actinyl ions, AcO2(n+) (high-oxidation-state actinide dioxo cations), mainly due to the complex electronic structure resulting from an interplay of s, p, d, and f valence orbitals. Traditional methods use a pair of molecules (“dimer”) to generate a potential energy surface (PES) for force field parametrization based on the assumption that many body polarization effects are negligible. We show that this is a poor approximation for aqueous phase uranyl ions and present an alternative approach for the development of actinyl ion force fields that includes important many body solvation effects. Force fields are developed for the UO2(2+) ion with the SPC/Fw, TIP3P, TIP4P, and TIP5P water models and are validated by carrying out detailed molecular simulations on the uranyl aqua ion, one of the most characterized actinide systems. It is shown that the force fields faithfully reproduce available experimental structural data and hydration free energies. Failure to account for solvation effects when generating PES leads to overbinding between UO2(2+) and water, resulting in incorrect hydration free energies and coordination numbers. A detailed analysis of arrangement of water molecules in the first and second solvation shell of UO2(2+) is presented. The use of a simple functional form involving the sum of Lennard-Jones + Coulomb potentials makes the new force field compatible with a large number of available molecular simulation engines and common force fields.
Torres-Herrera, E J; Santos, Lea F
2013-10-01
We explore the role of the initial state on the onset of thermalization in isolated quantum many-body systems after a quench. The initial state is an eigenstate of an initial Hamiltonian H(I) and it evolves according to a different final Hamiltonian H(F). If the initial state has a chaotic structure with respect to H(F), i.e., if it fills the energy shell ergodically, thermalization is certain to occur. This happens when H(I) is a full random matrix, because its states projected onto H(F), are fully delocalized. The results for the observables then agree with those obtained with thermal states at infinite temperature. However, finite real systems with few-body interactions, as the ones considered here, are deprived of fully extended eigenstates, even when described by a nonintegrable Hamiltonian. We examine how the initial state delocalizes as it gets closer to the middle of the spectrum of H(F), causing the observables to approach thermal averages, be the models integrable or chaotic. Our numerical studies are based on initial states with energies that cover the entire lower half of the spectrum of one-dimensional Heisenberg spin-1/2 systems.
Lao, Ka Un; Herbert, John M
2015-01-15
We present an overview of "XSAPT", a family of quantum chemistry methods for noncovalent interactions. These methods combine an efficient, iterative, monomer-based approach to computing many-body polarization interactions with a two-body version of symmetry-adapted perturbation theory (SAPT). The result is an efficient method for computing accurate intermolecular interaction energies in large noncovalent assemblies such as molecular and ionic clusters, molecular crystals, clathrates, or protein-ligand complexes. As in traditional SAPT, the XSAPT energy is decomposable into physically meaningful components. Dispersion interactions are problematic in traditional low-order SAPT, and two new approaches are introduced here in an attempt to improve this situation: (1) third-generation empirical atom-atom dispersion potentials, and (2) an empirically scaled version of second-order SAPT dispersion. Comparison to high-level ab initio benchmarks for dimers, water clusters, halide-water clusters, a methane clathrate hydrate, and a DNA intercalation complex illustrate both the accuracy of XSAPT-based methods as well as their limitations. The computational cost of XSAPT scales as O(N(3))-O(N(5)) with respect to monomer size, N, depending upon the particular version that is employed, but the accuracy is typically superior to alternative ab initio methods with similar scaling. Moreover, the monomer-based nature of XSAPT calculations makes them trivially parallelizable, such that wall times scale linearly with respect to the number of monomer units. XSAPT-based methods thus open the door to both qualitative and quantitative studies of noncovalent interactions in clusters, biomolecules, and condensed-phase systems.
Wall, Michael
2014-03-01
Experimental progress in generating and manipulating synthetic quantum systems, such as ultracold atoms and molecules in optical lattices, has revolutionized our understanding of quantum many-body phenomena and posed new challenges for modern numerical techniques. Ultracold molecules, in particular, feature long-range dipole-dipole interactions and a complex and selectively accessible internal structure of rotational and hyperfine states, leading to many-body models with long range interactions and many internal degrees of freedom. Additionally, the many-body physics of ultracold molecules is often probed far from equilibrium, and so algorithms which simulate quantum many-body dynamics are essential. Numerical methods which are to have significant impact in the design and understanding of such synthetic quantum materials must be able to adapt to a variety of different interactions, physical degrees of freedom, and out-of-equilibrium dynamical protocols. Matrix product state (MPS)-based methods, such as the density-matrix renormalization group (DMRG), have become the de facto standard for strongly interacting low-dimensional systems. Moreover, the flexibility of MPS-based methods makes them ideally suited both to generic, open source implementation as well as to studies of the quantum many-body dynamics of ultracold molecules. After introducing MPSs and variational algorithms using MPSs generally, I will discuss my own research using MPSs for many-body dynamics of long-range interacting systems. In addition, I will describe two open source implementations of MPS-based algorithms in which I was involved, as well as educational materials designed to help undergraduates and graduates perform research in computational quantum many-body physics using a variety of numerical methods including exact diagonalization and static and dynamic variational MPS methods. Finally, I will mention present research on ultracold molecules in optical lattices, such as the exploration of
Koop, E. J.; Lerescu, A. I.; Liu, J.; van Wees, B. J.; Reuter, D.; Wieck, A. D.; van der Wal, C. H.
2007-01-01
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
Non relativistic diffeomorphism and the geometry of the fractional quantum Hall effect
Banerjee, Rabin
2015-01-01
We show that our recently proposed method\\cite{BMM1,BMM2,BMM3,BM4} of constructing nonrelativistic diffeomorphism invariant field theories by gauging the Galilean symmetry provides a natural connection with the geometry of the fractional quantum Hall effect (FQHE). Specifically, the covariant derivative that appears on gauging, exactly reproduces the form that yields the Hall viscosity and Wen-Zee shift \\cite{CYF}.
Directory of Open Access Journals (Sweden)
Marcos Moshinsky
2007-11-01
Full Text Available A direct procedure for determining the propagator associated with a quantum mechanical problem was given by the Path Integration Procedure of Feynman. The Green function, which is the Fourier Transform with respect to the time variable of the propagator, can be derived later. In our approach, with the help of a Laplace transform, a direct way to get the energy dependent Green function is presented, and the propagator can be obtained later with an inverse Laplace transform. The method is illustrated through simple one dimensional examples and for time independent potentials, though it can be generalized to the derivation of more complicated propagators.
Coccia, Emanuele; Guidoni, Leonardo
2014-01-01
In this letter we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) {\\AA}, larger than the values obtained by DFT (PBE, B3LYP and CAM-B3LYP) and shorter than that calculated at the Hartree-Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO-LUMO major contribution of the Bu+-like (S2) bright excited state. Many Body Green's Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu+-like state for the VMC structure (VMC/MBGFT) provide excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed.
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,...
Santos, Lea F.; Távora, Marco; Pérez-Bernal, Francisco
2016-07-01
Excited-state quantum phase transitions (ESQPTs) are generalizations of quantum phase transitions to excited levels. They are associated with local divergences in the density of states. Here, we investigate how the presence of an ESQPT can be detected from the analysis of the structure of the Hamiltonian matrix, the level of localization of the eigenstates, the onset of bifurcation, and the speed of the system evolution. Our findings are illustrated for a Hamiltonian with infinite-range Ising interaction in a transverse field. This is a version of the Lipkin-Meshkov-Glick (LMG) model and the limiting case of the one-dimensional spin-1/2 system with tunable interactions realized with ion traps. From our studies for the dynamics, we uncover similarities between the LMG and the noninteracting XX models.
Gutierrez, Ricardo; Archimi, Matteo; Castellucci, Francesco; Arimondo, Ennio; Ciampini, Donatella; Marcuzzi, Matteo; Lesanovsky, Igor; Morsch, Oliver
2016-01-01
Understanding and probing phase transitions in non-equilibrium systems is an ongoing challenge in physics. A particular instance are phase transitions that occur between a non-fluctuating absorbing phase, e.g., an extinct population, and one in which the relevant order parameter, such as the population density, assumes a finite value. Here we report the observation of signatures of such a non-equilibrium phase transition in an open driven quantum system. In our experiment rubidium atoms in a quasi one-dimensional cold disordered gas are laser-excited to Rydberg states under so-called facilitation conditions. This conditional excitation process competes with spontaneous decay and leads to a crossover between a stationary state with no excitations and one with a finite number of excitations. We relate the underlying physics to that of an absorbing state phase transition in the presence of a field which slightly offsets the system from criticality. We observe a characteristic power-law scaling of the Rydberg exc...
Chin, Cheng
2011-05-01
Recent cold atom researches are reaching out far beyond the realm that was conventionally viewed as atomic physics. Many long standing issues in other physics disciplines or in Gedanken-experiments are nowadays common targets of cold atom physicists. Two prominent examples will be discussed in this talk: BEC-BCS crossover and Efimov physics. Here, cold atoms are employed to emulate electrons in superconductors, and nucleons in nuclear reactions, respectively. The ability to emulate exotic or thought systems using cold atoms stems from the precisely determined, simple, and tunable interaction properties of cold atoms. New experimental tools have also been devised toward an ultimate goal: a complete control and a complete characterization of a few- or many-body quantum system. We are tantalizingly close to this major milestone, and will soon open new venues to explore new quantum phenomena that may (or may not!) exist in scientists' dreams.
Energy Technology Data Exchange (ETDEWEB)
Barmettler, Peter; Gritsev, Vladimir [Department of Physics, University of Fribourg, CH-1700 Fribourg (Switzerland); Punk, Matthias [CPHT, Ecole Polytechnique, 91128 Palaiseau (France); Demler, Eugene [Department of Physics, Harvard University, Cambridge, MA 02138 (United States); Altman, Ehud, E-mail: peter.barmettler@cpht.polytechnique.f [Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)
2010-05-15
Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.
Directory of Open Access Journals (Sweden)
Abdelmadjid MAIRECHE
2015-09-01
Full Text Available We obtain here the modified bound-states solutions for central fraction power singular potential (C.F.P.S. in noncommutative 3-dimensional non relativistic quantum mechanics (NC-3D NRQM. It has been observed that the commutative energy spectra was changed, and replaced degenerate new states, depending on four quantum numbers: j, l and sz=±1/2 corresponding to the two spins states of electron by (up and down and the deformed Hamiltonian formed by two new operators: the first describes the spin-orbit interaction , while the second obtained Hamiltonian describes the modified Zeeman effect (containing ordinary Zeeman effect in addition to the usual commutative Hamiltonian. We showed that the isotropic commutative Hamiltonian HCFPS will be in non commutative space anisotropic Hamiltonian HNC-CFPS.
Laurent, Sébastien; Pierce, Matthieu; Delehaye, Marion; Yefsah, Tarik; Chevy, Frédéric; Salomon, Christophe
2017-03-10
We study three-body recombination in an ultracold Bose-Fermi mixture. We first show theoretically that, for weak interspecies coupling, the loss rate is proportional to Tan's contact. Second, using a ^{7}Li/^{6}Li mixture we probe the recombination rate in both the thermal and dual superfluid regimes. We find excellent agreement with our model in the BEC-BCS crossover. At unitarity where the fermion-fermion scattering length diverges, we show that the loss rate is proportional to n_{f}^{4/3}, where n_{f} is the fermionic density. This unusual exponent signals nontrivial two-body correlations in the system. Our results demonstrate that few-body losses can be used as a quantitative probe of quantum correlations in many-body ensembles.
Wachter, H
2007-01-01
The aim of these three papers (I, II, and III) is to develop a q-deformed version of non-relativistic Schroedinger theory. Paper I introduces the fundamental mathematical and physical concepts. The braided line and the three-dimensional q-deformed Euclidean space play the role of position space. For both cases the algebraic framework is extended by a time element. A short review of the elements of q-deformed analysis on the spaces under consideration is given. The time evolution operator is introduced in a consistent way and its basic properties are discussed. These reasonings are continued by proposing q-deformed analogs of the Schroedinger and the Heisenberg picture.
Reyes-Lillo, Sebastian E.; Rangel, Tonatiuh; Bruneval, Fabien; Neaton, Jeffrey B.
2016-07-01
The Ruddlesden-Popper (RP) homologous series Srn +1TinO3 n +1 provides a useful template for the study and control of the effects of dimensionality and quantum confinement on the excited state properties of the complex oxide SrTiO3. We use ab initio many-body perturbation theory within the G W approximation and the Bethe-Salpeter equation approach to calculate quasiparticle energies and absorption spectra of Srn +1TinO3 n +1 for n =1 -5 and ∞ . Our computed direct and indirect optical gaps are in excellent agreement with spectroscopic measurements. The calculated optical spectra reproduce the main experimental features and reveal excitonic structure near the gap edge. We find that electron-hole interactions are important across the series, leading to significant exciton binding energies that increase for small n and reach a value of 330 meV for n =1 , a trend attributed to increased quantum confinement. We find that the lowest-energy singlet exciton of Sr2TiO4 (n =1 ) localizes in the two-dimensional plane defined by the TiO2 layer, and we explain the origin of its localization.
Many-Body Physics with Trapped Ions
Schneider, Christian; Schaetz, Tobias
2011-01-01
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. We report on the progress in experimentally simulating quantum many-body physics with trapped ions.
Böhm, Michael C.; Schulte, Joachim; Utrera, Luis
Feynman path-integral quantum Monte Carlo (QMC) simulations and an analytic many-body approach are used to study the ground state properties of one-dimensional (1D) chains in the theoretical framework of model Hamiltonians of the Hubbard type. The QMC algorithm is employed to derive position-space quantities, while band structure properties are evaluated by combining QMC data with expressions derived in momentum (k) space. Bridging link between both representations is the quasi-chemical approximation (QCA). Electronic charge fluctuations and the fluctuations of the magnetic local moments are studied as a function of the on-site density and correlation strength, which is given by the ratio between two-electron interaction and kinetic hopping. Caused by the non-analytic behaviour of the chemical potential μ = ∂E/∂ (with E denoting the electronic energy), strict 1D systems with an on-site density of 1·0 do not exhibit the properties of a conductor for any non-zero interaction beyond the mean-field approximation. The QMC simulations lead to straightforward access to the probabilities Pi(n) of finding n = 0, 1, 2 electrons at the ith lattice site. The Pi(n) elements allow to calculate the enhancement factors on the electron spin susceptibility χ, effective electronic mass m* and Knight shift κ. m* is enhanced by a bandwidth renormalization factor D-10, κ by an element ηK mapping the additional localization of the correlated electrons in the presence of an external magnetic field B and χ by the product D-10 ηK. Available experimental data are discussed in the light of the present theoretical findings.
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Davydov, Alexander
2010-01-01
It is accepted wisdom that language and formalism of classical physics are inadequate for description of quantum phenomena. Here I confront this point of view by showing that there exists a surprisingly accurate mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, I demonstrate that such quintessentially quantum effect as tunneling through a potential barrier can be described in terms of classical physics without violating the energy conservation law at any time instance. A formula is presented that generates a wide class of one-dimensional potential barrier shapes in analytic form with the desired reflection (transmission) coefficient and transmission phase shift along with the corresponding exact solutions of the time-independent Schr\\"odinger's equation. Based on these results and numerical evidence, I put forward a conjecture that a classical (macroscopic) harmonic oscillator disturbed by a parametric ...
Radożycki, Tomasz
2016-11-01
The probability density distributions for the ground states of certain model systems in quantum mechanics and for their classical counterparts are considered. It is shown, that classical distributions are remarkably improved by incorporating into them the Heisenberg uncertainty relation between position and momentum. Even the crude form of this incorporation makes the agreement between classical and quantum distributions unexpectedly good, except for the small area, where classical momenta are large. It is demonstrated that the slight improvement of this form, makes the classical distribution very similar to the quantum one in the whole space. The obtained results are much better than those from the WKB method. The paper is devoted to ground states, but the method applies to excited states too.
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.
Covariant geometric quantization of non-relativistic Hamiltonian mechanics
Giachetta, G; Sardanashvily, G
2000-01-01
We provide geometric quantization of the vertical cotangent bundle V^*Q equipped with the canonical Poisson structure. This is a momentum phase space of non-relativistic mechanics with the configuration bundle Q -> R. The goal is the Schrodinger representation of V^*Q. We show that this quantization is equivalent to the fibrewise quantization of symplectic fibres of V^*Q -> R, that makes the quantum algebra of non-relativistic mechanics an instantwise algebra. Quantization of the classical evolution equation defines a connection on this instantwise algebra, which provides quantum evolution in non-relativistic mechanics as a parallel transport along time.
Fujisawa, Takeshi; Saitoh, Kunimasa
2015-01-01
Quantum-confined Stark effect (QCSE) of group IV Ge(Sn)/SiGe(Sn) quantum wells (QWs) on Si substrate is analyzed by microscopic many-body theory for mid-infrared (mid-IR) Si-based electroabsorption devices. To show the validity of the theory, QCSE of Ge/SiGe QW is investigated and very good agreement between theory and reported measured results is obtained. Next, the QCSE of GeSn/SiGeSn QWs is analyzed and the QW design for electroabsorption modulators to obtain large extinction ratio in mid-...
Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.
2017-09-01
The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.
Exotic Non-relativistic String
Casalbuoni, Roberto; Longhi, Giorgio
2007-01-01
We construct a classical non-relativistic string model in 3+1 dimensions. The model contains a spurion tensor field that is responsible for the non-commutative structure of the model. Under double dimensional reduction the model reduces to the exotic non-relativistic particle in 2+1 dimensions.
Renormalization group for non-relativistic fermions.
Shankar, R
2011-07-13
A brief introduction is given to the renormalization group for non-relativistic fermions at finite density. It is shown that Landau's theory of the Fermi liquid arises as a fixed point (with the Landau parameters as marginal couplings) and its instabilities as relevant perturbations. Applications to related areas, nuclear matter, quark matter and quantum dots, are briefly discussed. The focus will be on explaining the main ideas to people in related fields, rather than addressing the experts.
Monthus, Cécile
2016-07-01
The iterative methods to diagonalize matrices and many-body Hamiltonians can be reformulated as flows of Hamiltonians towards diagonalization driven by unitary transformations that preserve the spectrum. After a comparative overview of the various types of discrete flows (Jacobi, QR-algorithm) and differential flows (Toda, Wegner, White) that have been introduced in the past, we focus on the random XXZ chain with random fields in order to determine the best closed flow within a given subspace of running Hamiltonians. For the special case of the free-fermion random XX chain with random fields, the flow coincides with the Toda differential flow for tridiagonal matrices which is related to the classical integrable Toda chain and which can be seen as the continuous analog of the discrete QR-algorithm. For the random XXZ chain with random fields that displays a many-body-localization transition, the present differential flow should be an interesting alternative to compare with the discrete flow that has been proposed recently to study the many-body-localization properties in a model of interacting fermions (Rademaker and Ortuno 2016 Phys. Rev. Lett. 116, 010404).
Eriksen, Janus Juul
2016-01-01
It is demonstrated how the non-proprietary OpenACC standard of compiler directives may be used to compactly and efficiently accelerate the rate-determining steps of two of the most routinely applied many-body methods of electronic structure theory, namely the second-order M{\\o}ller-Plesset (MP2) model in its resolution-of-the-identity (RI) approximated form and the (T) triples correction to the coupled cluster singles and doubles model (CCSD(T)). By means of compute directives as well as the use of optimized device math libraries, the operations involved in the energy kernels have been ported to graphics processing unit (GPU) accelerators, and the associated data transfers correspondingly optimized to such a degree that the final implementations (using either double and/or single precision arithmetics) are capable of scaling to as large systems as allowed for by the capacity of the host central processing unit (CPU) main memory. The performance of the hybrid CPU/GPU implementations is assessed through calcula...
Mera, Bruno; Vlachou, Chrysoula; Paunković, Nikola; Vieira, Vítor R.
2017-09-01
We perform the fidelity analysis for Boltzmann-Gibbs-like states in order to investigate whether the topological order of 1D fermionic systems at zero temperature is maintained at finite temperatures. We use quantum walk protocols that are known to simulate topological phases and the respective quantum phase transitions for chiral symmetric Hamiltonians. Using the standard approaches of the fidelity analysis and the study of edge states, we conclude that no thermal-like phase transitions occur as temperature increases, i.e. the topological behaviour is washed out gradually. We also show that the behaviour of the Uhlmann geometric factor associated to the considered fidelity exhibits the same behaviour as the latter, thus confirming the results obtained using the previously established approaches.
Lampart, Jonas; Lewin, Mathieu
2015-12-01
We prove a generalized version of the RAGE theorem for N-body quantum systems. The result states that only bound states of systems with {0 ≤slant n ≤slant N} particles persist in the long time average. The limit is formulated by means of an appropriate weak topology for many-body systems, which was introduced by the second author in a previous work, and is based on reduced density matrices. This topology is connected to the weak-* topology of states on the algebras of canonical commutation or anti-commutation relations, and we give a formulation of our main result in this setting.
Many-body effects in intermolecular forces.
Elrod, M J; Saykally, R J
1994-11-01
The authors provide a review and literature survey of many-body effects in intermolecular forces. Topics include experimental methods, theoretical methods, many-body effects in atomic systems, and many-body effects in aqueous and nonaqueous molecular systems.
Dunn, M; Loeser, J G
2006-01-01
In this paper, the second in a series of two, we complete the derivation of the lowest-order wave function of a dimensional perturbation theory (DPT) treatment for the N-body quantum-confined system. Taking advantage of the symmetry of the zeroth-order configuration, we use group theoretic techniques and the FG matrix method from quantum chemistry to obtain analytic results for frequencies and normal modes. This method directly accounts for each two-body interaction, rather than an average interaction so that even lowest-order results include beyond-mean-field effects. It is thus appropriate for the study of both weakly and strongly interacting systems and the transition between them. While previous work has focused on energies, lowest-order wave functions yield important information such as the nature of excitations and expectation values of physical observables at low orders including density profiles. Higher orders in DPT also require as input the zeroth-order wave functions. In the earlier paper we presen...
Non-Relativistic Limit of the Dirac Equation
Ajaib, Muhammad Adeel
2016-01-01
We show that the first order form of the Schrodinger equation proposed in [1] can be obtained from the Dirac equation in the non-relativistic limit. We also show that the Pauli Hamiltonian is obtained from this equation by requiring local gauge invariance. In addition, we study the problem of a spin up particle incident on a finite potential barrier and show that the known quantum mechanical results are obtained. Finally, we consider the symmetric potential well and show that the quantum mechanical expression for the quantized energy levels of a particle is obtained with periodic boundary conditions. Based on these conclusions, we propose that the equation introduced in [1] is the non-relativistic limit of the Dirac equation and more appropriately describes spin 1/2 particles in the non-relativistic limit.
Weinberg, Phillip
2016-01-01
We present a new open-source Python package for exact diagonalization and quantum dynamics of spin(-photon) chains, called $\\mathcal{Q}^{\\mathrm{u}}\\!\\mathcal{S}\\mathcal{P}\\mathcal{I}\\mathcal{N}$, supporting the use of various symmetries and (imaginary) time evolution. 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, $\\mathcal{Q}^{\\mathrm{u}}\\!\\mathcal{S}\\mathcal{P}\\mathcal{I}\\mathcal{N}$'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 $\\mathcal{Q}^{\\mathrm{u}}\\!\\mathcal{S}\\mathcal{P}\\mathcal{I}\\mathcal{N}$ using three detailed examples: (i) adiabatic ramping of parameters in the many-body localised XXZ model, (ii) heating in the ...
Microscopic picture of non-relativistic classicalons
Energy Technology Data Exchange (ETDEWEB)
Berkhahn, Felix; Müller, Sophia; Niedermann, Florian; Schneider, Robert, E-mail: felix.berkhahn@physik.lmu.de, E-mail: sophia.x.mueller@physik.uni-muenchen.de, E-mail: florian.niedermann@physik.lmu.de, E-mail: robert.bob.schneider@physik.uni-muenchen.de [Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität, Theresienstraße 37, 80333 Munich (Germany)
2013-08-01
A theory of a non-relativistic, complex scalar field with derivatively coupled interaction terms is investigated. This toy model is considered as a prototype of a classicalizing theory and in particular of general relativity, for which the black hole constitutes a prominent example of a classicalon. Accordingly, the theory allows for a non-trivial solution of the stationary Gross-Pitaevskii equation corresponding to a black hole in the case of GR. Quantum fluctuations on this classical background are investigated within the Bogoliubov approximation. It turns out that the perturbative approach is invalidated by a high occupation of the Bogoliubov modes. Recently, it was proposed that a black hole is a Bose-Einstein condensate of gravitons that dynamically ensures to stay at the verge of a quantum phase transition. Our result is understood as an indication for that claim. Furthermore, it motivates a non-linear numerical analysis of the model.
Non-relativistic classical mechanics for spinning particles
Salesi, G
2004-01-01
We study the classical dynamics of non-relativistic particles endowed with spin. Non-vanishing Zitterbewegung terms appear in the equation of motion also in the small momentum limit. We derive a generalized work-energy theorem which suggests classical interpretations for tunnel effect and quantum potential.
Symmetry constraints on many-body localization
Potter, Andrew C.; Vasseur, Romain
2016-12-01
We derive general constraints on the existence of many-body localized (MBL) phases in the presence of global symmetries, and show that MBL is not possible with symmetry groups that protect multiplets (e.g., all non-Abelian symmetry groups). Based on simple representation theoretic considerations, we derive general Mermin-Wagner-type principles governing the possible alternative fates of nonequilibrium dynamics in isolated, strongly disordered quantum systems. Our results rule out the existence of MBL symmetry-protected topological phases with non-Abelian symmetry groups, as well as time-reversal symmetry-protected electronic topological insulators, and in fact all fermion topological insulators and superconductors in the 10-fold way classification. Moreover, extending our arguments to systems with intrinsic topological order, we rule out MBL phases with non-Abelian anyons as well as certain classes of symmetry-enriched topological orders.
Exploring the many-body localization transition in two dimensions
Choi, Jae-yoon; Hild, Sebastian; Zeiher, Johannes; Schauß, Peter; Rubio-Abadal, Antonio; Yefsah, Tarik; Khemani, Vedika; Huse, David A.; Bloch, Immanuel; Gross, Christian
2016-06-01
A fundamental assumption in statistical physics is that generic closed quantum many-body systems thermalize under their own dynamics. Recently, the emergence of many-body localized systems has questioned this concept and challenged our understanding of the connection between statistical physics and quantum mechanics. Here we report on the observation of a many-body localization transition between thermal and localized phases for bosons in a two-dimensional disordered optical lattice. With our single-site-resolved measurements, we track the relaxation dynamics of an initially prepared out-of-equilibrium density pattern and find strong evidence for a diverging length scale when approaching the localization transition. Our experiments represent a demonstration and in-depth characterization of many-body localization in a regime not accessible with state-of-the-art simulations on classical computers.
Non-Relativistic Spacetimes with Cosmological Constant
Aldrovandi, R.; Barbosa, A. L.; Crispino, L.C.B.; Pereira, J. G.
1998-01-01
Recent data on supernovae favor high values of the cosmological constant. Spacetimes with a cosmological constant have non-relativistic kinematics quite different from Galilean kinematics. De Sitter spacetimes, vacuum solutions of Einstein's equations with a cosmological constant, reduce in the non-relativistic limit to Newton-Hooke spacetimes, which are non-metric homogeneous spacetimes with non-vanishing curvature. The whole non-relativistic kinematics would then be modified, with possible ...
Relativistic and non-relativistic geodesic equations
Energy Technology Data Exchange (ETDEWEB)
Giambo' , R.; Mangiarotti, L.; Sardanashvily, G. [Camerino Univ., Camerino, MC (Italy). Dipt. di Matematica e Fisica
1999-07-01
It is shown that any dynamic equation on a configuration space of non-relativistic time-dependent mechanics is associated with connections on its tangent bundle. As a consequence, every non-relativistic dynamic equation can be seen as a geodesic equation with respect to a (non-linear) connection on this tangent bundle. Using this fact, the relationships between relativistic and non-relativistic equations of motion is studied.
Institute of Scientific and Technical Information of China (English)
李伟; 苏刚
2012-01-01
文章简述了数值重正化群方法的历史发展,包括威耳逊（Wilson）的数值重正化群算法,S.R.White的密度矩阵重正化群方法,以及近期迅速发展的处理强关联量子系统的几种张量网络态与张量网络算法.在此基础上,文章重点介绍了作者最近提出的用于研究量子多体系统热力学性质的线性张量重正化群方法,以及该方法在一维和二维量子系统中的应用.%We review the development of numerical renormalization group methods, including Wilson＇s numerical renormalization group , White＇s density matrix renormalization group, and several recent rapidly developing tensor network state-based algorithms. Among these, particular emphasis is laid on the linearized tensor renormalization group method, which was recently proposed to accurately calculate the thermo dynamic properties of quantum many-body lattice systems, and which may have broad applications in both one- and two-dimensional quantum systems.
Iterative variational approach to finite many-body systems
Sambataro, M.; Gambacurta, D.; Lo Monaco, L.
2011-01-01
A procedure is discussed that searches for the best description of the eigenstates of a Hamiltonian of a finite quantum many-body system in terms of a selected set of physically relevant configurations. The procedure resorts to iterative sequences of diagonalizations in spaces of very reduced size.
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.
Do non-relativistic neutrinos oscillate?
Akhmedov, Evgeny
2017-07-01
We study the question of whether oscillations between non-relativistic neutrinos or between relativistic and non-relativistic neutrinos are possible. The issues of neutrino production and propagation coherence and their impact on the above question are discussed in detail. It is demonstrated that no neutrino oscillations can occur when neutrinos that are non-relativistic in the laboratory frame are involved, except in a strongly mass-degenerate case. We also discuss how this analysis depends on the choice of the Lorentz frame. Our results are for the most part in agreement with Hinchliffe's rule.
Many-body diffusion algorithm for interacting harmonic fermions
Luczak, F.; Brosens, F.; Devreese, J. T.; Lemmens, L. F.
1999-09-01
A new quantum Monte Carlo algorithm is presented to numerically implement the recently developed many-body diffusion approach for identical particles. For fermions, the procedure avoids the sign problem by defining a set of independent stochastic diffusion processes. Based on a symmetry analysis of both the free density matrix and the potential, the total random process is restricted to a well-defined state space with absorbing or reflecting boundary conditions. The absorption rate of the walkers at absorbing boundaries contributes substantially to the ground-state energy. The feasibility of the many-body diffusion algorithm is illustrated by its application to interacting harmonic fermions.
Entropy current for non-relativistic fluid
Banerjee, Nabamita; Jain, Akash; Roychowdhury, Dibakar
2014-01-01
We study transport properties of a parity-odd, non-relativistic charged fluid in presence of background electric and magnetic fields. To obtain stress tensor and charged current for the non-relativistic system we start with the most generic relativistic fluid, living in one higher dimension and reduce the constituent equations along the light-cone direction. We also reduce the equation satisfied by the entropy current of the relativistic theory and obtain a consistent entropy current for the non-relativistic system (we call it "canonical form" of the entropy current). Demanding that the non-relativistic fluid satisfies the second law of thermodynamics we impose constraints on various first order transport coefficients. For parity even fluid, this is straight forward; it tells us positive definiteness of different transport coefficients like viscosity, thermal conductivity, electric conductivity etc. However for parity-odd fluid, canonical form of the entropy current fails to confirm the second law of thermody...
Molavian, Hamid R; Gingras, Michel J P; Canals, Benjamin
2007-04-13
The Tb2Ti2O7 pyrochlore magnetic material is attracting much attention for its spin liquid state, failing to develop long-range order down to 50 mK despite a Curie-Weiss temperature thetaCW approximately -14 K. In this Letter we reinvestigate the theoretical description of this material by considering a quantum model of independent tetrahedra to describe its low-temperature properties. The naturally tuned proximity of this system near a Néel to spin ice phase boundary allows for a resurgence of quantum fluctuation effects that lead to an important renormalization of its effective low-energy spin Hamiltonian. As a result, Tb2Ti2O7 is argued to be a quantum spin ice. We put forward an experimental test of this proposal using neutron scattering on a single crystal.
Many-Body Density Matrix Theory
Tymczak, C. J.; Borysenko, Kostyantyn
2014-03-01
We propose a novel method for obtaining an accurate correlated ground state wave function for chemical systems beyond the Hartree-Fock level of theory. This method leverages existing linear scaling methods to accurately and easily obtain the correlated wave functions. We report on the theoretical development of this methodology, which we refer to as Many Body Density Matrix Theory. This theory has many significant advantages over existing methods. One, its computational cost is equivalent to Hartree-Fock or Density Functional theory. Two it is a variational upper bound to the exact many-body ground state energy. Three, like Hartree-Fock, it has no self-interaction. Four, it is size extensive. And five, formally is scales with the complexity of the correlations that in many cases scales linearly. We show the development of this theory and give several relevant examples.
Logarithmic entanglement lightcone in many-body localized systems
Deng, Dong-Ling; Li, Xiaopeng; Pixley, J. H.; Wu, Yang-Le; Das Sarma, S.
2017-01-01
We theoretically study the response of a many-body localized system to a local quench from a quantum information perspective. We find that the local quench triggers entanglement growth throughout the whole system, giving rise to a logarithmic lightcone. This saturates the modified Lieb-Robinson bound for quantum information propagation in many-body localized systems previously conjectured based on the existence of local integrals of motion. In addition, near the localization-delocalization transition, we find that the final states after the local quench exhibit volume-law entanglement. We also show that the local quench induces a deterministic orthogonality catastrophe for highly excited eigenstates, where the typical wave-function overlap between the pre- and postquench eigenstates decays exponentially with the system size.
An Exactly Solvable Many-Body Model
Zettili, Nouredine; Boukahil, Abdelkrim
2012-03-01
We deal here with the construction of a simple many-body model that can be solved exactly. This model serves as a tool for testing the validity and accuracy of many-body approximation methods, most notably those encountered in nuclear theory. The model consists of a system of two distinguishable, one-dimensional sets fermions interacting via a schematic two-body force. We construct the Hamiltonian of the model by means of vector operators that satisfy a Lie algebra and which are the generators of an SO(2,1) group. The Hamiltonian depends on an adjustable parameter which regulates the strength of the two-body interaction. The size of the Hamiltonian's matrix is rendered finite by means of a built-in symmetry: the Hamiltonian is represented by a five-diagonal square matrix of finite size. The energy spectrum of the model is obtained by diagonalizing this matrix. The energy eigenvalues obtained from this diagonalization are exact, for we don't need to resort to any approximation in the diagonalization. This model offers a rich and flexible platform for testing quantitatively the various many-body approximation methods especially those that deal with nuclear collective motion.
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.
Emergent equilibrium in many-body optical bistability
Foss-Feig, M.; Niroula, P.; Young, J. T.; Hafezi, M.; Gorshkov, A. V.; Wilson, R. M.; Maghrebi, M. F.
2017-04-01
Many-body systems constructed of quantum-optical building blocks can now be realized in experimental platforms ranging from exciton-polariton fluids to ultracold Rydberg gases, establishing a fascinating interface between traditional many-body physics and the driven-dissipative, nonequilibrium setting of cavity QED. At this interface, the standard techniques and intuitions of both fields are called into question, obscuring issues as fundamental as the role of fluctuations, dimensionality, and symmetry on the nature of collective behavior and phase transitions. Here, we study the driven-dissipative Bose-Hubbard model, a minimal description of numerous atomic, optical, and solid-state systems in which particle loss is countered by coherent driving. Despite being a lattice version of optical bistability, a foundational and patently nonequilibrium model of cavity QED, the steady state possesses an emergent equilibrium description in terms of a classical Ising model. We establish this picture by making new connections between traditional techniques from many-body physics (functional integrals) and quantum optics (the system-size expansion). To lowest order in a controlled expansion—organized around the experimentally relevant limit of weak interactions—the full quantum dynamics reduces to nonequilibrium Langevin equations, which support a phase transition described by model A of the Hohenberg-Halperin classification. Numerical simulations of the Langevin equations corroborate this picture, revealing that canonical behavior associated with the Ising model manifests readily in simple experimental observables.
Random matrices, symmetries, and many-body states
Johnson, Calvin W
2011-01-01
All nuclei with even numbers of protons and of neutrons have ground states with zero angular momentum. This is ascribed to the pairing force between nucleons, but simulations with random interactions suggest a much broader many-body phenomenon. In this Letter I project out random Hermitian matrices that have good quantum numbers and, computing the width of the Hamiltonian in subspaces, find ground states dominated by low quantum numbers, e.g. J=0. Furthermore I find odd-$Z$, odd-$N$ systems with isospin conservation have relatively fewer J=0 ground states.
Interferometric measurement of many-body topological invariants using polarons
Grusdt, Fabian; Yao, Norman; Abanin, Dmitry; Demler, Eugene
2014-05-01
We present a scheme for the direct detection of many-body topological invariants in ultra cold quantum gases in optical lattices. We generalize single-particle interferometric schemes developed for the detection of topologically non-trivial band structures [Atala et al., Nature Physics 9, 795 (2013)] by coupling a spin-1/2 impurity to a (topological) excitation of an interacting many-body system. Performing Ramsey interferometry in combination with Bloch oscillations of the resulting polaronic particle allows to directly detect the many body-topological invariant. In particular we consider adiabatic Thouless pumps in the super-lattice Bose-Hubbard model, which transport a quantized amount of particles across a one-dimensional lattice. In the presence of inter-atomic interactions this quantized current is given by a many-body Chern number, which can be measured using our protocol. These systems also support symmetry-protected topological phases, the invariants of which can be obtained from our protocol as well.
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
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.
On the Theory of Resonances in Non-Relativistic QED and Related Models
DEFF Research Database (Denmark)
Abou Salem, Walid K.; Faupin, Jeremy; Froehlich, Juerg;
We study the mathematical theory of quantum resonances in the standard model of non-relativistic QED and in Nelson's model. In particular, we estimate the survival probability of metastable states corresponding to quantum resonances and relate the resonances to poles of an analytic continuation...
Many-body approach to electronic excitations concepts and applications
Bechstedt, Friedhelm
2015-01-01
The many-body-theoretical basis and applications of theoretical spectroscopy of condensed matter, e.g. crystals, nanosystems, and molecules are unified in one advanced text for readers from graduate students to active researchers in the field. The theory is developed from first principles including fully the electron-electron interaction and spin interactions. It is based on the many-body perturbation theory, a quantum-field-theoretical description, and Green's functions. The important expressions for ground states as well as electronic single-particle and pair excitations are explained. Based on single-particle and two-particle Green's functions, the Dyson and Bethe-Salpeter equations are derived. They are applied to calculate spectral and response functions. Important spectra are those which can be measured using photoemission/inverse photoemission, optical spectroscopy, and electron energy loss/inelastic X-ray spectroscopy. Important approximations are derived and discussed in the light of selected computa...
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.
Exploring many body interactions with Raman spectroscopy
Tian, Yao
Many-body interactions are cornerstones of contemporary solid state physics research. Especially, phonon related interactions such as phonon-phonon coupling, spin-phonon coupling and electron-phonon coupling constantly present new challenges. To study phonon related many-body interactions, temperature dependent Raman spectroscopy is employed. Firstly, a new design and construction of a Raman microscope aimed at high collection eciency, positional and thermal stability is discussed. The application of the home-built Raman microscope is shown in the context of two types of novel materials; Cr2Ge2Te6 (spin-phonon coupling) and Bi2Te3-xSex (phonon-phonon coupling). Cr2Ge2Te6 is one of the rare class of ferromagnetic semiconductors and recent thermal transport studies suggest the spin and lattice are strongly coupled in its cousin compound Cr2Si2Te6. In this work, the spin-phonon coupling in Cr2Ge2Te6 has been revealed in multiple ways: we observed a split of two phonon modes due to the breaking of time reversal symmetry; the anomalous hardening of an additional three modes; and a dramatic enhancement of the phonon lifetimes. It is well-known that the phonon-phonon interaction plays a signicant role in determining the thermal transport properties of thermoelectrics. A comprehensive study of the phonon dynamics of Bi2Te3-xSex has been performed. We found that the unusual temperature dependence of dierent phonon modes originates from both cubic and quartic anharmonicity. These results are consistent with the resonance bonding mechanism, suggesting that the resonance bonding may be a common feature for conventional thermoelectrics. In the Raman spectra of Bi2Te2Se, the origin of the extra Raman feature has been debated for decades. Through a temperature dependent Raman study, we were able to prove the feature is generated by a Te-Se antisite induced local mode. The anomalous linewidth of the local mode as well as the anharmonic behavior were explained through a statistical
Many-body localization in infinite chains
Enss, T.; Andraschko, F.; Sirker, J.
2017-01-01
We investigate the phase transition between an ergodic and a many-body localized phase in infinite anisotropic spin-1 /2 Heisenberg chains with binary disorder. Starting from the Néel state, we analyze the decay of antiferromagnetic order ms(t ) and the growth of entanglement entropy Sent(t ) during unitary time evolution. Near the phase transition we find that ms(t ) decays exponentially to its asymptotic value ms(∞ ) ≠0 in the localized phase while the data are consistent with a power-law decay at long times in the ergodic phase. In the localized phase, ms(∞ ) shows an exponential sensitivity on disorder with a critical exponent ν ˜0.9 . The entanglement entropy in the ergodic phase grows subballistically, Sent(t ) ˜tα , α ≤1 , with α varying continuously as a function of disorder. Exact diagonalizations for small systems, on the other hand, do not show a clear scaling with system size and attempts to determine the phase boundary from these data seem to overestimate the extent of the ergodic phase.
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.
Path Integrals in Quantum Physics
2012-01-01
These lectures aim at giving graduate students an introduction to and a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by standard examples and special applications including numerical ev...
Many-body chaos at weak coupling
Stanford, Douglas
2016-10-01
The strength of chaos in large N quantum systems can be quantified using λ L , the rate of growth of certain out-of-time-order four point functions. We calculate λ L to leading order in a weakly coupled matrix Φ4 theory by numerically diagonalizing a ladder kernel. The computation reduces to an essentially classical problem.
Relativistic Remnants of Non-Relativistic Electrons
Kashiwa, Taro
2015-01-01
Electrons obeying the Dirac equation are investigated under the non-relativistic $c \\mapsto \\infty$ limit. General solutions are given by derivatives of the relativistic invariant functions whose forms are different in the time- and the space-like region, yielding the delta function of $(ct)^2 - x^2$. This light-cone singularity does survive to show that the charge and the current density of electrons travel with the speed of light in spite of their massiveness.
Supersymmetric solutions for non-relativistic holography
Energy Technology Data Exchange (ETDEWEB)
Donos, Aristomenis [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Gauntlett, Jerome P. [Blackett Laboratory, Imperial College, London (United Kingdom)]|[Institute for Mathematical Sciences, Imperial College, London (United Kingdom)
2009-01-15
We construct families of supersymmetric solutions of type IIB and D=11 supergravity that are invariant under the non-relativistic conformal algebra for various values of dynamical exponent z{>=}4 and z{>=}3, respectively. The solutions are based on five- and seven-dimensional Sasaki-Einstein manifolds and generalise the known solutions with dynamical exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively. (orig.)
Many-Body Boson Systems Half a Century Later
Verbeure, André F
2011-01-01
Many-body Boson Systems: Half a Century Later offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statistical mechanics and the energy-entropy balance principle as equilibrium criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus. Bridging the gap between idea’s of general theoretical physics and the phenomenological research in the field of Bose systems, this book provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate structural relation with the phenomena of spontaneous symmetry breaking and off-diagonal long range order; the condensate equation; the issue concerning the choice of boundary conditions; solvable versus non-solvable boson models; the set of quasi-free boson states; the role of dissipative perturbations; and the surprising but general relation between general quantum fluctuations and ...
Critical quasienergy states in driven many-body systems
Bastidas Valencia, Victor Manuel; Engelhardt, Georg; Perez-Fernandez, Pedro; Vogl, Malte; Brandes, Tobias
2015-03-01
A quantum phase transition (QPT) is characterized by non-analyticities of ground-state properties at the critical points. Recently it has been shown that quantum criticality emerges also in excited states of the system, which is referred to as an excited-state quantum phase transition (ESQPT). This kind of quantum criticality is intimately related to a level clustering at critical energies, which results in a logarithmic singularity in the density of states. Most of the previous studies on quantum criticality in excited states have been focused on time independent systems. Here we study spectral singularities that appear in periodically-driven many-body systems and show how the external control allows one to engineer geometrical features of the quasienergy landscape. In particular, we study singularities in the quasienergy spectrum of a fully-connected network consisting of two-level systems with time-dependent interactions. We discuss the characteristic signatures of these singularities in observables like the magnetization, which should be measurable with current technology. The authors gratefully acknowledge financial support by the DFG via grants BRA 1528/7, BRA 1528/8, SFB 910 (V.M.B., T.B.), the Spanish Ministerio de Ciencia e Innovacion (Grants No. FIS2011-28738-C02-01) and Junta de Andalucia (Grants No. FQM160).
Non relativistic limit of integrable QFT and Lieb-Liniger models
Bastianello, Alvise; De Luca, Andrea; Mussardo, Giuseppe
2016-12-01
In this paper we study a suitable limit of integrable QFT with the aim to identify continuous non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda field theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.
Non Relativistic Limit of Integrable QFT and Lieb-Liniger Models
Bastianello, Alvise; Mussardo, Giuseppe
2016-01-01
In this paper we study a suitable limit of integrable QFT with the aim to identify non-relativistic integrable models with local interactions. This limit amounts to sending to infinity the speed of light c but simultaneously adjusting the coupling constant g of the quantum field theories in such a way to keep finite the energies of the various excitations. The QFT considered here are Toda Field Theories and the O(N) non-linear sigma model. In both cases the resulting non-relativistic integrable models consist only of Lieb-Liniger models, which are fully decoupled for the Toda theories while symmetrically coupled for the O(N) model. These examples provide explicit evidence of the universality and ubiquity of the Lieb-Liniger models and, at the same time, suggest that these models may exhaust the list of possible non-relativistic integrable theories of bosonic particles with local interactions.
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.
Chiral Floquet Phases of Many-Body Localized Bosons
Po, Hoi Chun; Fidkowski, Lukasz; Morimoto, Takahiro; Potter, Andrew C.; Vishwanath, Ashvin
2016-10-01
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.
Remark on charge conjugation in the non relativistic limit
Cabo-Montes de Oca, Alejandro; Rojas, H P; Socolovsky, M
2005-01-01
We study the non relativistic limit of the charge conjugation operation $\\cal C$ in the context of the Dirac equation coupled to an electromagnetic field. The limit is well defined and, as in the relativistic case, $\\cal C$, $\\cal P$ (parity) and $\\cal T$ (time reversal) are the generators of a matrix group isomorphic to a semidirect sum of the dihedral group of eight elements and $\\Z_2$. The existence of the limit is supported by an argument based in quantum field theory. Finally, if one complexifies the Lorentz group and therefore the galilean spacetime $x_\\mu$, then the explicit form of the matrix for $\\cal C$ allows to interpret it, in this context, as the complex conjugation of the spatial coordinates: $\\vec{x} \\to \\vec{x}^*$. This result is natural in a fiber bundle description.
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.
Factorization in large-scale many-body calculations
Johnson, Calvin W; Krastev, Plamen G
2013-01-01
One approach for solving interacting many-fermion systems is the configuration-interaction method, also sometimes called the interacting shell model, where one finds eigenvalues of the Hamiltonian in a many-body basis of Slater determinants (antisymmeterized products of single-particle wavefunctions). The resulting Hamiltonian matrix is typically very sparse, but for large systems the nonzero matrix elements can nonetheless require terabytes or more of storage. An alternate algorithm, applicable to a broad class of systems with symmetry, in our case rotational invariance, is to exactly factorize both the basis and the interaction using additive/multiplicative quantum numbers; such an algorithm can reduce the storage requirements by an order of magnitude or more. We discuss factorization in general as well as in the context of a specific configuration-interaction code, BIGSTICK, which runs both on serial and parallel machines.
Novel simulation model for many-body multipole dispersion interactions
van der Hoef Paul, Martin A.; Madden, A.
We present a novel simulation technique, within the framework of a molecular dynamics simulation, which accounts for both two- and three-body dispersion interactions, up to the triple-quadrupole interaction. This technique involves a unification of molecular dynamics and quantum-mechanical variational methods, in the spirit of the Car-Parrinello method. The advantage of this new method compared to existing techniques for simulating three-body dispersion forces, is that it allows for a consistent treatment of both dispersion damping and periodic boundary conditions at the pair and three-body level. The latter means that it would be possible, for the first time, to include many-body dispersion effects in the simulation of bulk properties of materials, without making use of effective pair potentials.
Charge optimized many-body potential for aluminum
Choudhary, Kamal; Liang, Tao; Chernatynskiy, Aleksandr; Lu, Zizhe; Goyal, Anuj; Phillpot, Simon R.; Sinnott, Susan B.
2015-01-01
An interatomic potential for Al is developed within the third generation of the charge optimized many-body (COMB3) formalism. The database used for the parameterization of the potential consists of experimental data and the results of first-principles and quantum chemical calculations. The potential exhibits reasonable agreement with cohesive energy, lattice parameters, elastic constants, bulk and shear modulus, surface energies, stacking fault energies, point defect formation energies, and the phase order of metallic Al from experiments and density functional theory. In addition, the predicted phonon dispersion is in good agreement with the experimental data and first-principles calculations. Importantly for the prediction of the mechanical behavior, the unstable stacking fault energetics along the direction on the (1 1 1) plane are similar to those obtained from first-principles calculations. The polycrsytal when strained shows responses that are physical and the overall behavior is consistent with experimental observations.
Critical Properties of the Many-Body Localization Transition
Khemani, Vedika; Lim, S. P.; Sheng, D. N.; Huse, David A.
2017-04-01
The transition from a many-body localized phase to a thermalizing one is a dynamical quantum phase transition that lies outside the framework of equilibrium statistical mechanics. We provide a detailed study of the critical properties of this transition at finite sizes in one dimension. We find that the entanglement entropy of small subsystems looks strongly subthermal in the quantum critical regime, which indicates that it varies discontinuously across the transition as the system size is taken to infinity, even though many other aspects of the transition look continuous. We also study the variance of the half-chain entanglement entropy, which shows a peak near the transition, and find substantial variation in the entropy across eigenstates of the same sample. Furthermore, the sample-to-sample variations in this quantity are strongly growing and are larger than the intrasample variations. We posit that these results are consistent with a picture in which the transition to the thermal phase is driven by an eigenstate-dependent sparse resonant "backbone" of long-range entanglement, which just barely gains enough strength to thermalize the system on the thermal side of the transition as the system size is taken to infinity. This discontinuity in a global quantity—the presence of a fully functional bath—in turn implies a discontinuity even for local properties. We discuss how this picture compares with existing renormalization group treatments of the transition.
Projection techniques to approach the nuclear many-body problem
Sun, Yang
2016-04-01
Our understanding of angular-momentum-projection goes beyond quantum-number restoration for symmetry-violated states. The angular-momentum-projection method can be viewed as an efficient way of truncating the shell-model space which is otherwise too large to handle. It defines a transformation from the intrinsic system, where dominant excitation modes in the low-energy region are identified with the concept of spontaneous symmetry breaking, to the laboratory frame with well-organized configuration states according to excitations. An energy-dictated, physically-guided shell-model truncation can then be carried out within the projected space and the Hamiltonian is thereby diagonalized in a compact basis. The present article reviews the theory of angular-momentum-projection applied in the nuclear many-body problem. Angular momentum projection emerges naturally if a deformed state is treated quantum-mechanically. To demonstrate how different physical problems in heavy, deformed nuclei can be efficiently described with different truncation schemes, we introduce the projected shell model and show examples of calculation in a basis with axial symmetry, a basis with triaxiality, and a basis with both quasiparticle and phonon excitations. Technical details of how to calculate the projected matrix elements and how to build a workable model with the projection techniques are given in the appendix.
Parametric excitation and squeezing in a many-body spinor condensate.
Hoang, T M; Anquez, M; Robbins, B A; Yang, X Y; Land, B J; Hamley, C D; Chapman, M S
2016-04-05
Atomic spins are usually manipulated using radio frequency or microwave fields to excite Rabi oscillations between different spin states. These are single-particle quantum control techniques that perform ideally with individual particles or non-interacting ensembles. In many-body systems, inter-particle interactions are unavoidable; however, interactions can be used to realize new control schemes unique to interacting systems. Here we demonstrate a many-body control scheme to coherently excite and control the quantum spin states of an atomic Bose gas that realizes parametric excitation of many-body collective spin states by time varying the relative strength of the Zeeman and spin-dependent collisional interaction energies at multiples of the natural frequency of the system. Although parametric excitation of a classical system is ineffective from the ground state, we show that in our experiment, parametric excitation from the quantum ground state leads to the generation of quantum squeezed states.
On the origin of spurious errors in many-body expansion for water cluster
Indian Academy of Sciences (India)
SOUMEN SAHA; M RAM VIVEK; G NARAHARI SASTRY
2017-07-01
Many-body expansion (MBE) has been carried out to investigate two- to five-body energy terms and their contributions to the interaction energy (IE) of (H₂O)₁₅ cluster. We have observed that the erroneous contribution of many-body terms on IE originated from cheaper convergence thresholds set as default in popular quantum mechanics packages. The propagation of errors from smaller to higher-body terms, due to the combinatorial nature of MBE, is also observed.
Relativistic and Non-relativistic Equations of Motion
Mangiarotti, L
1998-01-01
It is shown that any second order dynamic equation on a configuration space $X$ of non-relativistic time-dependent mechanics can be seen as a geodesic equation with respect to some (non-linear) connection on the tangent bundle $TX\\to X$ of relativistic velocities. Using this fact, the relationship between relativistic and non-relativistic equations of motion is studied.
Introducing many-body physics using atomic spectroscopy
Krebs, Dietrich; Santra, Robin
2013-01-01
Atoms constitute relatively simple many-body systems, making them suitable objects for developing an understanding of basic aspects of many-body physics. Photoabsorption spectroscopy is a prominent method to study the electronic structure of atoms and the inherent many-body interactions. In this article the impact of many-body effects on well-known spectroscopic features such as Rydberg series, Fano resonances, Cooper minima, and giant resonances is studied, and related many-body phenomena in other fields are outlined. To calculate photoabsorption cross sections the time-dependent configuration interaction singles (TDCIS) model is employed. The conceptual clearness of TDCIS in combination with the compactness of atomic systems allows for a pedagogical introduction to many-body phenomena.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Gomis, Joaquim; Not, Daniel
2017-02-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Extended Galilean symmetries of non-relativistic strings
Batlle, Carles; Not, Daniel
2016-01-01
We consider two non-relativistic strings and their Galilean symmetries. These strings are obtained as the two possible non-relativistic (NR) limits of a relativistic string. One of them is non-vibrating and represents a continuum of non-relativistic massless particles, and the other one is a non-relativistic vibrating string. For both cases we write the generator of the most general point transformation and impose the condition of Noether symmetry. As a result we obtain two sets of non-relativistic Killing equations for the vector fields that generate the symmetry transformations. Solving these equations shows that NR strings exhibit two extended, infinite dimensional space-time symmetries which contain, as a subset, the Galilean symmetries. For each case, we compute the associated conserved charges and discuss the existence of non-central extensions.
Simuluating quantum many-body systems subject to measurements
DEFF Research Database (Denmark)
Gammelmark, Søren
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....
Simulating quantum many-body systems subject to measurements
DEFF Research Database (Denmark)
Gammelmark, Søren
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....
Efficient quantum transport in disordered interacting many-body networks
Ortega, Adrian; Stegmann, Thomas; Benet, Luis
2016-10-01
The coherent transport of n fermions in disordered networks of l single-particle states connected by k -body interactions is studied. These networks are modeled by embedded Gaussian random matrix ensemble (EGE). The conductance bandwidth and the ensemble-averaged total current attain their maximal values if the system is highly filled n ˜l -1 and k ˜n /2 . For the cases k =1 and k =n the bandwidth is minimal. We show that for all parameters the transport is enhanced significantly whenever centrosymmetric embedded Gaussian ensemble (csEGE) are considered. In this case the transmission shows numerous resonances of perfect transport. Analyzing the transmission by spectral decomposition, we find that centrosymmetry induces strong correlations and enhances the extrema of the distributions. This suppresses destructive interference effects in the system and thus causes backscattering-free transmission resonances that enhance the overall transport. The distribution of the total current for the csEGE has a very large dominating peak for n =l -1 , close to the highest observed currents.
Energy shift of interacting non-relativistic fermions in noncommutative space
Directory of Open Access Journals (Sweden)
A. Jahan
2005-06-01
Full Text Available A local interaction in noncommutative space modifies to a non-local one. For an assembly of particles interacting through the contact potential, formalism of the quantum field theory makes it possible to take into account the effect of modification of the potential on the energy of the system. In this paper we calculate the energy shift of an assembly of non-relativistic fermions, interacting through the contact potential in the presence of the two-dimensional noncommutativity.
Intense-field many-body S-matrix theory
Energy Technology Data Exchange (ETDEWEB)
Becker, A [Max-Planck-Institut fuer Physik komplexer Systeme, Noethnitzer Str 38, D-01187 Dresden (Germany); Faisal, F H M [Fakultaet fuer Physik, Universitaet Bielefeld, Postfach 100131, D-33501 Bielefeld (Germany)
2005-02-14
Intense-field many-body S-matrix theory (IMST) provides a systematic ab initio approach to investigate the dynamics of atoms and molecules interacting with intense laser radiation. We review the derivation of IMST as well as its diagrammatic representation and point out its advantage over the conventional 'prior' and 'post' expansions which are shown to be special cases of IMST. The practicality and usefulness of the theory is illustrated by its application to a number of current problems of atomic and molecular ionization in intense fields. We also present a consistent S-matrix formulation of the quantum amplitude for high harmonic generation (HHG) and point out some of the most general properties of HHG radiation emitted by a single atom as well as its relation to coherent emission from many atoms. Experimental results for single and double (multiple) ionization of atoms and the observed distributions of coincidence measurements are analysed and the dominant mechanisms behind them are discussed. Ionization of more complex systems such as diatomic and polyatomic molecules in intense laser fields is analysed as well using IMST and the results are discussed with special attention to the role of molecular orbital symmetry and molecular orientation in space. The review ends with a summary and a brief outlook. (topical review)
Holographic thermalization from non relativistic branes
Roychowdhury, Dibakar
2016-01-01
In this paper, based on the fundamental principles of Gauge/gravity duality and considering a \\textit{global quench}, we probe the physics of thermalization for a special class of strongly coupled non relativistic QFTs by computing the entanglement entropy of the plasma. The isometry group of such QFTs is comprised of the generators of the Schr\\"odinger algebra which could be precisely realized as an isometry group of the killing generators of an asymptotically Schr\\"odinger $ Dp $ brane space time. In our analysis, we note that during the pre local stages of the thermal equilibrium the entanglement entropy has a faster growth in time compared to its relativistic cousin. However, it shows a linear growth during the post local stages of thermal equilibrium where the so called tsunami velocity associated with the linear growth of the entanglement entropy saturates to that of its value corresponding to the relativistic scenario. Finally, we explore the saturation region and it turns out that one must constraint ...
High precision module for Chaos Many-Body Engine
Grossu, I V; Felea, D; Jipa, Al
2014-01-01
In this paper we present a C# high precision relativistic many-body module integrated with Chaos Many-Body Engine. As a direct application, we used it for estimating the butterfly effect involved by the gravitational force in a specific nuclear relativistic collision toy-model.
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.
Non-relativistic particles in a thermal bath
Directory of Open Access Journals (Sweden)
Vairo Antonio
2014-04-01
Full Text Available Heavy particles are a window to new physics and new phenomena. Since the late eighties they are treated by means of effective field theories that fully exploit the symmetries and power counting typical of non-relativistic systems. More recently these effective field theories have been extended to describe non-relativistic particles propagating in a medium. After introducing some general features common to any non-relativistic effective field theory, we discuss two specific examples: heavy Majorana neutrinos colliding in a hot plasma of Standard Model particles in the early universe and quarkonia produced in heavy-ion collisions dissociating in a quark-gluon plasma.
Direct observation of ultrafast many-body electron dynamics in an ultracold Rydberg gas
Takei, Nobuyuki; Sommer, Christian; Genes, Claudiu; Pupillo, Guido; Goto, Haruka; Koyasu, Kuniaki; Chiba, Hisashi; Weidemüller, Matthias; Ohmori, Kenji
2016-11-01
Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with many-body correlations among Rydberg atoms beyond mean-field approximations. This coherent and ultrafast many-body dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate non-equilibrium dynamics of quantum many-body systems on the ultrafast timescale.
Many-body fits of phase-equivalent effective interactions
Johnson, Calvin W
2010-01-01
In many-body theory it is often useful to renormalize short-distance, high-momentum components of an interaction via unitary transformations. Such transformations preserve the on-shell physical observables of the two-body system (mostly phase-shifts, hence unitarily-connected effective interactions are often called phase-equivalent), while modifying off-shell T-matrix elements influential in many-body systems. In this paper I lay out a general and systematic approach for controlling the off-shell behavior of an effective interaction, which can be adjusted to many-body properties, and present an application to trapped fermions at the unitary
Many-body localization due to random interactions
Sierant, Piotr; Delande, Dominique; Zakrzewski, Jakub
2017-02-01
The possibility of observing many-body localization of ultracold atoms in a one-dimensional optical lattice is discussed for random interactions. In the noninteracting limit, such a system reduces to single-particle physics in the absence of disorder, i.e., to extended states. In effect, the observed localization is inherently due to interactions and is thus a genuine many-body effect. In the system studied, many-body localization manifests itself in a lack of thermalization visible in temporal propagation of a specially prepared initial state, in transport properties, in the logarithmic growth of entanglement entropy, and in statistical properties of energy levels.
Non-Relativistic Anti-Snyder Model and Some Applications
Ching, Chee Leong; Ng, Wei Khim
2016-01-01
We examine the (2+1)-dimensional Dirac equation in a homogeneous magnetic field under the non-relativistic anti-Snyder model which is relevant to deformed special relativity (DSR) since it exhibits an intrinsic upper bound of the momentum of free particles. After setting up the formalism, exact eigen solutions are derived in momentum space representation and they are expressed in terms of finite orthogonal Romanovski polynomials. There is a finite maximum number of allowable bound states due to the orthogonality of the polynomials and the maximum energy is truncated at the maximum n. Similar to the minimal length case, the degeneracy of the Dirac-Landau levels in anti- Snyder model are modified and there are states that do not exist in the ordinary quantum mechanics limit. By taking zero mass limit, we explore the motion of effective zero mass charged Fermions in Graphene like material and obtained a maximum bound of deformed parameter. Furthermore, we consider the modified energy dispersion relations and its...
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.
Stochastic many-body perturbation theory for anharmonic molecular vibrations.
Hermes, Matthew R; Hirata, So
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(-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.
Investigation of many-body forces in krypton and xenon
Salacuse, J. J.; Egelstaff, P. A.
1988-10-01
The simplicity of the state dependence at relatively high temperatures of the many-body potential contribution to the pressure and energy has been pointed out previously [J. Ram and P. A. Egelstaff, J. Phys. Chem. Liq. 14, 29 (1984); A. Teitsima and P. A. Egelstaff, Phys. Rev. A 21, 367 (1980)]. In this paper, we investigate how far these many-body potential terms may be represented by simple models in the case of krypton on the 423-, 273-, 190-, and 150-K isotherms, and xenon on the 170-, 210-, and 270-K isotherms. At the higher temperatures the best agreement is found for the mean-field type of theory, and some consequences are pointed out. On the lower isotherms a state point is found where the many-body energy vanishes, and large departures from mean-field behavior are observed. This is attributed to the influence of short-ranged many-body forces.
Radiative transitions in mesons in a non relativistic quark model
Bonnaz, R.; Silvestre-Brac, B.; Gignoux, C.
2001-01-01
In the framework of the non relativistic quark model, an exhaustive study of radiative transitions in mesons is performed. The emphasis is put on several points. Some traditional approximations (long wave length limit, non relativistic phase space, dipole approximation for E1 transitions, gaussian wave functions) are analyzed in detail and their effects commented. A complete treatment using three different types of realistic quark-antiquark potential is made. The overall agreement with experi...
Radiative transitions in mesons in a non relativistic quark model
Bonnaz, R; Gignoux, C
2002-01-01
In the framework of the non relativistic quark model, an exhaustive study of radiative transitions in mesons is performed. The emphasis is put on several points. Some traditional approximations (long wave length limit, non relativistic phase space, dipole approximation for E1 transitions, gaussian wave functions) are analyzed in detail and their effects commented. A complete treatment using three different types of realistic quark-antiquark potential is made. The overall agreement with experimental data is quite good, but some improvements are suggested.
Convex Decompositions of Thermal Equilibrium for Non-interacting Non-relativistic Particles
Chenu, Aurelia; Branczyk, Agata; Sipe, John
2016-05-01
We provide convex decompositions of thermal equilibrium for non-interacting non-relativistic particles in terms of localized wave packets. These quantum representations offer a new tool and provide insights that can help relate to the classical picture. Considering that thermal states are ubiquitous in a wide diversity of fields, studying different convex decompositions of the canonical ensemble is an interesting problem by itself. The usual classical and quantum pictures of thermal equilibrium of N non-interacting, non-relativistic particles in a box of volume V are quite different. The picture in classical statistical mechanics is about (localized) particles with a range of positions and velocities; in quantum statistical mechanics, one considers the particles (bosons or fermions) associated with energy eigenstates that are delocalized through the whole box. Here we provide a representation of thermal equilibrium in quantum statistical mechanics involving wave packets with a localized coordinate representation and an expectation value of velocity. In addition to derive a formalism that may help simplify particular calculations, our results can be expected to provide insights into the transition from quantum to classical features of the fully quantum thermal state.
Exact many-body dynamics with stochastic one-body density matrix evolution
Energy Technology Data Exchange (ETDEWEB)
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)
Isotropic Landau levels of relativistic and non-relativistic fermions in 3D flat space
Li, Yi; Wu, Congjun
2012-02-01
The usual Landau level quantization, as demonstrated in the 2D quantum Hall effect, is crucially based on the planar structure. In this talk, we explore its 3D counterpart possessing the full 3D rotational symmetry as well as the time reversal symmetry. We construct the Landau level Hamiltonians in 3 and higher dimensional flat space for both relativistic and non-relativistic fermions. The 3D cases with integer fillings are Z2 topological insulators. The non-relativistic version describes spin-1/2 fermions coupling to the Aharonov-Casher SU(2) gauge field. This system exhibits flat Landau levels in which the orbital angular momentum and the spin are coupled with a fixed helicity. Each filled Landau level contributes one 2D helical Dirac Fermi surface at an open boundary, which demonstrates the Z2 topological nature. A natural generalization to Dirac fermions is found as a square root problem of the above non-relativistic version, which can also be viewed as the Dirac equation defined on the phase space. All these Landau level problems can be generalized to arbitrary high dimensions systematically. [4pt] [1] Yi Li and Congjun Wu, arXiv:1103.5422.[0pt] [2] Yi Li, Ken Intriligator, Yue Yu and Congjun Wu, arXiv:1108.5650.
Local reversibility and entanglement structure of many-body ground states
Kuwahara, Tomotaka; Amico, Luigi; Vedral, Vlatko
2015-01-01
The low-temperature physics of quantum many-body systems is largely governed by the structure of their ground states. Minimizing the energy of local interactions, ground states often reflect strong properties of locality such as the area law for entanglement entropy and the exponential decay of correlations between spatially separated observables. In this letter we present a novel characterization of locality in quantum states, which we call `local reversibility'. It characterizes the type of operations that are needed to reverse the action of a general disturbance on the state. We prove that unique ground states of gapped local Hamiltonian are locally reversible. This way, we identify new fundamental features of many-body ground states, which cannot be derived from the aforementioned properties. We use local reversibility to distinguish between states enjoying microscopic and macroscopic quantum phenomena. To demonstrate the potential of our approach, we prove specific properties of ground states, which are ...
Accessing Many-Body Localized States through the Generalized Gibbs Ensemble
Inglis, Stephen; Pollet, Lode
2016-09-01
We show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. We devise a heuristic way of constructing local integrals of motion of high quality, which are added to the Hamiltonian in conjunction with Lagrange multipliers. The ground state simulation of the shifted Hamiltonian corresponds to a high-energy state of the original Hamiltonian in the case of exactly known local integrals of motion. The inevitable mixing between eigenstates as a consequence of nonperfect integrals of motion is weak enough such that the characteristics of many-body localized systems are not averaged out, unlike the standard ensembles of statistical mechanics. Our method paves the way to study higher dimensions and indicates that a fully many-body localized phase in 2D, where (nearly) all eigenstates are localized, is likely to exist.
Palge, Veiko; Dunningham, Jacob; Hasegawa, Yuji
2016-01-01
In quantum physics Wigner's rotation is commonly regarded as confirmed by the Thomas precession in a hydrogen like atom. In this paper we show that a direct experimental verification of Wigner's rotation is in principle accessible in the regime of non-relativistic velocities at $2 \\cdot 10^3\\,$m/s and propose an experiment using thermal neutrons. The experiment can be carried out in a laboratory and it provides a test of relativity in the quantum domain.
Failure of relativistic codes in the non-relativistic limit: the role of Brillouin configurations
Indelicato, P J; Desclaux, J P
2004-01-01
In the present letter we solve a long standing problem with relativistic calculations done with the widely used Multi-Configuration Dirac-Fock Method. We show, using Relativistic Many-Body Perturbation Theory (RMBPT), how even for relatively high-$Z$, relaxation or correlation causes the non-relativistic limit of states of different total angular momentum but identical orbital angular momentum to have different energies. We identify the role of single excitations obeying to Brillouin's theorem in this problem. We show that with large scale calculations in which this problem is properly treated, we can reproduce very accurately recent high-precision measurements in F-like Ar, and turn then into precise test of QED
Many Body Diffusion and Interacting Electrons in a Harmonic Confinement
Luczak, F.; Brosens, F.; Devreese, J. T.; Lemmens, L. F.
2001-06-01
We present numerically exact energy estimates for two-dimensional electrons in a parabolic confinement. By application of an extension of the recently introduced many-body diffusion algorithm, the ground-state energies are simulated very efficiently. The new algorithm relies on partial antisymmetrization under permutation of particle coordinates. A comparison is made with earlier theoretical results for that system.
Molecular Interactions with Many-Body Perturbation Theory.
1981-09-11
Medcine , Ne. York, York, June 4, 1979. R. J. Bartlett, "Many-Body Perturbation Thery", Aarhus University, Aarhus, Denmark, June 18, 1979. R. J. Bartlett...editor can be accepted for speedy publication. Permission is granted to authors of scientific articles and books to quote from this journal provided
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.
Fields and fluids on curved non-relativistic spacetimes
Geracie, Michael; Roberts, Matthew M
2015-01-01
We consider non-relativistic curved geometries and argue that the background structure should be generalized from that considered in previous works. In this approach the derivative operator is defined by a Galilean spin connection valued in the Lie algebra of the Galilean group. This includes the usual spin connection plus an additional "boost connection" which parameterizes the freedom in the derivative operator not fixed by torsion or metric compatibility. As an example of this approach we develop the theory of non-relativistic dissipative fluids and find significant differences in both equations of motion and allowed transport coefficients from those found previously. Our approach also immediately generalizes to systems with independent mass and charge currents as would arise in multicomponent fluids. Along the way we also discuss how to write general locally Galilean invariant non-relativistic actions for multiple particle species at any order in derivatives. A detailed review of the geometry and its rela...
Interferometric measurements of many-body topological invariants using mobile impurities
Grusdt, F.; Yao, N. Y.; Abanin, D.; Fleischhauer, M.; Demler, E.
2016-01-01
Topological quantum phases cannot be characterized by Ginzburg–Landau type order parameters, and are instead described by non-local topological invariants. Experimental platforms capable of realizing such exotic states now include synthetic many-body systems such as ultracold atoms or photons. Unique tools available in these systems enable a new characterization of strongly correlated many-body states. Here we propose a general scheme for detecting topological order using interferometric measurements of elementary excitations. The key ingredient is the use of mobile impurities that bind to quasiparticles of a host many-body system. Specifically, we show how fractional charges can be probed in the bulk of fractional quantum Hall systems. We demonstrate that combining Ramsey interference with Bloch oscillations can be used to measure Chern numbers characterizing the dispersion of individual quasiparticles, which gives a direct probe of their fractional charges. Possible extensions of our method to other many-body systems, such as spin liquids, are conceivable. PMID:27312285
Angular momentum in non-relativistic QED and photon contribution to spin of hydrogen atom
Energy Technology Data Exchange (ETDEWEB)
Chen Panying, E-mail: pychen@umd.ed [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Ji Xiangdong [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Institute of Particle Physics and Cosmology, Department of Physics, Shanghai Jiao Tong University, Shanghai, 200240 (China); Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China); Xu Yang [Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China); Zhang Yue [Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, MD 20742 (United States); Center for High-Energy Physics and Institute of Theoretical Physics, Peking University, Beijing, 100080 (China)
2010-04-26
We study angular momentum in non-relativistic quantum electrodynamics (NRQED). We construct the effective total angular momentum operator by applying Noether's theorem to the NRQED lagrangian. We calculate the NRQED matching for the individual components of the QED angular momentum up to one loop. We illustrate an application of our results by the first calculation of the angular momentum of the ground state hydrogen atom carried in radiative photons, alpha{sub em}{sup 3}/18pi, which might be measurable in future atomic experiments.
Irreducible many-body correlations in topologically ordered systems
Liu, Yang; Zeng, Bei; Zhou, D. L.
2016-02-01
Topologically ordered systems exhibit large-scale correlation in their ground states, which may be characterized by quantities such as topological entanglement entropy. We propose that the concept of irreducible many-body correlation (IMC), the correlation that cannot be implied by all local correlations, may also be used as a signature of topological order. In a topologically ordered system, we demonstrate that for a part of the system with holes, the reduced density matrix exhibits IMCs which become reducible when the holes are removed. The appearance of these IMCs then represents a key feature of topological phase. We analyze the many-body correlation structures in the ground state of the toric code model in external magnetic fields, and show that the topological phase transition is signaled by the IMCs.
Many-body interactions in quasi-freestanding graphene
Siegel, David A.; Park, Cheol-Hwan; Hwang, Choongyu; Deslippe, Jack; Fedorov, Alexei V.; Louie, Steven G.; Lanzara, Alessandra
2011-01-01
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. PMID:21709258
Quasi-Many-Body Localization in Translation-Invariant Systems
Yao, N. Y.; Laumann, C. R.; Cirac, J. I.; Lukin, M. D.; Moore, J. E.
2016-12-01
We examine localization phenomena associated with generic, high entropy, states of a translation-invariant, one-dimensional spin ladder. At early times, we find slow growth of entanglement entropy consistent with the known phenomenology of many-body localization in disordered, interacting systems. At intermediate times, however, anomalous diffusion sets in, leading to full spin polarization decay on an exponentially activated time scale. We identify a single length scale which parametrically controls both the spin transport times and the apparent divergence of the susceptibility to spin glass ordering. Ultimately, at the latest times, the exponentially slow anomalous diffusion gives way to diffusive thermal behavior. We dub the intermediate dynamical behavior, which persists over many orders of magnitude in time, quasi-many-body localization.
Path Integrals in Quantum Physics
Rosenfelder, R
2012-01-01
These lectures aim at giving graduate students an introduction to and a working knowledge of path integral methods in a wide variety of fields in physics. Consequently, the lecture notes are organized in three main parts dealing with non-relativistic quantum mechanics, many-body physics and field theory. In the first part the basic concepts of path integrals are developed in the usual heuristic, non-mathematical way followed by standard examples and special applications including numerical evaluation of (euclidean) path integrals by Monte-Carlo methods with a program for the anharmonic oscillator. The second part deals with the application of path integrals in statistical mechanics and many-body problems treating the polaron problem, dissipative quantum systems, path integrals over ordinary and Grassmannian coherent states and perturbation theory for both bosons and fermions. Again a simple Fortran program is included for illustrating the use of strong-coupling methods. Finally, in the third part path integra...
Kirilyuk, Andrei P
2012-01-01
We review the recently proposed unreduced, complex-dynamical solution to many-body problem with arbitrary interaction and its application to unified solution of fundamental problems, including foundations of causally complete quantum mechanics, relativity, particle properties and cosmology. We first analyse the universal properties of many-body problem solution without any perturbative reduction and show that the emerging new quality of fundamental dynamic multivaluedness (or redundance) of resulting system configuration leads to universal concept of dynamic complexity, chaoticity and fractality of any real system behaviour. We then consider unified features of this complex dynamics. Applications of that universal description to systems at various complexity levels have been performed and in this paper we review those at the lowest, fundamental complexity levels leading to causal understanding of unified origins of quantum mechanics, relativity (special and general), elementary particles, their intrinsic prop...
0{sup +} ground state dominance in many-body systems
Energy Technology Data Exchange (ETDEWEB)
Zhao, Yu-Min [Southeast Univ., Dept. of Physics, Nanjing (China); Arima, Akito [The House of Councilors, Tokyo (Japan); Yoshinaga, Naotaka [Saitama Univ., Physics Dept., Saitama (Japan)
2002-12-01
We propose a simple approach to predict the angular momentum I ground states (Ig.s.) probabilities of many-body systems without diagonalization of the hamiltonian using random interactions. It is suggested that the 0g.s. dominance in boson systems and even valence nucleon systems is not given by the model space as previously assumed, but by specific two-body interactions. (author)
Efficient variational diagonalization of fully many-body localized Hamiltonians
Pollmann, Frank; Khemani, Vedika; Cirac, J. Ignacio; Sondhi, S. L.
2016-07-01
We introduce a variational unitary matrix product operator based variational method that approximately finds all the eigenstates of fully many-body localized one-dimensional Hamiltonians. The computational cost of the variational optimization scales linearly with system size for a fixed depth of the UTN ansatz. We demonstrate the usefulness of our approach by considering the Heisenberg chain in a strongly disordered magnetic field for which we compare the approximation to exact diagonalization results.
Many-Body Electronic Structure of Curium metal
Toropova, Antonina; Haule, Kristjan; Kotliar, Gabriel
2006-03-01
We report computer-based simulations for the many-body electronic structure of Curium metal. Cm belongs to the actinide series and has a half-filled shell with seven 5f electrons. As a function of pressure, curium exhibits five different crystallographic phases. At low temperatures all phases demonstrate either antiferromagnetic or ferrimagnetic ordering. In this study we perform LDA+DMFT calculations for the antiferromagnetic state of high-pressure fcc modification of Curium metal.
Scale-free entanglement replication in driven-dissipative many body systems
Zippilli, S; Adesso, G; Illuminati, F
2012-01-01
We study the dynamics of independent arrays of many-body dissipative systems, subject to a common driving by an entangled light field. We show that in the steady state the global system orders in a series of inter-array strongly entangled pairs over all distances. Such scale-free entanglement replication and long-distance distribution mechanism has potential applications for the implementation of robust quantum networked communication.
Accessing many-body localized states through the Generalized Gibbs Ensemble
Inglis, Stephen; Pollet, Lode
2016-01-01
We show how the thermodynamic properties of large many-body localized systems can be studied using quantum Monte Carlo simulations. To this end we devise a heuristic way of constructing local integrals of motion of very high quality, which are added to the Hamiltonian in conjunction with Lagrange multipliers. The ground state simulation of the shifted Hamiltonian corresponds to a high-energy state of the original Hamiltonian in case of exactly known local integrals of motion. We can show that...
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary coordinat
A brief introduction to non-relativistic supergravity
Energy Technology Data Exchange (ETDEWEB)
Zojer, Thomas [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen (Netherlands)
2016-04-15
Non-relativistic geometries have received more attention lately. We review our attempts to construct supersymmetric extensions of this so-called Newton-Cartan geometry in three space-time dimensions. (copyright 2015 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Non-relativistic supergravity in three space-time dimensions
Zojer, Thomas
2016-01-01
This year Einstein's theory of general relativity celebrates its one hundredth birthday. It supersedes the non-relativistic Newtonian theory of gravity in two aspects: i) there is a limiting velocity, nothing can move quicker than the speed of light and ii) the theory is valid in arbitrary
Theory of non-relativistic three-particle scattering
Malfliet, R.; Ruijgrok, Th.
1967-01-01
A new method, using asymptotically stationary states, is developed to calculate the S-matrix for the scattering of a non-relativistic particle by the bound state of two other particles. For the scattering with breakup of this bound state, we obtain a simplified form of the Faddeev integral
Mixed s-sourcery: Building many-body states using bubbles of Nothing
Swingle, Brian
2016-01-01
In arXiv:1407.8203, we introduced the idea of s-sourcery, a general formalism for building many-body quantum ground states using renormalization-group-inspired quantum circuits. Here we define a generalized notion of s-sourcery that applies to mixed states, and study its properties and applicability. We prove a number of theorems establishing the prevalence of mixed s-source fixed points. For our examples we focus on thermal states of local Hamiltonians. Thermal double states (also called thermofield double states) and the machinery of approximate conditional independence are used heavily in the constructions.
Takei, Nobuyuki; Genes, Claudiu; Pupillo, Guido; Goto, Haruka; Koyasu, Kuniaki; Chiba, Hisashi; Weidemüller, Matthias; Ohmori, Kenji
2015-01-01
Many-body interactions govern a variety of important quantum phenomena ranging from superconductivity and magnetism in condensed matter to solvent effects in chemistry. Understanding those interactions beyond mean field is a holy grail of modern sciences. AMO physics with advanced laser technologies has recently emerged as a new platform to study quantum many-body systems. One of its latest developments is the study of long-range interactions among ultracold particles to reveal the effects of many-body correlations. Rydberg atoms distinguish themselves by their large dipole moments and tunability of dipolar interactions. Most of ultracold Rydberg experiments have been performed with narrow-band lasers in the Rydberg blockade regime. Here we demonstrate an ultracold Rydberg gas in a complementary regime, where electronic coherence is created using a broadband picosecond laser pulse, thus circumventing the Rydberg blockade to induce strong many-body correlations. The effects of long-range Rydberg interactions h...
Many-body localization in Ising models with random long-range interactions
Li, Haoyuan; Wang, Jia; Liu, Xia-Ji; Hu, Hui
2016-12-01
We theoretically investigate the many-body localization phase transition in a one-dimensional Ising spin chain with random long-range spin-spin interactions, Vi j∝|i-j |-α , where the exponent of the interaction range α can be tuned from zero to infinitely large. By using exact diagonalization, we calculate the half-chain entanglement entropy and the energy spectral statistics and use them to characterize the phase transition towards the many-body localization phase at infinite temperature and at sufficiently large disorder strength. We perform finite-size scaling to extract the critical disorder strength and the critical exponent of the divergent localization length. With increasing α , the critical exponent experiences a sharp increase at about αc≃1.2 and then gradually decreases to a value found earlier in a disordered short-ranged interacting spin chain. For α localized and the increase in the disorder strength may drive a transition between two many-body localized phases. In contrast, for α >αc , the transition is from a thermalized phase to the many-body localization phase. Our predictions could be experimentally tested with an ion-trap quantum emulator with programmable random long-range interactions, or with randomly distributed Rydberg atoms or polar molecules in lattices.
Many-body approximations for atomic binding energies
Schuster, Micah D; Staker, Joshua T
2011-01-01
We benchmark three approximations for the many-body problem -- the Hartree-Fock, projected Hartree-Fock, and random phase approximations -- against full numerical configuration-interaction calculations of the electronic structure of atoms, from Li through to Ne. Each method uses exactly the same input, i.e., the same single-particle basis and Coulomb matrix elements, so any differences are strictly due to the approximation itself. Although it consistently overestimates the ground state binding energy, the random phase approximation has the smallest overall errors; furthermore, we suggest it may be useful as a method for efficient optimization of single-particle basis functions.
Meson Structure in a Relativistic Many-Body Approach
Llanes-Estrada, F J; Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2000-01-01
Results from an extensive relativistic many-body analysis utilizing a realistic effective QCD Hamiltonian are presented for the meson spectrum. A comparative numerical study of the BCS, TDA and RPA treatments provides new, significant insight into the condensate structure of the vacuum, the chiral symmetry governance of the pion and the meson spin, orbital and flavor mass splitting contributions. In contrast to a previous glueball application, substantial quantitative differences are computed between TDA and RPA for the light quark sector with the pion emerging as a Goldstone boson only in the RPA.
Many-Body Theory of the Electroweak Nuclear Response
Benhar, Omar
2008-01-01
After a brief review of the theoretical description of nuclei based on nonrelativistic many-body theory and realistic hamiltonians, these lectures focus on its application to the analysis of the electroweak response. Special emphasis is given to electron-nucleus scattering, whose experimental study has provided a wealth of information on nuclear structure and dynamics, exposing the limitations of the shell model. The extension of the formalism to the case of neutrino-nucleus interactions, whose quantitative understanding is required to reduce the systematic uncertainty of neutrino oscillation experiments, is also discussed.
General theory of many body localized systems coupled to baths
Nandkishore, Rahul; Gopalakrishnan, Sarang
2016-01-01
We consider what happens when a many body localized system is coupled to a heat bath. Unlike previous works, we do not restrict ourselves to the limit where the bath is large and effectively Markovian, nor to the limit where back action on the bath is negligible. We identify limits where the effect of the bath can be captured by classical noise, and limits where it cannot. We also identify limits in which the bath delocalizes the system, as well as limits in which the system localizes the bat...
Methods of Computer Algebra and the Many Bodies Algebra
Grebenikov, E. A.; Kozak-Skoworodkina, D.; Yakubiak, M.
2001-07-01
The monograph concerns with qualitative methoids in n>3 bodies restricted problems by methods of computer algebra. The book consists of 4 chapters. The first two chapters contain the theory of homographic solutions in the many bodies problem. Other two chapters concern with Lyapunov stability of new solutions of differential equations based on KAM -theory. The computer method of the Birkhoff's normalisation method of the hamiltonians for the restricted 4, 5, 6, and 7 bodies is presented in detail. The book is designed for scientific researchers, doctorants, and students of the Physical-Mathematical departments. It could be used as well in University courses of qualitative theory of differential equations.
Fundamentals of many-body physics principles and methods
Nolting, Wolfgang
2009-01-01
This textbook addresses the special physics of many-particle systems, especially those dominated by correlation effects. It develops modern methods to treat such systems and demonstrates their application through numerous appropriate exercises, mainly from the field of solid state physics. The book is written in a tutorial style appropriate for those who want to learn many-body theory and eventually to use this to do research work in this field. The exercises, together with full solutions for evaluating one's performance, help to deepen understanding of the main aspects of many-particle systems.
Many-body methods in agent-based epidemic models
Nakamura, Gilberto M
2016-01-01
The susceptible-infected-susceptible (SIS) agent-based model is usually employed in the investigation of epidemics. The model describes a Markov process for a single communicable disease among susceptible (S) and infected (I) agents. However, the disease spreading forecasting is often restricted to numerical simulations, while analytic formulations lack both general results and perturbative approaches since they are subjected to asymmetric time generators. Here, we discuss perturbation theory, approximations and application of many-body techniques in epidemic models in the framework for squared norm of probability vector $|P(t)| ^2$, in which asymmetric time generators are replaced by their symmetric counterparts.
The many-body expansion combined with neural networks
Yao, Kun; Herr, John E.; Parkhill, John
2017-01-01
Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of calculations required for chemical accuracy is still prohibitively expensive for the ab initio MBE to compete with force field approximations for applications beyond single-point energies. Alongside the MBE, empirical models of ab initio potential energy surfaces have improved, especially non-linear models based on neural networks (NNs) which can reproduce ab initio potential energy surfaces rapidly and accurately. Although they are fast, NNs suffer from their own curse of dimensionality; they must be trained on a representative sample of chemical space. In this paper we examine the synergy of the MBE and NN's and explore their complementarity. The MBE offers a systematic way to treat systems of arbitrary size while reducing the scaling problem of large systems. NN's reduce, by a factor in excess of 106, the computational overhead of the MBE and reproduce the accuracy of ab initio calculations without specialized force fields. We show that for a small molecule extended system like methanol, accuracy can be achieved with drastically different chemical embeddings. To assess this we test a new chemical embedding which can be inverted to predict molecules with desired properties. We also provide our open-source code for the neural network many-body expansion, Tensormol.
Giant many-body effects in liquid ammonia absorption spectrum
Ziaei, Vafa; Bredow, Thomas
2016-11-01
In the present work, we accurately calculate the absorption spectrum of liquid ammonia up to 13 eV using many-body perturbation approach. The electronic bandgap of liquid NH3 is perfectly described as the combination of density functional theory, Coulomb-hole screened exchange, and G0W0 approximation to the electronic self-energy, yielding a direct gap (Γ → Γ) of 7.71 eV, fully consistent with the experimentally measured gap from photo-emission spectroscopy. With respect to the NH3 optical properties, the entire spectrum in particular the low lying first absorption band is extremely affected by electron-hole interactions, leading to a fundamental redistribution of spectral weights of the independent-particle spectrum. Three well separated but broad main peaks are identified at 7.0, 9.8, and 11.8 eV with steadily increasing intensities in excellent agreement with the experimental data. Furthermore, we observe a giant net blue-shift of the first absorption peak of about 1.4 eV from gaseous to liquid phase as the direct consequence of many-body effects, allowing the associated liquid ammonia absorption band exciton to delocalize and feel more effectively the repulsion effects imposed by the surrounding solvent shells. Further, the spectrum is insensitive to the coupling of resonant and anti-resonant contributions. Concerning electronic response structure of liquid NH3, it is most sensitive to excitations at energies lower than its electronic gap.
Improved variational many-body wave function in light nuclei
Usmani, Q. N.; Singh, A.; Anwar, K.; Rawitscher, G.
2009-09-01
We propose and implement a simple method for improving the variational wave function of a many-body system. We have obtained a significant improvement in the binding energies, wave functions, and variance for the light nuclei H3, He4, and Li6, using the fully realistic Argonne (AV18) two-body and Urbana-IX (UIX) three-body interactions. The energy of He4 was improved by about 0.2 MeV and the Li6 binding energy was increased by ≈1.7 MeV compared to earlier variational Monte Carlo results. The latter result demonstrates the significant progress achieved by our method, and detailed analyses of the improved results are given. With central interactions the results are found to be in agreement with the “exact” calculations. Our study shows that the relative error in the many-body wave functions, compared to two-body pair correlations, increases rapidly at least proportionally to the number of pairs in the system. However, this error does not increase indefinitely since the pair interactions saturate owing to convergence of cluster expansion.
Nonequilibrium many-body steady states via Keldysh formalism
Maghrebi, Mohammad F.; Gorshkov, Alexey V.
2016-01-01
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 nonequilibrium dynamics. While these states and their phase transitions have been studied extensively with mean-field theory, the validity of the mean-field approximation has not been systematically investigated. In this paper, we employ a field-theoretic approach based on the Keldysh formalism to study nonequilibrium phases and phase transitions in a variety of models. In all cases, a complete description via the Keldysh formalism indicates a partial or complete failure of the mean-field analysis. Furthermore, we find that an effective temperature emerges as a result of dissipation, and the universal behavior including the dynamics near the steady state is generically described by a thermodynamic universality class.
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...
Strain Control of Fermiology and Many-Body Interactions in Two-Dimensional Ruthenates
Burganov, B.; Adamo, C.; Mulder, A.; Uchida, M.; King, P. D. C.; Harter, J. W.; Shai, D. E.; Gibbs, A. S.; Mackenzie, A. P.; Uecker, R.; Bruetzam, M.; Beasley, M. R.; Fennie, C. J.; Schlom, D. G.; Shen, K. M.
2016-05-01
Here we demonstrate how the Fermi surface topology and quantum many-body interactions can be manipulated via epitaxial strain in the spin-triplet superconductor Sr2RuO4 and its isoelectronic counterpart Ba2RuO4 using oxide molecular beam epitaxy, in situ angle-resolved photoemission spectroscopy, and transport measurements. Near the topological transition of the γ Fermi surface sheet, we observe clear signatures of critical fluctuations, while the quasiparticle mass enhancement is found to increase rapidly and monotonically with increasing Ru-O bond distance. Our work demonstrates the possibilities for using epitaxial strain as a disorder-free means of manipulating emergent properties, many-body interactions, and potentially the superconductivity in correlated materials.
Many-body delocalization with random vector potentials
Cheng, Chen; Mondaini, Rubem
2016-11-01
We study 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 noninteracting limit, we show that arbitrarily small values of this complex off-diagonal disorder trigger 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. When short-range 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.
Effective Operators from Exact Many-Body Renormalization
Energy Technology Data Exchange (ETDEWEB)
Lisetskiy, A F; Kruse, M G; Barrett, B R; Navratil, P; Stetcu, I; Vary, J P
2009-06-11
We construct effective two-body Hamiltonians and E2 operators for the p-shell by performing 16{h_bar}{Omega} ab initio no-core shell model (NCSM) calculations for A = 5 and A = 6 nuclei and explicitly projecting the many-body Hamiltonians and E2 operator onto the 0{h_bar}{Omega} space. We then separate the effective E2 operator into one-body and two-body contributions employing the two-body valence cluster approximation. We analyze the convergence of proton and neutron valence one-body contributions with increasing model space size and explore the role of valence two-body contributions. We show that the constructed effective E2 operator can be parametrized in terms of one-body effective charges giving a good estimate of the NCSM result for heavier p-shell nuclei.
Relativistic Many-Body Hamiltonian Approach to Mesons
Llanes-Estrada, F J; Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2002-01-01
We represent QCD at the hadronic scale by means of an effective Hamiltonian, $H$, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is explicity broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. This interaction generates an infrared integrable singularity and we detail the computationally intensive procedure necessary for numerical solution. We focus upon applications for the $u, d, s$ and $c$ quark flavors and compute the mass spectrum for the pseudoscalar, scalar and vector mesons. We also perform a comparative study of alternative many-body techniques for approximately diagonalizing $H$: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. The Dirac structure of the field theoretical Hamiltonian naturally generates spin-dependent interactions, including tensor, spin-orbit and hyperfine, and we clarify the degree of level splitting due to both spin an...
Particle diagrams and embedded many-body random matrix theory.
Small, R A; Müller, S
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤ m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k = m,3 k = m,...,nk = m.
Particle diagrams and embedded many-body random matrix theory
Small, R. A.; Müller, S.
2014-07-01
We present a method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplifications. We use it here to find the fourth, sixth, and eighth moments of the level density of an m-body system with k fermions or bosons interacting through a random Hermitian potential (k ≤m) in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k=m, from moments arising from a semicircular level density to Gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k=m,3k=m,...,nk=m.
Many-body Physics with Alkaline-Earth Rydberg lattices
Mukherjee, R; Nath, R; Jones, M P A; Pohl, T
2011-01-01
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_6 coefficients for the 5sns 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 (GHZ) states.
Negative ion formation in lanthanide atoms: Many-body effects
Felfli, Z; Sokolovski, D
2016-01-01
Investigations of low-energy electron-scattering of the lanthanide atoms Eu, Nd, Tb, Tm demonstrate that electron-correlation effects and core polarization are the dominant fundamental many-body effects responsible for the formation of metastable states of negative ions. Ramsauer Townsend minima, shape resonances and binding energies of the resultant anions are identified and extracted from the elastic total cross sections calculated using the complex angular momentum method. The large discrepancy between the recently measured electron affinity of 0.116 and the previously measured value of 1.053 eV for Eu is resolved. Also, the previously measured electron affinities for Nd, Tb and Tm are reconciled and new values are extracted from the calculated total cross sections. The large electron affinities found here for these atoms, should be useful in negative ion nanocatalysis, including methane conversion to methanol without CO2 emission, with significant environmental impact.. The powerful complex angular moment...
Statistical theory of the many-body nuclear system
De Pace, A
2002-01-01
A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to nuclear matter, in addition to the mean field energies we obtain their fluctuations as well, together with the ones of the wavefunctions, in first order of the expansion in the complexity of the Q-space states. The physics described by the latter is assumed to be random. To extract numerical predictions out of our scheme we develop a schematic version of the approach, which, while much simplified, yields results of significance on the size of the error affecting the mean fields, on the magnitude of the residual effective interaction, on the ground state spectroscopic factor and on the mixing occurring between the vectors spanning the P-space.
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
We develop a non-relativistic twistor theory, in which Newton--Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle ${\\mathcal O}\\oplus{\\mathcal O}(2)$. We show that the Newton--Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton--Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non--trivial on twistor lines. The resulting geometries agree with non--relativistic limits of anti-self-dual gravitational instantons.
Do non-relativistic neutrinos constitute the dark matter?
Nieuwenhuizen, T.M.
2009-01-01
The dark matter of the Abell 1689 Galaxy Cluster is modeled by thermal, non-relativistic gravitating fermions and its galaxies and X-ray gas by isothermal distributions. A fit yields a mass of h(70)(1/2) (12/(g) over bar)(1)/(4) 1.445(30) eV. A dark-matter fraction Omega(nu) = h(70)(-3/2) 0.1893(39)
Curved non-relativistic spacetimes, Newtonian gravitation and massive matter
Energy Technology Data Exchange (ETDEWEB)
Geracie, Michael, E-mail: mgeracie@uchicago.edu; Prabhu, Kartik, E-mail: kartikp@uchicago.edu; Roberts, Matthew M., E-mail: matthewroberts@uchicago.edu [Kadanoff Center for Theoretical Physics, Enrico Fermi Institute and Department of Physics, The University of Chicago, Chicago, Illinois 60637 (United States)
2015-10-15
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print http://arxiv.org/abs/1503.02680 ], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids.
Symmetries and couplings of non-relativistic electrodynamics
Energy Technology Data Exchange (ETDEWEB)
Festuccia, Guido [Department of Physics and Astronomy, Uppsala University,Lägerhyddsvägen 1, Uppsala (Sweden); Hansen, Dennis [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark); Hartong, Jelle [Physique Théorique et Mathématique and International Solvay Institutes,Université Libre de Bruxelles, C.P. 231, Brussels, 1050 (Belgium); Obers, Niels A. [The Niels Bohr Institute, Copenhagen University,Blegdamsvej 17, Copenhagen Ø, DK-2100 (Denmark)
2016-11-08
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell’s equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a U(1) current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galilei algebra plus two dilatations remain. Hence one can scale time and space independently, allowing Lifshitz scale symmetries for any value of the critical exponent z.
Symmetries and Couplings of Non-Relativistic Electrodynamics
Festuccia, Guido; Hartong, Jelle; Obers, Niels A
2016-01-01
We examine three versions of non-relativistic electrodynamics, known as the electric and magnetic limit theories of Maxwell's equations and Galilean electrodynamics (GED) which is the off-shell non-relativistic limit of Maxwell plus a free scalar field. For each of these three cases we study the couplings to non-relativistic dynamical charged matter (point particles and charged complex scalars). The GED theory contains besides the electric and magnetic potentials a so-called mass potential making the mass parameter a local function. The electric and magnetic limit theories can be coupled to twistless torsional Newton-Cartan geometry while GED can be coupled to an arbitrary torsional Newton-Cartan background. The global symmetries of the electric and magnetic limit theories on flat space consist in any dimension of the infinite dimensional Galilean conformal algebra and a $U(1)$ current algebra. For the on-shell GED theory this symmetry is reduced but still infinite dimensional, while off-shell only the Galile...
The confined hydrogenoid ion in non-relativistic quantum electrodynamics
Amour, L
2006-01-01
We consider a system of a nucleus with an electron together with the quantized electromagnetic field. Instead of fixing the nucleus, the system is confined by its center of mass. This model is used in theoretical physics to explain the Lamb-Dicke and the M\\"ossbauer effects (see [CTDRG]). When an ultraviolet cut-off is imposed we initiate the spectral analysis of the Hamiltonian describing the system and we derive the existence of a ground state. This is achieved without conditions on the fine structure constant. [CTDRG] C. Cohen-Tannoudji, J. Dupont-Roc and G. Grynberg. Processus d'interaction entre photons et atomes. Edition du CNRS, 2001.
Unconventional decay law for excited states in closed many-body systems
Flambaum, V V
2001-01-01
We study the time evolution of an initially excited many-body state in a finite system of interacting Fermi-particles in the situation when the interaction gives rise to the ``chaotic'' structure of compound states. This situation is generic for highly excited many-particle states in quantum systems, such as heavy nuclei, complex atoms, quantum dots, spin systems, and quantum computers. For a strong interaction the leading term for the return probability $W(t)$ has the form $W(t)\\simeq \\exp (-\\Delta_E^2t^2)$ with $\\Delta_E^2$ as the variance of the strength function. The conventional exponential linear dependence $W(t)=C\\exp (-\\Gamma t)$ formally arises for a very large time. However, the prefactor $C$ turns out to be exponentially large, thus resulting in a strong difference from the conventional estimate for $W(t)$.
On the possibility of many-body localization in a doped Mott insulator
He, Rong-Qiang; Weng, Zheng-Yu
2016-01-01
Many-body localization (MBL) is currently a hot issue of interacting systems, in which quantum mechanics overcomes thermalization of statistical mechanics. Like Anderson localization of non-interacting electrons, disorders are usually crucial in engineering the quantum interference in MBL. For translation invariant systems, however, the breakdown of eigenstate thermalization hypothesis due to a pure many-body quantum effect is still unclear. Here we demonstrate a possible MBL phenomenon without disorder, which emerges in a lightly doped Hubbard model with very strong interaction. By means of density matrix renormalization group numerical calculation on a two-leg ladder, we show that whereas a single hole can induce a very heavy Nagaoka polaron, two or more holes will form bound pair/droplets which are all localized excitations with flat bands at low energy densities. Consequently, MBL eigenstates of finite energy density can be constructed as composed of these localized droplets spatially separated. We further identify the underlying mechanism for this MBL as due to a novel ‘Berry phase’ of the doped Mott insulator, and show that by turning off this Berry phase either by increasing the anisotropy of the model or by hand, an eigenstate transition from the MBL to a conventional quasiparticle phase can be realized. PMID:27752064
Open-system many-body dynamics through interferometric measurements and feedback
Lammers, Jonas; Weimer, Hendrik; Hammerer, Klemens
2016-11-01
Light-matter interfaces enable the generation of entangled states of light and matter which can be exploited to steer the quantum state of matter through measurement of light and feedback. Here we consider continuous-time, interferometric homodyne measurements of light on an array of light-matter interfaces followed by local feedback acting on each material system individually. While the systems are physically noninteracting, the feedback master equation we derive describes driven-dissipative, interacting many-body quantum dynamics, and comprises pairwise Hamiltonian interactions and collective jump operators. We characterize the general class of driven-dissipative many-body systems which can be engineered in this way, and derive necessary conditions on models supporting nontrivial quantum dynamics beyond what can be generated by local operations and classical communication. We provide specific examples of models which allow for the creation of stationary many-particle entanglement, and the emulation of dissipative Ising models. Since the interaction between the systems is mediated via feedback only, there is no intrinsic limit on the range or geometry of the interaction, making the scheme quite versatile.
Direct observation of many-body charge density oscillations in a two-dimensional electron gas
Sessi, Paolo; Silkin, Vyacheslav M.; Nechaev, Ilya A.; Bathon, Thomas; El-Kareh, Lydia; Chulkov, Evgueni V.; Echenique, Pedro M.; Bode, Matthias
2015-10-01
Quantum interference is a striking manifestation of one of the basic concepts of quantum mechanics: the particle-wave duality. A spectacular visualization of this effect is the standing wave pattern produced by elastic scattering of surface electrons around defects, which corresponds to a modulation of the electronic local density of states and can be imaged using a scanning tunnelling microscope. To date, quantum-interference measurements were mainly interpreted in terms of interfering electrons or holes of the underlying band-structure description. Here, by imaging energy-dependent standing-wave patterns at noble metal surfaces, we reveal, in addition to the conventional surface-state band, the existence of an `anomalous' energy band with a well-defined dispersion. Its origin is explained by the presence of a satellite in the structure of the many-body spectral function, which is related to the acoustic surface plasmon. Visualizing the corresponding charge oscillations provides thus direct access to many-body interactions at the atomic scale.
Many-body forces, isospin asymmetry and dense hyperonic matter
Gomes, R O; Schramm, S; Vascconcellos, C A Z
2015-01-01
The equation of state (EoS) of asymmetric nuclear matter at high densities is a key topic for the description of matter inside neutron stars. The determination of the properties of asymmetric nuclear matter, such as the symmetry energy ($a_{sym}$) and the slope of the symmetry energy ($L_0$) at saturation density, has been exaustively studied in order to better constrain the nuclear matter EoS. However, differently from symmetric matter properties that are reasonably constrained, the symmetry energy and its slope still large uncertainties in their experimental values. Regarding this subject, some studies point towards small values of the slope of the symmetry energy, while others suggest rather higher values. Such a lack of agreement raised a certain debate in the scientific community. In this paper, we aim to analyse the role of these properties on the behavior of asymmetric hyperonic matter. Using the formalism presented in Ref. (R.O. Gomes et al 2014}, which considers many-body forces contributions in the ...
Charge optimized many body (COMB) potentials for Pt and Au
Antony, A. C.; Akhade, S. A.; Lu, Z.; Liang, T.; Janik, M. J.; Phillpot, S. R.; Sinnott, S. B.
2017-06-01
Interatomic potentials for Pt and Au are developed within the third generation charge optimized many-body (COMB3) formalism. The potentials are capable of reproducing phase order, lattice constants, and elastic constants of Pt and Au systems as experimentally measured or calculated by density functional theory. We also fit defect formation energies, surface energies and stacking fault energies for Pt and Au metals. The resulting potentials are used to map a 2D contour of the gamma surface and simulate the tensile test of 16-grain polycrystalline Pt and Au structures at 300 K. The stress-strain behaviour is investigated and the primary slip systems {1 1 1} are identified. In addition, we perform high temperature (1800 K for Au and 2300 K for Pt) molecular dynamics simulations of 30 nm Pt and Au truncated octahedron nanoparticles and examine morphological changes of each particle. We further calculate the activation energy barrier for surface diffusion during simulations of several nanoseconds and report energies of 0.62+/- 0.16 eV for Pt and 1.44+/- 0.06 eV for Au. This initial parameterization and application of the Pt and Au potentials demonstrates a starting point for the extension of these potentials to multicomponent systems within the COMB3 framework.
Many-Body Coulomb Gauge Exotic and Charmed Hybrids
Llanes-Estrada, F J; Llanes-Estrada, Felipe J.; Cotanch, Stephen R.
2001-01-01
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 quasiparticle ($q\\bar{q}g$) calculation with the 9 dimensional Hamiltonian matrix elements evaluated variationally by Monte Carlo techniques. Our new TDA spectrum for the nonexotic $1^{--}$ charmed ($c\\bar{c}$ and $c\\bar{c}g$) system provides an explanation for the overpopulation of the observed $J/\\psi$ states. For the important $1^{-+}$ light exotic channel we obtain hybrid masses above 2 $GeV$, in broad agreement with lattice and flux tube models, indicating that the recently observed resonances at 1.4 and 1.6 $GeV$ are of di...
Many-Body Approach to Mesons, Hybrids and Glueballs
Cotanch, S R; Cotanch, Stephen R.; Llanes-Estrada, Felipe J.
2000-01-01
We represent QCD at the hadronic scale by means of an effective Hamiltonian, H, formulated in the Coulomb gauge. As in the Nambu-Jona-Lasinio model, chiral symmetry is dynamically broken, however our approach is renormalizable and also includes confinement through a linear potential with slope specified by lattice gauge theory. We perform a comparative study of alternative many-body techniques for approximately diagonalizing H: BCS for the vacuum ground state; TDA and RPA for the excited hadron states. We adequately describe the experimental meson and lattice glueball spectra and perform the first relativistic, three quasiparticle calculation for hybrid mesons. In general agreement with alternative theoretical approaches, we predict the lightest hybrid states near but above 2 GeV, indicating the two recently observed $J^{PC} = 1^{-+}$ exotics at 1.4 and 1.6 GeV are of a different, perhaps four quark, structure. We also detail a new isospin dependent interaction from $q\\bar{q}$ color octet annihilation (analog...
Many-body central force potentials for tungsten
Bonny, G.; Terentyev, D.; Bakaev, A.; Grigorev, P.; Van Neck, D.
2014-07-01
Tungsten and tungsten-based alloys are the primary candidate materials for plasma facing components in fusion reactors. The exposure to high-energy radiation, however, severely degrades the performance and lifetime limits of the in-vessel components. In an effort to better understand the mechanisms driving the materials' degradation at the atomic level, large-scale atomistic simulations are performed to complement experimental investigations. At the core of such simulations lies the interatomic potential, on which all subsequent results hinge. In this work we review 19 central force many-body potentials and benchmark their performance against experiments and density functional theory (DFT) calculations. As basic features we consider the relative lattice stability, elastic constants and point-defect properties. In addition, we also investigate extended lattice defects, namely: free surfaces, symmetric tilt grain boundaries, the 1/2{1 1 0} and 1/2 {1 1 2} stacking fault energy profiles and the 1/2 screw dislocation core. We also provide the Peierls stress for the 1/2 edge and screw dislocations as well as the glide path of the latter at zero Kelvin. The presented results serve as an initial guide and reference list for both the modelling of atomically-driven phenomena in bcc tungsten, and the further development of its potentials.
Revised scaling variables in systems with many-body interactions
Goldstein, Raymond E.; Parola, Alberto
1987-06-01
Thermodynamic perturbation theory and the Kirkwood-Salsburg correlation function identities are used to study nearest-neighbor lattice gases with certain weak symmetry-breaking many-body interactions. It is shown that such systems may be mapped onto symmetric models by the introduction of suitable effective interactions and a shifted chemical potential, both of which depend explicitly on the temperature and fugacity of the original model. In the critical region, such a thermodynamic-state dependence implies the existence of a thermal scaling field which depends on the bare chemical potential, and this ``field mixing'' leads to a breakdown in the classical law of the rectilinear diameter. These results give a microscopic interpretation to a field-theoretic renormalization-group analysis which derives such a diameter singularity from the presence of terms cubic and higher in the order parameter and its gradients in an asymmetric Landau-Ginzburg-Wilson Hamiltonian. For a primarily repulsive three-body potential like the Axilrod-Teller interaction in classical insulating fluids, and in comparison with recent experiments, the analysis correctly describes the observed trends in the critical and near-critical behavior of the diameters with increasing particle polarizability.
Electron-phonon coupling using many-body GW theory
Monserrat, Bartomeu; Vanderbilt, David
Electron-phonon coupling drives a plethora of phenomena, such as superconductivity in metals, or the temperature dependence of optical properties in semiconductors. There is increasing evidence that semi-local density functional theory (DFT) is not adequate for the description of electron-phonon coupling, and instead effects such as electronic correlation need to be included. Unfortunately, methods beyond semi-local DFT are computationally demanding, limiting the study of these phenomena. In this talk we will introduce the idea of ``thermal lines'', which can be used to explore the vibrational phase space of solids and molecules at small computational cost. In particular, we will describe how thermal lines can be exploited to calculate the temperature dependence of band structures beyond semi-local DFT, by using many-body GW theory, or by including the effects of spin-orbit coupling. We will present first-principles results showing the effects of electron correlation on the strength of electron-phonon coupling, and the effects of electron-phonon coupling on topological states of matter. Supported by Robinson College, Cambridge, and the Cambridge Philosophical Society.
Another New Solvable Many-Body Model of Goldfish Type
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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.
The Many-Body Expansion Combined with Neural Networks
Yao, Kun; Parkhill, John
2016-01-01
Fragmentation methods such as the many-body expansion (MBE) are a common strategy to model large systems by partitioning energies into a hierarchy of decreasingly significant contributions. The number of fragments required for chemical accuracy is still prohibitively expensive for ab-initio MBE to compete with force field approximations for applications beyond single-point energies. Alongside the MBE, empirical models of ab-initio potential energy surfaces have improved, especially non-linear models based on neural networks (NN) which can reproduce ab-initio potential energy surfaces rapidly and accurately. Although they are fast, NNs suffer from their own curse of dimensionality; they must be trained on a representative sample of chemical space. In this paper we examine the synergy of the MBE and NN's, and explore their complementarity. The MBE offers a systematic way to treat systems of arbitrary size and intelligently sample chemical space. NN's reduce, by a factor in excess of $10^6$ the computational ove...
Toward Hamiltonian Adaptive QM/MM: Accurate Solvent Structures Using Many-Body Potentials.
Boereboom, Jelle M; Potestio, Raffaello; Donadio, Davide; Bulo, Rosa E
2016-08-09
Adaptive quantum mechanical (QM)/molecular mechanical (MM) methods enable efficient molecular simulations of chemistry in solution. Reactive subregions are modeled with an accurate QM potential energy expression while the rest of the system is described in a more approximate manner (MM). As solvent molecules diffuse in and out of the reactive region, they are gradually included into (and excluded from) the QM expression. It would be desirable to model such a system with a single adaptive Hamiltonian, but thus far this has resulted in distorted structures at the boundary between the two regions. Solving this long outstanding problem will allow microcanonical adaptive QM/MM simulations that can be used to obtain vibrational spectra and dynamical properties. The difficulty lies in the complex QM potential energy expression, with a many-body expansion that contains higher order terms. Here, we outline a Hamiltonian adaptive multiscale scheme within the framework of many-body potentials. The adaptive expressions are entirely general, and complementary to all standard (nonadaptive) QM/MM embedding schemes available. We demonstrate the merit of our approach on a molecular system defined by two different MM potentials (MM/MM'). For the long-range interactions a numerical scheme is used (particle mesh Ewald), which yields energy expressions that are many-body in nature. Our Hamiltonian approach is the first to provide both energy conservation and the correct solvent structure everywhere in this system.
Atomic many-body effects and Lamb shifts in alkali metals
Ginges, J. S. M.; Berengut, J. C.
2016-05-01
We present a detailed study of the radiative potential method [V. V. Flambaum and J. S. M. Ginges, Phys. Rev. A 72, 052115 (2005), 10.1103/PhysRevA.72.052115], which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms and ions over the range 10 ≤Z ≤120 , where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s , p , and d waves over the series of alkali-metal atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many-body effects of core relaxation and second- and higher-order perturbation theory on the interaction of the valence electron with the core are calculated. The inclusion of many-body effects tends to increase the size of the shifts, with the enhancement particularly significant for d waves; for K to E119, the self-energy shifts for d waves are only an order of magnitude smaller than the s -wave shifts. It is shown that taking into account many-body effects is essential for an accurate description of the Lamb shift.
Many-Body Treatment of Navier-Stokes Fluids.
1986-09-01
Haken, Reviews of Modern Physics, 47, (1) (1975). E2. H. Haken and W. Weidlich , p. 630 in Quantum Ootics, R. J. Glauber, ed., (Academic Press, New York...1969). E3. Hermann Haken, Light, Vol. 1, (North Holland, New York, 1981). E4. H. Heken and W. Weidlich , Zeltsehrlft fur Physik, 181, 96, (1964). ES
Holographic Duality with a View Toward Many-Body Physics
Directory of Open Access Journals (Sweden)
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.
Are non-relativistic neutrinos the dark matter particles?
Nieuwenhuizen, Theo M.
2010-06-01
. Thereby the spead up the intracluster gas to virial speeds of 10 keV, which causes reionization without assistance of heavy stars. Within the analysis, the baryons are poor tracers of the dark matter density. This work is described in Theo M. Nieuwenhuizen, Do non-relativistic neutrinos constitute the dark matter? Europhysics Letters 86, 59001 (2009). This text of this paper is an update of this work. Structure formation is presently believed to need cold dark matter. However, hydrodynamics alone may explain baryonic clustering without this trigger. Th. M. Nieuwenhuizen, C. H. Gibson and R. E. Schild, Gravitational hydrodynamics of large scale structure formation, Europhysics Letters 2009, to appear.
Non-relativistic Bondi–Metzner–Sachs algebra
Batlle, Carles; Delmastro, Diego; Gomis, Joaquim
2017-09-01
We construct two possible candidates for non-relativistic bms4 algebra in four space-time dimensions by contracting the original relativistic bms4 algebra. bms4 algebra is infinite-dimensional and it contains the generators of the Poincaré algebra, together with the so-called super-translations. Similarly, the proposed nrbms4 algebras can be regarded as two infinite-dimensional extensions of the Bargmann algebra. We also study a canonical realization of one of these algebras in terms of the Fourier modes of a free Schrödinger field, mimicking the canonical realization of relativistic bms4 algebra using a free Klein–Gordon field.
An advective-spectral-mixed method for time-dependent many-body Wigner simulations
Xiong, Yunfeng; Shao, Sihong
2016-01-01
As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic numerical solutions have been almost exclusively confined to one-dimensional one-body systems and few results are reported even for one-dimensional two-body problems. This paper serves as the first attempt to solve the time-dependent many-body Wigner equation through a grid-based advective-spectral-mixed method. The main feature of the method is to resolve the linear advection in $(\\bm{x},t)$-space by an explicit three-step characteristic scheme coupled with the piecewise cubic spline interpolation, while the Chebyshev spectral element method in $\\bm k$-space is adopted for accurate calculation of the nonlocal pseudo-differential term. Not only the time step of the resulting method is not restricted by the usual CFL condition and thus a large time step is allowed, but also th...
Observation of discrete time-crystalline order in a disordered dipolar many-body system
Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D.
2017-03-01
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic ‘time-crystalline’ phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive. Here we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of about one million dipolar spin impurities in diamond at room temperature. We observe long-lived temporal correlations, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. This order is remarkably stable to perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.
Many-body ab initio study of antiferromagnetic {Cr7M } molecular rings
Chiesa, A.; Carretta, S.; Santini, P.; Amoretti, G.; Pavarini, E.
2016-12-01
Antiferromagnetic molecular rings are widely studied both for fundamental quantum-mechanical issues and for technological applications, particularly in the field of quantum information processing. Here we present a detailed first-principles study of two families—purple and green—of {Cr7M } antiferromagnetic rings, where M is a divalent transition metal ion (M =Ni2 + , Mn2 +, and Zn2 +). We employ a recently developed flexible and efficient scheme to build ab initio system-specific Hubbard models. From such many-body models we systematically derive the low-energy effective spin Hamiltonian for the rings. Our approach allows us to calculate isotropic as well as anisotropic terms of the spin Hamiltonian, without any a priori assumption on its form. For each compound we calculate magnetic exchange couplings, zero-field splitting tensors, and gyromagnetic tensors, finding good agreement with experimental results.
Observation of discrete time-crystalline order in a disordered dipolar many-body system
Choi, Soonwon; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y; Demler, Eugene; Lukin, Mikhail D
2016-01-01
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of $\\sim 10^6$ dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experi...
Characterizing many-body localization by out-of-time-ordered correlation
He, Rong-Qiang; Lu, Zhong-Yi
2017-02-01
The out-of-time-ordered (OTO) correlation is a key quantity for quantifying quantum chaoticity and has been recently used in the investigation of quantum holography. Here we use it to study and characterize many-body localization (MBL). We find that a long-time logarithmic variation of the OTO correlation occurs in the MBL phase but is absent in the Anderson localized and ergodic phases. We extract a localization length in the MBL phase, which depends logarithmically on interaction and diverges at a critical interaction. Furthermore, the infinite-time "thermal" fluctuation of the OTO correlation is zero (finite) in the ergodic (MBL) phase and thus can be considered as an order parameter for the ergodic-MBL transition, through which the transition can be identified and characterized. Specifically, the critical point and the related critical exponents can be calculated.
Semi-classical locality for the non-relativistic path integral in configuration space
Gomes, Henrique
2015-01-01
In an accompanying paper, we have put forward an interpretation of quantum mechanics grounded on a non-relativistic Lagrangian 3+1 formalism of a closed Universe, existing on timeless configuration space. However, not much was said there about the role of locality, which was not assumed. In this paper, I describe how subsystems existing in (spatial) regions with fixed boundary conditions can be represented as submanifolds of the complete configuration space. I show that if the action functional can be put in the form of Riemannian distance element, then dynamical independence of the subsystem implies that the respective submanifolds are totally geodesic. When two regions are mutually independent the semi-classical path integral kernel factorizes, showing cluster decomposition. To exemplify these constructions I then construct a specific gravitational system with two propagating physical degrees of freedom and no refoliation-invariance. Finally, considering the path integral in this 3+1 context, I implement an...
Introduction to Integrable Many-Body Systems II
Šamaj, Ladislav
2010-04-01
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-1/2 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 Sect. 18. Sect. 19 deals with integrable cases of isotropic spin chains with an arbitrary spin.
ON THE KINEMATIC GEOMETRY OF MANY BODY SYSTEMS
Institute of Scientific and Technical Information of China (English)
Wu-YIHSIANG
1999-01-01
In mechanics, both classical and quantum, one studies the profound interaction between two types of energy, namely, the kinetic energy and the potential energy. The former can be organized as the kinematic metric on the configuration space while the latter can be represented by a suitable potential function, such as the Newtonian potential in celestial mechanics and the Coulomb potential in quantum mechanics of atomic and molecular physics. In this paper, the author studies the kinematic geometry of n-body systems. The main results axe (i) the introduction of a canonical coordinate system which reveals the total amount of kinematic symmetry by an SO(З) × O(n - 1) action in such a canonieal coordinate representation; (ii) an in depth analysis of the above kinematic system both in the setting of classical invariant theory and by the technique of equivarjant Riemannian geometry; (iii) a remarkably simple formula for the potential function in such a canonical coordinate system which reveals the well-fitting between the kinematic symmetry and the potential energy.
Simulation of non-equilibrium many body electrons in RTD
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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: Many-Body Theory of Atomic Systems: Proceedings of the Nobel Symposium 46
Lindgren, Ingvar; Lundqvist, Stig
1980-01-01
corresponding experimental results, which will eventually lead to a better understanding of the behaviour of many-electron systems and possibly also of many-fermion systems in general. In addition to the static properties of atomic systems there is nowadays a great interest in the dynamics of the excitation process, which is of fundamental importance for our understanding of photoelectron and photoabsorption spectra. The experimental data being produced in this field are enormous and many intricate physical problems appear, which can only be understood by considering the atom as a fully interacting many-body system. All the new developments mentioned here have opened entirely new areas in atomic many-body theory, and we are evidently just at the verge of a very interesting period of rapid progress. It is quite evident that we could have limited the Symposium to atomic problems of the type described here. However, related problems appear in atoms bound in solids and in atoms/molecules bound to solid surfaces. Therefore, we proposed to include also some aspects of these fields in our program, which brought together scientists with different backgrounds, such as atomic and molecular physicists, theoretical chemists, solid state and surface physicists as well as nuclear physicists and quantum- liquid experts. The Symposium then got a distinctive inter-disciplinary character at the same time as it was concentrated on the specific atomic many-body problem. The response to our invitations to the Nobel Symposium was overwhelming. Many other participants were suggested and we extended the number of participants as far as we could. With the wide scope of the Symposium program and small format with regard to number, only a few representatives of each major area could be invited. The symposium gave an excellent picture how the various areas are developing. The various methods to treat the many-body problem were thoroughly discussed and many new results were reported. The relativistic many-body
Energy as a Detector of Nonlocality of Many-Body Spin Systems
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J. Tura
2017-04-01
Full Text Available We present a method to show that low-energy states of quantum many-body interacting systems in one spatial dimension are nonlocal. We assign a Bell inequality to the Hamiltonian of the system in a natural way and we efficiently find its classical bound using dynamic programing. The Bell inequality is such that its quantum value for a given state, and for appropriate observables, corresponds to the energy of the state. Thus, the presence of nonlocal correlations can be certified for states of low enough energy. The method can also be used to optimize certain Bell inequalities: in the translationally invariant (TI case, we provide an exponentially faster computation of the classical bound and analytically closed expressions of the quantum value for appropriate observables and Hamiltonians. The power and generality of our method is illustrated through four representative examples: a tight TI inequality for eight parties, a quasi-TI uniparametric inequality for any even number of parties, ground states of spin-glass systems, and a nonintegrable interacting XXZ-like Hamiltonian. Our work opens the possibility for the use of low-energy states of commonly studied Hamiltonians as multipartite resources for quantum information protocols that require nonlocality.
Formulation of the Relativistic Quantum Hall Effect and "Parity Anomaly"
Yonaga, Kouki; Shibata, Naokazu
2016-01-01
We present a relativistic formulation of the quantum Hall effect on a Riemann sphere. An explicit form of the pseudopotential is derived for the relativistic quantum Hall effect with/without mass term.We clarify particular features of the relativistic quantum Hall states with use of the exact diagonalization study of the pseudopotential Hamiltonian. Physical effects of the mass term to relativistic quantum Hall states are investigated in detail.The mass term acts as an interporating parameter between the relativistic and non-relativistic quantum Hall effects. It is pointed out that the mass term inequivalently affects to many-body physics of the positive and negative Landau levels and brings instability of the Laughlin state of the positive first relativistic Landau level as a consequence of the "parity anomaly".
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...
Atomic many-body effects and Lamb shifts in alkali metals
Ginges, J S M
2016-01-01
We present a detailed study of the Flambaum-Ginges radiative potential method which enables the accurate inclusion of quantum electrodynamics (QED) radiative corrections in a simple manner in atoms, ions, and molecules over the range 10<=Z<=120, where Z is the nuclear charge. Calculations are performed for binding energy shifts to the lowest valence s, p, and d waves over the series of alkali atoms Na to E119. The high accuracy of the radiative potential method is demonstrated by comparison with rigorous QED calculations in frozen atomic potentials, with deviations on the level of 1%. The many-body effects of core relaxation and second- and higher-order perturbation theory on the interaction of the valence electron with the core are calculated. The inclusion of many-body effects tends to increase the size of the shifts, with the enhancement particularly significant for d waves; for K to E119, the self-energy shifts for d waves are only an order of magnitude smaller than the s-wave shifts. It is shown th...
Role of interactions in a dissipative many-body localized system
Everest, Benjamin; Lesanovsky, Igor; Garrahan, Juan P.; Levi, Emanuele
2017-01-01
Recent experimental and theoretical efforts have focused on the effect of dissipation on quantum many-body systems in their many-body localized (MBL) phase. While in the presence of dephasing noise such systems reach a unique ergodic state, their dynamics is characterized by slow relaxation manifested in nonexponential decay of self-correlations. Here we shed light on a currently much debated issue, namely, the role of interactions for this relaxation dynamics. We focus on the experimentally relevant situation of the evolution from an initial charge density wave in the presence of strong dephasing noise. We find a crossover from a regime dominated by disorder to a regime dominated by interactions, with an accompanying change of time correlators from stretched exponential to compressed exponential form. The strongly interacting regime can be explained in terms of nucleation and growth dynamics of relaxing regions—reminiscent of the kinetics of crystallization in soft matter systems—and should be observable experimentally. This interaction-driven crossover suggests that the competition between interactions and noise gives rise to a much richer structure of the MBL phase than anticipated so far.
The Thomas-Fermi Quark Model: Non-Relativistic Aspects
Liu, Quan
2012-01-01
Non-relativistic aspects of the Thomas-Fermi statistical quark model are developed. A review is given and our modified approach to spin in the model is explained. Our results are limited so far to two inequivalent simultaneous wave functions which can apply to multiple degenerate flavors. An explicit spin interaction is introduced, which requires the introduction of a generalized spin "flavor". Although the model is designed to be most reliable for many-quark states, we find surprisingly that it may be used to fit the low energy spectrum of octet and decouplet baryons. The low energy fit allows us to investigate the six-quark doubly strange H-dibaryon state, possible 6 quark nucleon-nucleon resonances and flavor symmetric strange states of higher quark content.
Differential Regularization of a Non-relativistic Anyon Model
Freedman, Daniel Z; Rius, N
1994-01-01
Differential regularization is applied to a field theory of a non-relativistic charged boson field $\\phi$ with $\\lambda (\\phi {}^{*} \\phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the $\\phi {}^{*} \\phi {}^{*} \\phi \\phi$ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the $\\beta$-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions to $\\beta(\\lambda,e)$ vanish, and $\\beta(\\lambda,e)$ itself vanishes when the ``self-dual'' condition relating $\\lambda$ to the gauge coupling $e$ is imposed.
Ion Injection at Non-relativistic Collisionless Shocks
Caprioli, Damiano; Spitkovsky, Anatoly
2014-01-01
We use kinetic hybrid simulations (kinetic ions - fluid electrons) to characterize the fraction of ions that are accelerated to non-thermal energies at non-relativistic collisionless shocks. We investigate the properties of the shock discontinuity and show that shocks propagating almost along the background magnetic field (quasi-parallel shocks) reform quasi-periodically on ion cyclotron scales. Ions that impinge on the shock when the discontinuity is the steepest are specularly reflected. This is a necessary condition for being injected, but it is not sufficient. Also by following the trajectories of reflected ions, we calculate the minimum energy needed for injection into diffusive shock acceleration, as a function of the shock inclination. We construct a minimal model that accounts for the ion reflection from quasi-periodic shock barrier, for the fraction of injected ions, and for the ion spectrum throughout the transition from thermal to non-thermal energies. This model captures the physics relevant for i...
Many-body decoherence dynamics and optimised operation of a single-photon switch
Murray, Callum R; Pohl, Thomas
2016-01-01
We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimised switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments [arXiv:1511.09445] and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.
Blood-Forsythe, Martin A; DiStasio, Robert A; Car, Roberto; Aspuru-Guzik, Alán
2015-01-01
Accurate treatment of the long-range electron correlation energy, including van der Waals (vdW) or dispersion interactions, is essential for describing the structure, dynamics, and function of a wide variety of systems. Among the most accurate models for including dispersion into density functional theory (DFT) is the range-separated many-body dispersion (MBD) method [A. Ambrossetti et al., J. Chem. Phys. 140, 18A508 (2014)], in which the correlation energy is modeled at short-range by a semi-local density functional and at long-range by a model system of coupled quantum harmonic oscillators. In this work, we develop analytical gradients of the MBD energy with respect to nuclear coordinates, including all implicit coordinate dependencies arising from the partitioning of the charge density into Hirshfeld effective volumes. To demonstrate the efficiency and accuracy of these MBD gradients for geometry optimizations of systems with intermolecular and intramolecular interactions, we optimized conformers of the be...
Preparation of Low Entropy Correlated Many-body States via Conformal Cooling Quenches
Zaletel, Michael P; Yao, Norman Y
2016-01-01
We analyze a method for preparing low-entropy many-body states in isolated quantum optical systems of atoms, ions and molecules. Our approach is based upon shifting entropy between different regions of a system by spatially modulating the magnitude of the effective Hamiltonian. We conduct two case studies, on a topological spin chain and the spinful fermionic Hubbard model, focusing on the key question: can a "conformal cooling quench" remove sufficient entropy within experimentally accessible timescales? Finite temperature, time-dependent matrix product state calculations reveal that even moderately sized "bath" regions can remove enough energy and entropy density to expose coherent low temperature physics. The protocol is particularly natural in systems with long-range interactions such lattice-trapped polar molecules and Rydberg dressed atoms where the magnitude of the Hamiltonian scales directly with the density. To this end, we propose a simple implementation of conformal cooling quenches in a dilutely-f...
Many-body decoherence dynamics and optimized operation of a single-photon switch
Murray, C. R.; Gorshkov, A. V.; Pohl, T.
2016-09-01
We develop a theoretical framework to characterize the decoherence dynamics due to multi-photon scattering in an all-optical switch based on Rydberg atom induced nonlinearities. By incorporating the knowledge of this decoherence process into optimal photon storage and retrieval strategies, we establish optimized switching protocols for experimentally relevant conditions, and evaluate the corresponding limits in the achievable fidelities. Based on these results we work out a simplified description that reproduces recent experiments (Nat. Commun. 7 12480) and provides a new interpretation in terms of many-body decoherence involving multiple incident photons and multiple gate excitations forming the switch. Aside from offering insights into the operational capacity of realistic photon switching capabilities, our work provides a complete description of spin wave decoherence in a Rydberg quantum optics setting, and has immediate relevance to a number of further applications employing photon storage in Rydberg media.
Designing exotic many-body states of atomic spin and motion in photonic crystals
Manzoni, Marco T.; Mathey, Ludwig; Chang, Darrick E.
2017-01-01
Cold atoms coupled to photonic crystals constitute an exciting platform for exploring quantum many-body physics. For example, such systems offer the potential to realize strong photon-mediated forces between atoms, which depend on the atomic internal (spin) states, and where both the motional and spin degrees of freedom can exhibit long coherence times. An intriguing question then is whether exotic phases could arise, wherein crystalline or other spatial patterns and spin correlations are fundamentally tied together, an effect that is atypical in condensed matter systems. Here, we analyse one realistic model Hamiltonian in detail. We show that this previously unexplored system exhibits a rich phase diagram of emergent orders, including spatially dimerized spin-entangled pairs, a fluid of composite particles comprised of joint spin-phonon excitations, phonon-induced Néel ordering, and a fractional magnetization plateau associated with trimer formation. PMID:28272466
Many-body effects in LuNi{sub 2}B{sub 2}C
Energy Technology Data Exchange (ETDEWEB)
Bergk, B; Bartkowiak, M; Ignatchik, O; Wosnitza, J [Hochfeld-Magnetlabor Dresden (HLD), Forschungszentrum Dresden-Rossendorf, D-01314 Dresden (Germany); Petzold, V; Rosner, H [Max-Planck-Institut fuer Chemische Physik fester Stoffe, D-01187 Dresden (Germany); Drechsler, S-L; Sheikin, I [Leibniz-Institute for Solid State and Materials Research (IFW-Dresden), D-01171 Dresden (Germany); Canfield, P C, E-mail: b.bergk@fzd.d [Grenoble High Magnetic Field Laboratory, CNRS, BP 166, F-38042 Grenoble Cedex 09 (France)
2009-03-01
We present de Haas-van Alphen measurements of the nonmagnetic borocarbide superconductor LuNi{sub 2}B{sub 2}C. The electronic band structure is extracted from the magnetic quantum oscillations in the normal state. In accordance with previous investigations we find a complex band structure with different open and closed Fermi-surface sheets. From the temperature dependence of the oscillations amplitude the effective mass of the single bands can be determined. Due to many-body interactions we observe enhancements of the effective masses compared to the results by full-potential-density-functional calculations. Therefore, we are able to determine the angular dependence of the interaction strength for the different bands separately.
Accessing Rydberg-dressed interactions using many-body Ramsey dynamics
Mukherjee, Rick; Killian, Thomas; Hazzard, Kaden
2016-05-01
We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system. Our scheme operates comfortably within experimentally measured lifetimes, and accesses a regime where quantum superpositions are crucial. We build a spin-1/2 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, for which we derive an exact solution. Due to the structure of Rydberg interactions, the dynamics differs significantly from that in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results are relevant for the current ongoing experiments, including those at Rice University.
Lattice oscillator model, scattering theory and a many-body problem
Energy Technology Data Exchange (ETDEWEB)
Valiente, Manuel, E-mail: mvalien@phys.au.dk [Department of Physics and Astronomy, Lundbeck Foundation Theoretical Center for Quantum System Research, Aarhus University, DK-8000 Aarhus C (Denmark)
2011-11-18
We propose a model for the quantum harmonic oscillator on a discrete lattice which can be written in a supersymmetric form, in contrast with the more direct discretization of the harmonic oscillator. Its ground state is easily found to be annihilated by the annihilation operator defined here, and its excitation spectrum is obtained numerically. We then define an operator whose continuum limit corresponds to an angular momentum in terms of the creation-annihilation operators of our model. Coherent states with the correct continuum limit are also constructed. The versatility of the model is then used to calculate, in a simple way, the generalized position-dependent scattering length for a particle colliding with a single static impurity in a periodic potential and the exact ground state of an interacting many-body problem in a one-dimensional ring. (paper)
Designing exotic many-body states of atomic spin and motion in photonic crystals
Manzoni, Marco T.; Mathey, Ludwig; Chang, Darrick E.
2017-03-01
Cold atoms coupled to photonic crystals constitute an exciting platform for exploring quantum many-body physics. For example, such systems offer the potential to realize strong photon-mediated forces between atoms, which depend on the atomic internal (spin) states, and where both the motional and spin degrees of freedom can exhibit long coherence times. An intriguing question then is whether exotic phases could arise, wherein crystalline or other spatial patterns and spin correlations are fundamentally tied together, an effect that is atypical in condensed matter systems. Here, we analyse one realistic model Hamiltonian in detail. We show that this previously unexplored system exhibits a rich phase diagram of emergent orders, including spatially dimerized spin-entangled pairs, a fluid of composite particles comprised of joint spin-phonon excitations, phonon-induced Néel ordering, and a fractional magnetization plateau associated with trimer formation.
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.
Exploring the few- to many-body crossover using cold atoms in one dimension
Directory of Open Access Journals (Sweden)
Zinner Nikolaj Thomas
2016-01-01
Full Text Available Cold atomic gases have provided us with a great number of opportunities for studying various physical systems under controlled conditions that are seldom offered in other fields. We are thus at the point where one can truly do quantum simulation of models that are relevant for instance in condensed-matter or high-energy physics, i.e. we are on the verge of a ’cool’ quantum simulator as envisioned by Feynman. One of the avenues under exploration is the physics of one-dimensional systems. Until recently this was mostly in the many-body limit but now experiments can be performed with controllable particle numbers all the way down to the few-body regime. After a brief introduction to some of the relevant experiments, I will review recent theoretical work on one-dimensional quantum systems containing bosons, fermions, or mixtures of the two, with a particular emphasis on the case where the particles are held by an external trap.
Newton-Cartan (super)gravity as a non-relativistic limit
Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas
2015-01-01
We define a procedure that, starting from a relativistic theory of supergravity, leads to a consistent, non-relativistic version thereof. As a first application we use this limiting procedure to show how the Newton-Cartan formulation of non-relativistic gravity can be obtained from general relativit
2012-02-24
field. o We obtained an analytic solution beyond adiabatic approximation by transferring the ID Schrodinger equation into the Ricatti equation. Then we...we obtained the time-dependent Schrodinger equation, with time, t, and position, r, being regarded as parameters, not operators. We then examined...applications in chemical physics and other fields. It enables, e.g., the calculation of the energies of the Schrodinger equation with Coulomb
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.
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
Mixed s -sourcery: Building many-body states using bubbles of nothing
Swingle, Brian; McGreevy, John
2016-10-01
We recently introduced the idea of s -sourcery [B. Swingle and J. McGreevy, Phys. Rev. B 93, 045127 (2016), 10.1103/PhysRevB.93.045127], a general formalism for building many-body quantum ground states using renormalization-group-inspired quantum circuits. Here we define a generalized notion of s -sourcery that applies to mixed states and study its properties and applicability. For our examples we focus on thermal states of local Hamiltonians. We prove a number of theorems establishing the prevalence of mixed s -source fixed points, giving results for free fermion models, conformal field theories, holographic models, and topological phases. Thermal double states (also called thermofield double states) and the machinery of approximate conditional independence are used heavily in the constructions. For a large class of models we provide an information theoretic argument for the existence of a local Hamiltonian whose ground state is the thermal double state, and in some cases we construct such a Hamiltonian.
Long-distance entanglement in many-body atomic and optical systems
Giampaolo, Salvatore M
2009-01-01
We discuss the phenomenon of long-distance entanglement 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 different patterns of site-dependent interaction couplings, singling out two general settings: Patterns that allow for perfect long-distance entanglement (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 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...
Many-body localization phase in a spin-driven chiral multiferroic chain
Stagraczyński, S.; Chotorlishvili, L.; Schüler, M.; Mierzejewski, M.; Berakdar, J.
2017-08-01
Many-body localization (MBL) is an emergent phase in correlated quantum systems with promising applications, particularly in quantum information. Here, we unveil the existence and analyze this phase in a chiral multiferroic model system. Conventionally, MBL occurrence is traced via level statistics by implementing a standard finite-size scaling procedure. Here, we present an approach based on the full distribution of the ratio of adjacent energy spacings. We find a strong broadening of the histograms of counts of these level spacings directly at the transition point from MBL to the ergodic phase. The broadening signals reliably the transition point without relying on an averaging procedure. The fast convergence of the histograms even for relatively small systems allows monitoring the MBL dynamics with much less computational effort. Numerical results are presented for a chiral spin chain with a dynamical Dzyaloshinskii-Moriya interaction, an established model to describe the spin excitations in a single-phase spin-driven multiferroic system. The multiferroic MBL phase is uncovered and it is shown how to steer it via electric fields.
Holographic energy loss in non-relativistic backgrounds
Atashi, Mahdi; Farahbodnia, Mitra
2016-01-01
In this paper, we study some aspects of energy loss in non-relativistic theories from holography. We analyze the energy lost by a rotating heavy point particle along a circle of radius $l$ with angular velocity $\\omega$ in theories with general dynamical exponent $z$ and hyperscaling violation exponent $\\theta$. It is shown that this problem provides a novel perspective on the energy loss in such theories. A general computation at zero and finite temperature is done and it is shown that how the total energy loss rate depends non-trivially on two characteristic exponents $(z,\\theta)$. We find that at zero temperature there is a special radius $l_c$ where the energy loss is independent of different values of $(z,\\theta)$. Also, there is a crossover between a regime in which the energy loss is dominated by the linear drag force and by the radiation because of the acceleration of the rotating particle. We discover different behaviors at finite temperature case.
Continuity properties of the semi-group and its integral kernel in non-relativistic QED
Matte, Oliver
2016-07-01
Employing recent results on stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics by B. Güneysu, J. S. Møller, and the present author, we study the continuity of the corresponding semi-group between weighted vector-valued Lp-spaces, continuity properties of elements in the range of the semi-group, and the pointwise continuity of an operator-valued semi-group kernel. We further discuss the continuous dependence of the semi-group and its integral kernel on model parameters. All these results are obtained for Kato decomposable electrostatic potentials and the actual assumptions on the model are general enough to cover the Nelson model as well. As a corollary, we obtain some new pointwise exponential decay and continuity results on elements of low-energetic spectral subspaces of atoms or molecules that also take spin into account. In a simpler situation where spin is neglected, we explain how to verify the joint continuity of positive ground state eigenvectors with respect to spatial coordinates and model parameters. There are no smallness assumptions imposed on any model parameter.
Radiation of non-relativistic particle on a conducting sphere and a string of spheres
Shul'ga, N F; Larikova, E A
2016-01-01
The radiation arising under uniform motion of non-relativistic charged particle by (or through) perfectly conducting sphere is considered. The rigorous results are obtained using the method of images known from electrostatics.
Many-body topological invariants in fermionic symmetry protected topological phases
Shiozaki, Ken; Ryu, Shinsei
2016-01-01
We propose the definitions of many-body topological invariants to detect symmetry-protected topological phases protected by point group symmetry, using partial point group transformations on a given short-range entangled quantum ground state. Partial point group transformations $g_D$ are defined by point group transformations restricted to a spatial subregion $D$, which is closed under the point group transformations and sufficiently larger than the bulk correlation length $\\xi$. By analytical and numerical calculations,we find that the ground state expectation value of the partial point group transformations behaves generically as $\\langle GS | g_D | GS \\rangle \\sim \\exp \\Big[ i \\theta+ \\gamma - \\alpha \\frac{{\\rm Area}(\\partial D)}{\\xi^{d-1}} \\Big]$. Here, ${\\rm Area}(\\partial D)$ is the area of the boundary of the subregion $D$, and $\\alpha$ is a dimensionless constant. The complex phase of the expectation value $\\theta$ is quantized and serves as the topological invariant, and $\\gamma$ is a scale-independe...
Fast and Accurate Electronic Excitations in Cyanines with the Many-Body Bethe-Salpeter Approach.
Boulanger, Paul; Jacquemin, Denis; Duchemin, Ivan; Blase, Xavier
2014-03-11
The accurate prediction of the optical signatures of cyanine derivatives remains an important challenge in theoretical chemistry. Indeed, up to now, only the most expensive quantum chemical methods (CAS-PT2, CC, DMC, etc.) yield consistent and accurate data, impeding the applications on real-life molecules. Here, we investigate the lowest lying singlet excitation energies of increasingly long cyanine dyes within the GW and Bethe-Salpeter Green's function many-body perturbation theory. Our results are in remarkable agreement with available coupled-cluster (exCC3) data, bringing these two single-reference perturbation techniques within a 0.05 eV maximum discrepancy. By comparison, available TD-DFT calculations with various semilocal, global, or range-separated hybrid functionals, overshoot the transition energies by a typical error of 0.3-0.6 eV. The obtained accuracy is achieved with a parameter-free formalism that offers similar accuracy for metallic or insulating, finite size or extended systems.
Reduced-density-matrix spectrum and block entropy of permutationally invariant many-body systems.
Salerno, Mario; Popkov, Vladislav
2010-07-01
Spectral properties of the reduced density matrix (RDM) of permutational invariant quantum many-body systems are investigated. The RDM block diagonalization which accounts for all symmetries of the Hamiltonian is achieved. The analytical expression of the RDM spectrum is provided for arbitrary parameters and rigorously proved in the thermodynamical limit. The existence of several sum rules and recurrence relations among RDM eigenvalues is also demonstrated and the distribution function of RDM eigenvalues (including degeneracies) characterized. In particular, we prove that the distribution function approaches a two-dimensional Gaussian in the limit of large subsystem sizes n>1. As a physical application we discuss the von Neumann entropy (VNE) of a block of size n for a system of hard-core bosons on a complete graph, as a function of n and of the temperature T. The occurrence of a crossover of VNE from purely logarithmic behavior at T=0 to a purely linear behavior in n for T≥Tc, is demonstrated.
An exacting transition probability measurement - a direct test of atomic many-body theories
Dutta, T; Yum, D; Rebhi, R; Mukherjee, M
2016-01-01
A new protocol for measuring the branching fraction of hydrogenic atoms with only statistically limited uncertainty is proposed and demonstrated for the decay of the P$_{3/2}$ level of the barium ion, with precision below $0.5\\%$. Heavy hydrogenic atoms like the barium ion are test beds for fundamental physics such as atomic parity violation and they also hold the key to understanding nucleo-synthesis in stars. To draw definitive conclusion about possible physics beyond the standard model by measuring atomic parity violation in the barium ion it is necessary to measure the dipole transition probabilities of low-lying excited states with precision better than $1\\%$. Furthermore, enhancing our understanding of the $\\it{barium-puzzle}$ in barium stars requires branching fraction data for proper modelling of nucleo-synthesis. Our measurements are the first to provide a direct test of quantum many-body calculations on the barium ion with precision below one percent and more importantly with no known systematic unc...
Three-Body Interactions in Many-Body Effective Field Theory
Furnstahl, R J
2003-01-01
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.
Relativistic and non-relativistic solitons in plasmas
Barman, Satyendra Nath
This thesis entitled as "Relativistic and Non-relativistic Solitons in Plasmas" is the embodiment of a number of investigations related to the formation of ion-acoustic solitary waves in plasmas under various physical situations. The whole work of the thesis is devoted to the studies of solitary waves in cold and warm collisionless magnetized or unmagnetized plasmas with or without relativistic effect. To analyze the formation of solitary waves in all our models of plasmas, we have employed two established methods namely - reductive perturbation method to deduce the Korteweg-de Vries (KdV) equation, the solutions of which represent the important but near exact characteristic concepts of soliton-physics. Next, the pseudopotential method to deduce the energy integral with total nonlinearity in the coupling process for exact characteristic results of solitons has been incorporated. In Chapter 1, a brief description of plasma in nature and laboratory and its generation are outlined elegantly. The nonlinear differential equations to characterize solitary waves and the relevant but important methods of solutions have been mentioned in this chapter. The formation of solitary waves in unmagnetized and magnetized plasmas, and in relativistic plasmas has been described through mathematical entity. Applications of plasmas in different fields are also put forwarded briefly showing its importance. The study of plasmas as they naturally occur in the universe encompasses number of topics including sun's corona, solar wind, planetary magnetospheres, ionospheres, auroras, cosmic rays and radiation. The study of space weather to understand the universe, communications and the activities of weather satellites are some useful areas of space plasma physics. The surface cleaning, sterilization of food and medical appliances, killing of bacteria on various surfaces, destroying of viruses, fungi, spores and plasma coating in industrial instruments ( like computers) are some of the fields
Semi-classical Locality for the Non-relativistic Path Integral in Configuration Space
Gomes, Henrique
2017-09-01
In an accompanying paper Gomes (arXiv:1504.02818, 2015), we have put forward an interpretation of quantum mechanics based on a non-relativistic, Lagrangian 3+1 formalism of a closed Universe M, existing on timeless configuration space Q of some field over M. However, not much was said there about the role of locality, which was not assumed. This paper is an attempt to fill that gap. Locality in full can only emerge dynamically, and is not postulated. This new understanding of locality is based solely on the properties of extremal paths in configuration space. I do not demand locality from the start, as it is usually done, but showed conditions under which certain systems exhibit it spontaneously. In this way we recover semi-classical local behavior when regions dynamically decouple from each other, a notion more appropriate for extension into quantum mechanics. The dynamics of a sub-region O within the closed manifold M is independent of its complement, M-O, if the projection of extremal curves on Q onto the space of extremal curves intrinsic to O is a surjective map. This roughly corresponds to e^{i\\hat{H}t}circ prO= prOcirc e^{i\\hat{H}t}, where prO:Q→ Q_O^{partial O} is a linear projection. This criterion for locality can be made approximate—an impossible feat had it been already postulated—and it can be applied for theories which do not have hyperbolic equations of motion, and/or no fixed causal structure. When two regions are mutually independent according to the criterion proposed here, the semi-classical path integral kernel factorizes, showing cluster decomposition which is the ultimate aim of a definition of locality.
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
The many facets of the (non relativistic) Nuclear Equation of State
Giuliani, G; Bonasera, A
2013-01-01
A nucleus is a quantum many body system made of strongly interacting Fermions, protons and neutrons (nucleons). This produces a rich Nuclear Equation of State whose knowledge is crucial to our understanding of the composition and evolution of celestial objects. The nuclear equation of state displays many different features; first neutrons and protons might be treated as identical particles or nucleons, but when the differences between protons and neutrons are spelled out, we can have completely different scenarios, just by changing slightly their interactions. At zero temperature and for neutron rich matter, a quantum liquid gas phase transition at low densities or a quark-gluon plasma at high densities might occur. Furthermore, the large binding energy of the $\\alpha$ particle, a Boson, might also open the possibility of studying a system made of a mixture of Bosons and Fermions, which adds to the open problems of the nuclear equation of state.
Applications of many-body physics to relativistic heavy ion collisions
Fillion-Gourdeau, Francois
In this dissertation, many-body physics techniques are used to study and improve ideas related to the description of heavy ion collisions at very high energy. The first part of the thesis concerns the production of tensor mesons in proton-proton (pp) collisions. An effective theory where the f2 meson couples to the energy-momentum tensor is proposed and a comparison of the inclusive cross-section computed in the collinear factorization, the k⊥-factorization and the color glass condensate is performed. A study of the phenomenology in pp collisions then shows a strong dependence on the parametrization of the unintegrated distribution function. The conclusion is that f2 meson production can be utilized to improve the understanding of the proton wave-function. In the second part, a similar investigation is performed by analysing the production cross-section of the eta' meson in pp and proton-nucleus (pA) collisions. The nucleus and proton are described by the CGC and the k⊥ -factorization respectively. A new technique for the computation of Wilson lines---color charge densities correlators in the McLerran-Venugopalan model is developped. The phenomenology shows that the cross-section in pA collisions is very sensitive to the value of the saturation scale, a crucial ingredient of the CGC picture. In the third part of the thesis, the collision term of the Boltzmann equation is derived from first principles at all orders and for any number of participating particles, starting from the full out-of-equilibrium quantum field theory and using the multiple scattering expansion. Finally, the emission of photons from a non-abelian strong classical field is investigated. A formalism based on Schwinger-Keldysh propagators relating the production rate of photons to the retarded solution of the Dirac equation in a background field is presented.
Lim, S. P.; Sheng, D. N.
2016-07-01
A many-body localized (MBL) state is a new state of matter emerging in a disordered interacting system at high-energy densities through a disorder-driven dynamic phase transition. The nature of the phase transition and the evolution of the MBL phase near the transition are the focus of intense theoretical studies with open issues in the field. We develop an entanglement density matrix renormalization group (En-DMRG) algorithm to accurately target highly excited states for MBL systems. By studying the one-dimensional Heisenberg spin chain in a random field, we demonstrate the accuracy of the method in obtaining energy eigenstates and the corresponding statistical results of quantum states in the MBL phase. Based on large system simulations by En-DMRG for excited states, we demonstrate some interesting features in the entanglement entropy distribution function, which is characterized by two peaks: one at zero and another one at the quantized entropy S =ln2 with an exponential decay tail on the S >ln2 side. Combining En-DMRG with exact diagonalization simulations, we demonstrate that the transition from the MBL phase to the delocalized ergodic phase is driven by rare events where the locally entangled spin pairs develop power-law correlations. The corresponding phase diagram contains an intermediate or crossover regime, which has power-law spin-z correlations resulting from contributions of the rare events. We discuss the physical picture for the numerical observations in this regime, where various distribution functions are distinctly different from results deep in the ergodic and MBL phases for finite-size systems. Our results may provide new insights for understanding the phase transition in such systems.
Many-body theory for the anti shielding factor of lithium atom
Mahapatra, P. C.; Rao, B. K.
1990-03-01
The Sternheimer anti-shielding factor of lithium atom has been calculated using linked cluster many-body perturbation theoretical technique. The results obtained compare well with some of the values available in the literature.
Persico, Franco; Power, Edwin A.
1988-01-01
The physics of the electromagnetic vacuum, its fluctuations and its role in spontaneous emission has been studied since the early days of the quantum theory of radiation. In recent years there has been a renewed interest in the nature of the vacuum state and its potency in giving rise to observable effects. For example the question of amplification of photon signals and the way vacuum fluctuations may provide inescapable noise is fundamental to the theory of measurement. Quantum electrodynamics in cavities has become a very active area of research both experimentally and theoretically and the way the radiation field, even in vacuo, is changed by confinement is of interest and importance. The effective Einstein A-coefficient can be much smaller than in free space because the available modes are sparser in a cavity. Radiative connections such as the Lamb shift energies are also changed as the virtual photon modes are varied by the confinement. The existence of electromagnetic field energy (from the vacuum fluctuations) in the neighbourhood of atoms/molecules in their ground state is demonstrated by its effect on test molecules brought into the vicinity of the original sources. All the forces analogous to that of Van der Waals, including of course their Casimir retardations at long range, are explicable in terms of these virtual cloud effects. The Adriatico Conference on "Vacuum in Non-Relativistic Matter-Radiation Systems" held in July 1987 brought together scientists in quantum optics, quantum field theorists and others interested in the electromagnetic vacuum. It was most successful in that the participants found enough mutual agreement but with clearly defined tensions between them to provide excitement and argument throughout the four days' meeting. This volume consists of most of the papers presented at the conference. It is clear that the collection ranges from the pedagogical and the review type article to research papers with original material. The
Use of supersymmetric isospectral formalism to realistic quantum many-body problems
Indian Academy of Sciences (India)
Barnali Chakrabarti
2009-08-01
We propose a novel mathematical approach for the calculation of resonances in weakly bound systems. For any potential, families of strictly isospectral potentials (with very different shape) having desirable and adjustable features can be generated. For systems having no bound ground state, an isospectral potential with a bound state in the continuum is possible. The quasi-bound state in the original shallow potential will be effectively trapped in the deep well of the isospectral family, facilitating more accurate calculation of resonance energy. Application to 6He, 6Li and 6Be yield excellent results. Another application is the calculation of Efimov states in weakly bound three-body system. We present the result of 4He trimer, where the first excited state is claimed to be an Efimov state.
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.
Signature of clustering in quantum many-body systems probed by the giant dipole resonance
Pandit, Deepak; Mondal, Debasish; Dey, Balaram; Bhattacharya, Srijit; Mukhopadhyay, S.; Pal, Surajit; De, A.; Banerjee, S. R.
2017-03-01
The present experimental study illustrates how large deformations attained by nuclei due to cluster formation are perceived through the giant dipole resonance (GDR) strength function. The high energy GDR γ rays have been measured from 32S at different angular momenta (J ) but similar temperatures in the reactions 4He(Elab=45 MeV )+28Si and 20Ne(Elab=145 MeV )+12C . The experimental data at lower J (˜10 ℏ ) suggests a normal deformation, similar to the ground state value, showing no potential signature of clustering. However, it is found that the GDR lineshape is fragmented into two prominent peaks at high J (˜20 ℏ ) providing a direct measurement of the large deformation developed in the nucleus. The observed lineshape is also completely different from the ones seen for Jacobi shape transition at high J pointing towards the formation of cluster structure in superdeformed states of 32S at such high spin. Thus, the GDR can be regarded as a unique tool to study cluster formation at high excitation energies and angular momenta.
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
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....
Physical stress, mass, and energy for non-relativistic spinful matter
Geracie, Michael; Roberts, Matthew M
2016-01-01
For theories of relativistic matter fields with spin there exist two possible definitions of the stress-energy tensor, one defined by a variation of the action with the coframes at fixed connection, and the other at fixed torsion. These two stress-energy tensors do not necessarily coincide and it is the latter that corresponds to the Cauchy stress measured in the lab. In this note we discuss the corresponding issue for non-relativistic matter theories. We point out that while the physical non-relativistic stress, momentum, and mass currents are defined by a variation of the action at fixed torsion, the energy current does not admit such a description and is naturally defined at fixed connection. Any attempt to define an energy current at fixed torsion results in an ambiguity which cannot be resolved from the background spacetime data or conservation laws. We also provide computations of these quantities for some simple non-relativistic actions.
Itinerant type many-body theories for photo-induced structural phase transitions
Nasu, Keiichiro
2004-09-01
Itinerant type quantum many-body theories for photo-induced structural phase transitions (PSPTs) are reviewed in close connection with various recent experimental results related to this new optical phenomenon. There are two key concepts: the hidden multi-stability of the ground state, and the proliferations of optically excited states. Taking the ionic (I) rarr neutral (N) phase transition in the organic charge transfer (CT) crystal, TTF-CA, as a typical example for this type of transition, we, at first, theoretically show an adiabatic path which starts from CT excitons in the I-phase, but finally reaches an N-domain with a macroscopic size. In connection with this I-N transition, the concept of the initial condition sensitivity is also developed so as to clarify experimentally observed nonlinear characteristics of this material. In the next, using a more simplified model for the many-exciton system, we theoretically study the early time quantum dynamics of the exciton proliferation, which finally results in the formation of a domain with a large number of excitons. For this purpose, we derive a stepwise iterative equation to describe the exciton proliferation, and clarify the origin of the initial condition sensitivity. Possible differences between a photo-induced nonequilibrium phase and an equilibrium phase at high temperatures are also clarified from general and conceptional points of view, in connection with recent experiments on the photo-induced phase transition in an organo-metallic complex crystal. It will be shown that the photo-induced phase can make a new interaction appear as a broken symmetry only in this phase, even when this interaction is almost completely hidden in all the equilibrium phases, such as the ground state and other high-temperature phases. The relation between the photo-induced nonequilibrium phase and the hysteresis induced nonequilibrium one is also qualitatively discussed. We will be concerned with a macroscopic parity violation
Itinerant type many-body theories for photo-induced structural phase transitions
Energy Technology Data Exchange (ETDEWEB)
Nasu, Keiichiro [Solid State Theory Division, Institute of Materials Structure Science, KEK, Graduate University for Advanced Study, 1-1, Oho, Tsukuba, Ibaraki, 305-0801 (Japan)
2004-09-01
Itinerant type quantum many-body theories for photo-induced structural phase transitions (PSPTs) are reviewed in close connection with various recent experimental results related to this new optical phenomenon. There are two key concepts: the hidden multi-stability of the ground state, and the proliferations of optically excited states. Taking the ionic (I) {yields} neutral (N) phase transition in the organic charge transfer (CT) crystal, TTF-CA, as a typical example for this type of transition, we, at first, theoretically show an adiabatic path which starts from CT excitons in the I-phase, but finally reaches an N-domain with a macroscopic size. In connection with this I-N transition, the concept of the initial condition sensitivity is also developed so as to clarify experimentally observed nonlinear characteristics of this material. In the next, using a more simplified model for the many-exciton system, we theoretically study the early time quantum dynamics of the exciton proliferation, which finally results in the formation of a domain with a large number of excitons. For this purpose, we derive a stepwise iterative equation to describe the exciton proliferation, and clarify the origin of the initial condition sensitivity. Possible differences between a photo-induced nonequilibrium phase and an equilibrium phase at high temperatures are also clarified from general and conceptional points of view, in connection with recent experiments on the photo-induced phase transition in an organo-metallic complex crystal. It will be shown that the photo-induced phase can make a new interaction appear as a broken symmetry only in this phase, even when this interaction is almost completely hidden in all the equilibrium phases, such as the ground state and other high-temperature phases. The relation between the photo-induced nonequilibrium phase and the hysteresis induced nonequilibrium one is also qualitatively discussed. We will be concerned with a macroscopic parity
Potential of mean force between like-charged nanoparticles: Many-body effect
Zhang, Xi; Shi, Ya-Zhou; Zhu, Xiao-Long; Tan, Zhi-Jie
2016-01-01
Ion-mediated interaction is important for the properties of polyelectrolytes such as colloids and nucleic acids. The effective pair interactions between two polyelectrolytes have been investigated extensively, but the many-body effect for multiple polyelectrolytes still remains elusive. In this work, the many-body effect in potential of mean force (PMF) between like-charged nanoparticles in various salt solutions has been comprehensively examined by Monte Carlo simulation and the nonlinear Poisson-Boltzmann theory. Our calculations show that, at high 1:1 salt, the PMF is weakly repulsive and appears additive, while at low 1:1 salt, the additive assumption overestimates the repulsive many-body PMF. At low 2:2 salt, the pair PMF appears weakly repulsive while the many-body PMF can become attractive. In contrast, at high 2:2 salt, the pair PMF is apparently attractive while the many-body effect can cause a weaker attractive PMF than that from the additive assumption. Our microscopic analyses suggest that the elu...
Grossu, I. V.; Besliu, C.; Jipa, Al.; Felea, D.; Esanu, T.; Stan, E.; Bordeianu, C. C.
2013-04-01
In this paper we present a new version of the Chaos Many-Body Engine C# application (Grossu et al. 2012 [1]). In order to benefit from the latest technological advantages, we migrated the application from .Net Framework 2.0 to .Net Framework 4.0. New tools were implemented also. Trying to estimate the particle interactions dependence on initial conditions, we considered a new distance, which takes into account only the structural differences between two systems. We used this distance for implementing the “Structural Lyapunov” function. We propose also a new precision test based on temporal reversed simulations. New version program summaryProgram title: Chaos Many-Body Engine v03 Catalogue identifier: AEGH_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEGH_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 214429 No. of bytes in distributed program, including test data, etc.: 9512380 Distribution format: tar.gz Programming language: Visual C# .Net 2010 Computer: PC Operating system: .Net Framework 4.0 running on MS Windows RAM: 128 MB Classification: 24.60.Lz, 05.45.a Catalogue identifier of previous version: AEGH_v2_0 Journal reference of previous version: Computer Physics Communications 183 (2012) 1055-1059 Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm. Implementation of temporal reversed simulation precision test, and “Structural Lyapunov” function. In order to benefit from the advantages involved in the latest technologies (e.g. LINQ Queries [2]), Chaos Many-Body Engine was migrated from .Net Framework 2.0 to .Net Framework 4.0. In addition to existing energy conservation
Dahlke, Erin E; Truhlar, Donald G
2007-01-01
The use of background molecular charge to incorporate environmental effects on a molecule or active site is widely employed in quantum chemistry. In the present article we employ this practice in conjunction with many-body expansions. In particular, we present electrostatically embedded two-body and three-body expansions for calculating the energies of molecular clusters. The system is divided into fragments, and dimers or trimers of fragments are calculated in a field of point charges representing the electrostatic potential of the other fragments. We find that including environmental point charges can lower the errors in the electrostatically embedded pairwise additive (EE-PA) energies for a series of water clusters by as much as a factor of 10 when compared to the traditional pairwise additive approximation and that for the electrostatically embedded three-body (EE-3B) method the average mean unsigned error over nine different levels of theory for a set of six tetramers and one pentamer is only 0.05 kcal/mol, which is only 0.4% of the mean unsigned net interaction energy. We also test the accuracy of the EE-PA and EE-3B methods for a cluster of 21 water molecules and find that the errors relative to a full MP2/aug'-cc-pVTZ calculation to be only 2.97 and 0.38 kcal/mol, respectively, which are only 1.5% and 0.2%, respectively, of the net interaction energy. This method offers the advantage over some other fragment-based methods in that it does not use an iterative method to determine the charges and thus provides substantial savings for large clusters. The method is convenient to adapt to a variety of electronic structure methods and program packages, it has N(2) or N(3) computational scaling for large systems (where N is the number of fragments), it is easily converted to an O(N) method, and its linearity allows for convenient analytic gradients.
Many-body dipole-induced dipole model for electrorheological fluids
Institute of Scientific and Technical Information of China (English)
Huang Ji-Ping; Yu Kin-Wah
2004-01-01
Theoretical investigations on electrorheological (ER) fluids usually rely on computer simulations. An initial approach for these studies would be the point-dipole (PD) approximation, which is known to err considerably when the particles approach and finally touch each other due to many-body and multipolar interactions. Thus various works have attempted to go beyond the PD model. Being beyond the PD model, previous attempts have been restricted to either local-field effects only or multipolar effects only, but not both. For instance, we recently proposed a dipoleinduced-dipole (DID) model which is shown to be both more accurate than the PD model and easy to use. This work is necessary because the many-body (local-field) effect is included to put forth the many-body DID model. The results show that the multipolar interactions can indeed be dominant over the dipole interaction, while the local-field effect may yield a correction.
Helium atom excitations by the GW and Bethe-Salpeter many-body formalism
Li, Jing; Duchemin, Ivan; Blase, Xavier; Olevano, Valerio
2016-01-01
Helium atom is the simplest many-body electronic system provided by nature. The exact solution to the Schr\\"odinger equation is known for helium ground and excited states, and represents a workbench for any many-body methodology. Here we check ab initio many-body GW approximation and Bethe-Salpeter equation (BSE) against helium exact solution. Starting from Hartree-Fock, we show that GW and BSE yield impressingly accurate results on excitation energies and oscillator strength. These findings suggest that the accuracy of BSE and GW approximations is not significantly limited by self-interaction and self-screening problems even in this few electron limit. We further discuss our results in comparison to those obtained by time-dependent density-functional theory.
Encoding the structure of many-body localization with matrix product operators
Pekker, David; Clark, Bryan K.
2017-01-01
Anderson insulators are noninteracting disordered systems which have localized single-particle eigenstates. The interacting analog of Anderson insulators are the many-body localized (MBL) phases. The spectrum of the many-body eigenstates of an Anderson insulator is efficiently represented as a set of product states over the single-particle modes. We show that product states over matrix product operators of small bond dimension is the corresponding efficient description of the spectrum of an MBL insulator. In this language all of the many-body eigenstates are encoded by matrix product states (i.e., density matrix renormalization group wave functions) consisting of only two sets of low bond dimension matrices per site: the Gi matrices corresponding to the local ground state on site i and the Ei matrices corresponding to the local excited state. All 2n eigenstates can be generated from all possible combinations of these sets of matrices.
Thermal supercurrent in non-reciprocal many-body near field electromagnetic heat transfer
Zhu, Linxiao
2016-01-01
We consider the consequence of non-reciprocity in near-field heat transfer by studying systems consisting of magneto-optical nanoparticles. We demonstrate that in thermal equilibrium, non-reciprocal many-body system can support a persistent directional heat current, i.e. thermal supercurrent, without violating the second law of thermodynamics. Such a thermal supercurrent can not occur in reciprocal systems, and can only arise in many-body systems. The use of non-reciprocity therefore points to a new regime of near-field heat transfer for the control of heat flow in the nanoscale.
Zhu, Linxiao; Fan, Shanhui
2016-09-01
We consider the consequence of nonreciprocity in near-field heat transfer by studying systems consisting of magneto-optical nanoparticles. We demonstrate that, in thermal equilibrium, a nonreciprocal many-body system in heat transfer can support a persistent directional heat current, without violating the second law of thermodynamics. Such a persistent directional heat current cannot occur in reciprocal systems, and can only arise in many-body systems in heat transfer. The use of nonreciprocity therefore points to a new regime of near-field heat transfer for the control of heat flow in the nanoscale.
Relativistic multireference many-body perturbation theory calculations on Au64+ - Au69+ ions
Energy Technology Data Exchange (ETDEWEB)
Vilkas, M J; Ishikawa, Y; Trabert, E
2006-03-31
Many-body perturbation theory (MBPT) calculations are an adequate tool for the description of the structure of highly charged multi-electron ions and for the analysis of their spectra. They demonstrate this by way of a re-investigation of n=3, {Delta}n=0 transitions in the EUV spectra of Na-, Mg-, Al-like, and Si-like ions of Au that have been obtained previously by heavy-ion accelerator based beam-foil spectroscopy. They discuss the evidence and propose several revisions on the basis of the multi-reference many-body perturbation theory calculations of Ne- through P-like ions of Au.
Ginges, J S M
2015-01-01
We consider the largest (Uehling) contribution to the one-loop vacuum polarization correction to the binding energies in neutral alkali atoms, from Na through to the superheavy element E119. We use the relativistic Hartree-Fock method to demonstrate the importance of core relaxation effects. These effects are sizeable everywhere, though particularly important for orbitals with angular momentum quantum number l > 0. For d waves, the Uehling shift is enhanced by many orders of magnitude: for Cs the enhancement is more than four orders of magnitude and for the lighter alkali atoms it is even larger. We also study the effects of second- and higher-order many-body perturbation theory on the valence level shifts through inclusion of the correlation potential. The many-body enhancement mechanisms that operate in the case of the Uehling potential apply also to the case of the larger QED self-energy radiative corrections. The huge enhancement for d level shifts makes high-precision studies of transition frequencies in...
Light Fermion Finite Mass Effects in Non-relativistic Bound States
Eiras, D; Eiras, Dolors; Soto, Joan
2000-01-01
We present analytic expressions for the vacuum polarization effects due to a light fermion with finite mass in the binding energy and in the wave function at the origin of QED and (weak coupling) QCD non-relativistic bound states. Applications to exotic atoms, \\Upsilon (1s) and t\\bar{t} production near threshold are briefly discussed.
Many-body problems with composite particles and q-Heisenberg algebras
Energy Technology Data Exchange (ETDEWEB)
Avancini, S.S. [Santa Catarina Univ., Florianopolis, SC (Brazil). Dept. de Fisica; Krein, G.
1994-07-01
It is proposed to employ deformed communication relations to treat many body problems of composite particles. The deformation parameter is interpreted as a measure of the effects of the statistics of the internal degrees of freedom of the composite particles. A simple application of the method is made for the case of a gas of composite bosons. (author). 14 refs.
Yu, Xiongjie; Pekker, David; Clark, Bryan K.
2017-01-01
A key property of many-body localized Hamiltonians is the area law entanglement of even highly excited eigenstates. Matrix product states (MPS) can be used to efficiently represent low entanglement (area law) wave functions in one dimension. An important application of MPS is the widely used density matrix renormalization group (DMRG) algorithm for finding ground states of one-dimensional Hamiltonians. Here, we develop two algorithms, the shift-and-invert MPS (SIMPS) and excited state DMRG which find highly excited eigenstates of many-body localized Hamiltonians. Excited state DMRG uses a modified sweeping procedure to identify eigenstates, whereas SIMPS applies the inverse of the shifted Hamiltonian to a MPS multiple times to project out the targeted eigenstate. To demonstrate the power of these methods, we verify the breakdown of the eigenstate thermalization hypothesis in the many-body localized phase of the random field Heisenberg model, show the saturation of entanglement in the many-body localized phase, and generate local excitations.
Efficient molecular dynamics simulations with many-body potentials on graphics processing units
Fan, Zheyong; Vierimaa, Ville; Harju, Ari
2016-01-01
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 [Phys. Rev. B 92 (2015) 094301]. 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 potentia...
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).
Wei, Wei; Dai, Ying; Huang, Baibiao; Jacob, Timo
2013-10-14
In order to study many-body effects in ZnO structures with reduced-dimensionality, electronic and optical absorption properties of ZnO monolayer and armchair ZnO nanoribbons (AZnONRs) are studied by means of Green's function perturbation theory using the GW+Bethe-Salpeter equation approach. In both ZnO monolayer and AZnONRs, as a consequence of enhanced quantum confinement, the quasi-particle corrections are significant and the optical absorption properties are dominated by strong excitonic effects with considerable binding energies (1-2 eV) assigned to the lowest-energy bound excitons. It reveals that inclusion of excitonic effects, which are neglected in calculations at single-particle approximation, is crucial to qualitatively and quantitatively describe the optical properties of such materials with reduced-dimensionality.
Li, Jing; D'Avino, Gabriele; Duchemin, Ivan; Beljonne, David; Blase, Xavier
2016-07-21
We present an original hybrid QM/MM scheme merging the many-body Green's function GW formalism with classical discrete polarizable models and its application to the paradigmatic case of a pentacene crystal. Our calculated transport gap is found to be in excellent agreement with reference periodic bulk GW calculations, together with properly parametrized classical microelectrostatic calculations, and with photoionization measurements at crystal surfaces. More importantly, we prove that the gap is insensitive to the partitioning of pentacene molecules in QM and MM subsystems, as a result of the mutual compensation of quantum and classical polarizabilities, clarifying the relation between polarization energy and delocalization. The proposed hybrid method offers a computationally attractive strategy to compute the full spectrum of charged excitations in complex molecular environments, accounting for both QM and MM contributions to the polarization energy, a crucial requirement in the limit of large QM subsystems.
Abyaneh, V; Abyaneh, Varqa; Kay, Bernard S.
2005-01-01
In ``Decoherence of macroscopic closed systems within Newtonian quantum gravity'' (Kay B S 1998 Class. Quantum Grav. 15 L89-L98) it was argued that, given a many-body Schroedinger wave function \\psi(x_1,...,x_N) for the centre-of-mass degrees of freedom of a closed system of N identical uniform-mass balls of mass M and radius R, taking account of quantum gravitational effects and then tracing over the gravitational field amounts to multiplying the position-space density matrix \\rho(x_1,...,x_N; x_1',...,x_N')= \\psi(x_1,...,x_N)\\psi*(x_1',...,x_N') by a multiplicative factor, which, if the positions {x_1,...,x_N; x_1',...,x_N'} are all much further away from one another than R, is well-approximated by the product from 1 to N over I, J, K (I 0) of radius r with centres at the vertices of a cubic lattice of spacing a (assumed to be very much bigger than 2r) and side 2La we establish the bound 0.7(r/a)^{1/n}La < R_eff < 3.1(r/a)^{1/n} La.
Entropy production and wave packet dynamics in the Fock space of closed chaotic many-body systems
Flambaum, V V
2001-01-01
Highly excited many-particle states in quantum systems such as nuclei, atoms, quantum dots, spin systems, quantum computers etc., can be considered as ``chaotic'' superpositions of mean-field basis states (Slater determinants, products of spin or qubit states). This is due to a very high level density of many-body states that are easily mixed by a residual interaction between particles (quasi-particles). For such systems, we have derived simple analytical expressions for the time dependence of energy width of wave packets, as well as for the entropy, number of principal basis components and inverse participation ratio, and tested them in numerical experiments. It is shown that the energy width $\\Delta (t)$ increases linearly and very quickly saturates. The entropy of a system increases quadratically, $S(t) \\sim t^2$ at small times, and after, can grow linearly, $S(t) \\sim t$, before the saturation. Correspondingly, the number of principal components determined by the entropy, $N_{pc} \\sim exp{(S(t))}$, or by ...
Construction of an exactly solvable model of the many-body problem
Energy Technology Data Exchange (ETDEWEB)
Zettili, N. [King Fahd Univ. of Petrolium and Minerals, Dhahran (Saudi Arabia). Dept. of Phys.]|[Institut de Physique, Universite de Blida, Blida (Algeria); Bouayad, N. [Institut de Physique, Universite de Blida, Blida (Algeria)
1996-11-11
We propose here a new model for the many-body problem that can be solved exactly through the diagonalization of its Hamiltonian. This model, which is founded on a Lie algebra, serves as a useful tool for testing the accuracy of many-body approximation methods. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct this model`s Hamiltonian by means of vector operators that are the generators of an SO(2,1) group and which satisfy a Lie algebra. We incorporate into the Hamiltonian a symmetry that yields a constant of the motion which, in turn, renders the size of the Hamiltonian matrix finite. The diagonalization of this finitely dimensional matrix gives the exact values of the energy spectrum. (orig.).
Construction of an exactly solvable model of the many-body problem
Zettili, Nouredine; Bouayad, Nouredine
1996-02-01
We propose here a new model for the many-body problem that can be solved exactly through the diagonalization of its Hamiltonian. This model, which is founded on a Lie algebra, serves as a useful tool for testing the accuracy of many-body approximation methods. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. We construct this model's Hamiltonian by means of vector operators that are the generators of an SO(2, 1) group and which satisfy a Lie algebra. We incorporate into the Hamiltonian a symmetry that yields a constant of the motion which, in turn, renders the size of the Hamiltonian matrix finite. The diagonalization of this finitely dimensional matrix gives the exact values of the energy spectrum.
Universal dynamics of density correlations at the transition to the many-body localized state
Mierzejewski, M.; Herbrych, J.; Prelovšek, P.
2016-12-01
Within one-dimensional disordered models of interacting fermions, we perform a numerical study of several dynamical density correlations, which can serve as hallmarks of the transition to the many-body localized state. The results confirm that density-wave correlations exhibit quite an abrupt change with increasing disorder, with a nonvanishing long-time value characteristic for the nonergodic phase. In addition, our results reveal a logarithmic variation of correlations in time in a wide time window, which we can bring in connection with the anomalous behavior of the dynamical conductivity near the transition. Our results support the view that the transition to many-body localization can be characterized by universal dynamical exponents.
Lattice methods and the nuclear few- and many-body problem
Lee, Dean
2016-01-01
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.
A many-body potential approach to modelling the thermomechanical properties of actinide oxides.
Cooper, M W D; Rushton, M J D; Grimes, R W
2014-03-12
A many-body potential model for the description of actinide oxide systems, which is robust at high temperatures, is reported for the first time. The embedded atom method is used to describe many-body interactions ensuring good reproduction of a range of thermophysical properties (lattice parameter, bulk modulus, enthalpy and specific heat) between 300 and 3000 K for AmO2, CeO2, CmO2, NpO2, ThO2, PuO2 and UO2. Additionally, the model predicts a melting point for UO2 between 3000 and 3100 K, in close agreement with experiment. Oxygen-oxygen interactions are fixed across the actinide oxide series because it facilitates the modelling of oxide solid solutions. The new potential is also used to predict the energies of Schottky and Frenkel pair disorder processes.
Non-equilibrium many-body effects in driven nonlinear resonator arrays
Grujic, T; Angelakis, D G; Jaksch, D
2012-01-01
We study the non-equilibrium behavior of optically driven dissipative coupled resonator arrays. Assuming each resonator is coupled with a two-level system via a Jaynes-Cummings interaction, we calculate the many-body steady state behavior of the system under coherent pumping and dissipation. We propose and analyze the many-body phases using experimentally accessible quantities such as the total excitation number, the emitted photon spectra and photon coherence functions for different parameter regimes. In parallel, we also compare and contrast the expected behavior of this system assuming the local nonlinearity in the cavities is generated by a generic Kerr effect rather than a Jaynes-Cummings interaction. We find that the behavior of the experimentally accessible observables produced by the two models differs for realistic regimes of interactions even when the corresponding nonlinearities are of similar strength. We analyze in detail the extra features available in the Jaynes-Cummings-Hubbard (JCH) model ori...
You, Yi-Zhuang; Qi, Xiao-Liang; Xu, Cenke
We introduce the spectrum bifurcation renormalization group (SBRG) as a generalization of the real-space renormalization group for the many-body localized (MBL) system without truncating the Hilbert space. Starting from a disordered many-body Hamiltonian in the full MBL phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local conserved quantities and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the MBL phase. In particular, we focus on the 1 d interacting Majorana chain with strong disorder, and map out its phase diagram using the entanglement entropy. The SBRG flow also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space decorated with small blackholes.
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.
Dielectric many-body effects in arrays of charged cylindrical macromolecules
Sinkovits, Daniel W.; Barros, Kipton; Dobnikar, Jure; Kandu&{Caron; C}, Matej; Naji, Ali; Podgornik, Rudolf; Luijten, Erik
2012-02-01
Nonuniform dielectric constants are a ubiquitous aspect of condensed-matter systems, but nevertheless widely ignored in simulations. Analytical work suggests that the polarization effects resulting from these inhomogeneities can produce many-body interactions that qualitatively alter the behavior of systems driven by electrostatic interactions, but such work relies on approximations. Recently, we have developed an algorithm that computes the fluctuating polarization charge at the interface between dielectric materials during a molecular dynamics simulation, without approximation. Here, we apply this approach to investigate arrays of charged cylindrical macromolecules in the presence of explicit counterions. We study the dielectric many-body effects as a function of separation, dielectric constant variation, and counterion valency. Our findings have implications for the aggregation of polyelectrolytes such as F-actin or DNA.
Many-body effects of Coulomb interaction on Landau levels in graphene
Sokolik, A. A.; Zabolotskiy, A. D.; Lozovik, Yu. E.
2017-03-01
In strong magnetic fields, massless electrons in graphene populate relativistic Landau levels with the square-root dependence of each level energy on its number and magnetic field. Interaction-induced deviations from this single-particle picture were observed in recent experiments on cyclotron resonance and magneto-Raman scattering. Previous attempts to calculate such deviations theoretically using the unscreened Coulomb interaction resulted in overestimated many-body effects. This work presents many-body calculations of cyclotron and magneto-Raman transitions in single-layer graphene in the presence of Coulomb interaction, which is statically screened in the random-phase approximation. We take into account self-energy and excitonic effects as well as Landau level mixing, and achieve good agreement of our results with the experimental data for graphene on different substrates. The important role of a self-consistent treatment of the screening is found.
Flow equation approach to one-body and many-body localization
Quito, Victor; Bhattacharjee, Paraj; Pekker, David; Refael, Gil
2014-03-01
We study one-body and many-body localization using the flow equation technique applied to spin-1/2 Hamiltonians. This technique, first introduced by Wegner, allows us to exact diagonalize interacting systems by solving a set of first-order differential equations for coupling constants. Besides, by the flow of individual operators we also compute physical properties, such as correlation and localization lengths, by looking at the flow of probability distributions of couplings in the Hilbert space. As a first example, we analyze the one-body localization problem written in terms of spins, the disordered XY model with a random transverse field. We compare the results obtained in the flow equation approach with the diagonalization in the fermionic language. For the many-body problem, we investigate the physical properties of the disordered XXZ Hamiltonian with a random transverse field in the z-direction.
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.
Partial dynamical symmetry as a selection criterion for many-body interactions
Leviatan, A; Van Isacker, P
2013-01-01
We propose the use of partial dynamical symmetry (PDS) as a selection criterion for higher-order terms in situations when a prescribed symmetry is obeyed by some states and is strongly broken in others. The procedure is demonstrated in a first systematic classification of many-body interactions with SU(3) PDS that can improve the description of deformed nuclei. As an example, the triaxial features of the nucleus 156Gd are analyzed.
Ground state spin 0$^+$ dominance of many-body systems with random interactions and related topics
Arima, A; Zhao, Y M
2003-01-01
In this talk we shall show our recent results in understanding the spin$^{\\rm parity}$ 0$^+$ ground state (0 g.s.) dominance of many-body systems. We propose a simple approach to predict the spin $I$ g.s. probabilities which does not require the diagonalization of a Hamiltonian with random interactions. Some findings related to the 0 g.s. dominance will also be discussed.
Many-body subradiant excitations in metamaterial arrays: Experiment and theory
Jenkins, Stewart D; Papasimakis, Nikitas; Savo, Salvatore; Zheludev, Nikolay I
2016-01-01
We demonstrate spatially extended subradiant excitations in planar metamaterial arrays comprising over 1000 metamolecules. By comparing the near- and far-field response in large-scale numerical simulations with those in experimental observations we identify correlated multimetamolecule subradiant states that dominate the total excitation energy. We show that spatially extended many-body subradiance can also exist in plasmonic metamaterial arrays at optical frequencies.
Integrable many-body systems of Calogero-Moser-Sutherland type in high dimension
Sheinman, O K
1995-01-01
A new series of integrable cases of the many-body problem in many-dimensional spaces is found. That series appears as a part of the larger series of integrable problems, which are in 1-1 correspondence with Krichever-Novikov algebras of affine type (that is with pairs each one consisting of some finite root system and some Riemann surface of finite genus with two marked points).
Lattice methods and the nuclear few- and many-body problem
Lee, Dean
2016-01-01
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 a...
Probing many-body states of ultracold atoms via noise correlations
Altman, Ehud; Demler, Eugene A.; Lukin, Mikhail D.
2004-01-01
We propose to utilize density-density correlations in the image of an expanding gas cloud to probe complex many-body states of trapped ultracold atoms. In particular, we show how this technique can be used to detect superfluidity of fermionic gases and to study spin correlations of multicomponent atoms in optical lattices. The feasibility of the method is investigated by analysis of the relevant signal to noise ratio including experimental imperfections.
Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems
Deng, Dong-Ling; Pixley, J. H.; Li, Xiaopeng
We investigate the statistical orthogonality catastrophe (StOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the StOC gives rise to a wave function overlap between the pre- and post-quench ground states that has an exponential decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe in metallic systems. This exponential decay arises from a statistical charge transfer process where a particle can be effectively ``transported'' to an arbitrary lattice site. We show that in a many-body localized phase, this non-local transport and the associated exponential StOC phenomenon persist in the presence of interactions. We study the possible experimental consequences of the exponential StOC on the Loschmidt echo and spectral function, establishing that this phenomenon might be observable in cold atomic experiments through Ramsey interference and radio-frequency spectroscopy. We thank S.-T. Wang, Z.-X. Gong, Y.-L. Wu, J. D. Sau, and Z. Ovadyahu for discussions. This work is supported by LPS-MPO-CMTC, JQI-NSF-PFC, and ARO-Atomtronics-MURI. The authors acknowledge the University of Maryland supercomputing resources.
Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
Lazarian, A; Takamoto, M; Pino, E M de Gouveia Dal; Cho, J
2015-01-01
Realistic astrophysical environments are turbulent due to the extremely high Reynolds numbers. Therefore, the theories of reconnection intended for describing astrophysical reconnection should not ignore the effects of turbulence on magnetic reconnection. Turbulence is known to change the nature of many physical processes dramatically and in this review we claim that magnetic reconnection is not an exception. We stress that not only astrophysical turbulence is ubiquitous, but also magnetic reconnection itself induces turbulence. Thus turbulence must be accounted for in any realistic astrophysical reconnection setup. We argue that due to the similarities of MHD turbulence in relativistic and non-relativistic cases the theory of magnetic reconnection developed for the non-relativistic case can be extended to the relativistic case and we provide numerical simulations that support this conjecture. We also provide quantitative comparisons of the theoretical predictions and results of numerical experiments, includi...
Bruce, Adam L
2015-01-01
We show the traditional rocket problem, where the ejecta velocity is assumed constant, can be reduced to an integral quadrature of which the completely non-relativistic equation of Tsiolkovsky, as well as the fully relativistic equation derived by Ackeret, are limiting cases. By expanding this quadrature in series, it is shown explicitly how relativistic corrections to the mass ratio equation as the rocket transitions from the Newtonian to the relativistic regime can be represented as products of exponential functions of the rocket velocity, ejecta velocity, and the speed of light. We find that even low order correction products approximate the traditional relativistic equation to a high accuracy in flight regimes up to $0.5c$ while retaining a clear distinction between the non-relativistic base-case and relativistic corrections. We furthermore use the results developed to consider the case where the rocket is not moving relativistically but the ejecta stream is, and where the ejecta stream is massless.
Vortex solutions in axial or chiral coupled non-relativistic spinor- Chern-Simons theory
Németh, Z A
1997-01-01
The interaction of a spin 1/2 particle (described by the non-relativistic "Dirac" equation of Lévy-Leblond) with Chern-Simons gauge fields is studied. It is shown, that similarly to the four dimensional spinor models, there is a consistent possibility of coupling them also by axial or chiral type currents. Static self dual vortex solutions together with a vortex-lattice are found with the new couplings.
Hyperfine splitting of the dressed hydrogen atom ground state in non-relativistic QED
Amour, L
2010-01-01
We consider a spin-1/2 electron and a spin-1/2 nucleus interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. For a fixed total momentum sufficiently small, we study the multiplicity of the ground state of the reduced Hamiltonian. We prove that the coupling between the spins of the charged particles and the electromagnetic field splits the degeneracy of the ground state.
Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state
Amour, Laurent
2011-01-01
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a spin-1/2 electron in the standard model of non-relativistic QED. We study the Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum. For small enough values of the fine-structure constant, we prove that the ground state is unique. This result reflects the hyperfine structure of the hydrogen atom ground state.
Quantization of Interacting Non-Relativistic Open Strings using Extended Objects
Arias, P J; Fuenmayor, E; Leal, L; Leal, Lorenzo
2005-01-01
Non-relativistic charged open strings coupled with Abelian gauge fields are quantized in a geometric representation that generalizes the Loop Representation. The model comprises open-strings interacting through a Kalb-Ramond field in four dimensions. It is shown that a consistent geometric-representation can be built using a scheme of ``surfaces and lines of Faraday'', provided that the coupling constant (the ``charge'' of the string) is quantized.
Condensation for non-relativistic matter in Hořava–Lifshitz gravity
Directory of Open Access Journals (Sweden)
Jiliang Jing
2015-10-01
Full Text Available We study condensation for non-relativistic matter in a Hořava–Lifshitz black hole without the condition of the detailed balance. We show that, for the fixed non-relativistic parameter α2 (or the detailed balance parameter ϵ, it is easier for the scalar hair to form as the parameter ϵ (or α2 becomes larger, but the condensation is not affected by the non-relativistic parameter β2. We also find that the ratio of the gap frequency in conductivity to the critical temperature decreases with the increase of ϵ and α2, but increases with the increase of β2. The ratio can reduce to the Horowitz–Roberts relation ωg/Tc≈8 obtained in the Einstein gravity and Cai's result ωg/Tc≈13 found in a Hořava–Lifshitz gravity with the condition of the detailed balance for the relativistic matter. Especially, we note that the ratio can arrive at the value of the BCS theory ωg/Tc≈3.5 by taking proper values of the parameters.
Energy Technology Data Exchange (ETDEWEB)
Hussain, S.; Mahmood, S.; Rehman, Aman-ur- [Theoretical Physics Division (TPD), PINSTECH, P.O. Nilore, Islamabad 44000, Pakistan and Pakistan Institute of Engineering and Applied Sciences (PIEAS), P.O. Nilore, Islamabad 44000 (Pakistan)
2014-11-15
Linear and nonlinear propagation of magnetosonic waves in the perpendicular direction to the ambient magnetic field is studied in dense plasmas for non-relativistic and ultra-relativistic degenerate electrons pressure. The sources of nonlinearities are the divergence of the ions and electrons fluxes, Lorentz forces on ions and electrons fluids and the plasma current density in the system. The Korteweg-de Vries equation for magnetosonic waves propagating in the perpendicular direction of the magnetic field is derived by employing reductive perturbation method for non-relativistic as well as ultra-relativistic degenerate electrons pressure cases in dense plasmas. The plots of the magnetosonic wave solitons are also shown using numerical values of the plasma parameters such a plasma density and magnetic field intensity of the white dwarfs from literature. The dependence of plasma density and magnetic field intensity on the magnetosonic wave propagation is also pointed out in dense plasmas for both non-relativistic and ultra-relativistic degenerate electrons pressure cases.
Many-body forces and stability of the alkaline-earth tetramers
Energy Technology Data Exchange (ETDEWEB)
Diaz-Torrejon, C.C. [Centro Nacional de Supercomputo, IPICyT, A.C., Camino a la Presa San Jose 2055, 78216 San Luis Potosi, SLP (Mexico); Centro de Investigacion en Materiales Avanzados, S.C., Av. Miguel de Cervantes 120, 31109 Chihuahua, Chih. (Mexico); Kaplan, Ilya G., E-mail: kaplan@iim.unam.mx [Instituto de Investigaciones en Materiales, UNAM, Apdo. Postal 70-360, 04510 Mexico D.F. (Mexico)
2011-03-18
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{sub 4}, Mg{sub 4}, and Ca{sub 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{sub b}/N in Be{sub 3} is 7 times larger and in Be{sub 4} is 18.4 times larger than in Be{sub 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: {yields} The alkaline-earths trimers and tetramers are stabilized by the three-body forces. {yields} Two- and four-body forces are repulsive for trimers and tetramers. {yields} The attractive contribution to the three-body forces has a three-atom electron exchange origin. {yields} 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{sub 4}, Mg{sub 4}, and Ca{sub 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
Calculation of local pressure tensors in systems with many-body interactions.
Heinz, Hendrik; Paul, Wolfgang; Binder, Kurt
2005-12-01
Local pressures are important in the calculation of interface tensions and in analyzing micromechanical behavior. The calculation of local pressures in computer simulations has been limited to systems with pairwise interactions between the particles, which is not sufficient for chemically detailed systems with many-body potentials such as angles and torsions. We introduce a method to calculate local pressures in systems with n-body interactions (n=2,3,4,) based on a micromechanical definition of the pressure tensor. The local pressure consists of a kinetic contribution from the linear momentum of the particles and an internal contribution from dissected many-body interactions by infinitesimal areas. To define dissection by a small area, respective n-body interactions are divided into two geometric centers, effectively reducing them to two-body interactions. Consistency with hydrodynamics-derived formulas for systems with two-body interactions [J. H. Irving and J. G. Kirkwood, J. Chem. Phys. 18, 817 (1950)], for average cross-sectional pressures [B. D. Todd, D. J. Evans, and P. J. Daivis, Phys. Rev. E 52, 1627 (1995)], and for volume averaged pressures (virial formula) is shown. As a simple numerical example, we discuss liquid propane in a cubic box. Local, cross-sectional, and volume-averaged pressures as well as relative contributions from two-body and three-body forces are analyzed with the proposed method, showing full numerical equivalence with the existing approaches. The method allows computing local pressures in the presence of many-body interactions in atomistic simulations of complex materials and biological systems.
Many-body localization and thermalization: Insights from the entanglement spectrum
Geraedts, Scott D.; Nandkishore, Rahul; Regnault, Nicolas
2016-05-01
We study the entanglement spectrum in the many-body localizing and thermalizing phases of one- and two-dimensional Hamiltonian systems and periodically driven "Floquet" systems. We focus on the level statistics of the entanglement spectrum as obtained through numerical diagonalization, finding structure beyond that revealed by more limited measures such as entanglement entropy. In the thermalizing phase the entanglement spectrum obeys level statistics governed by an appropriate random matrix ensemble. For Hamiltonian systems this can be viewed as evidence in favor of a strong version of the eigenstate thermalization hypothesis (ETH). Similar results are also obtained for Floquet systems, where they constitute a result "beyond ETH" and show that the corrections to ETH governing the Floquet entanglement spectrum have statistical properties governed by a random matrix ensemble. The particular random matrix ensemble governing the Floquet entanglement spectrum depends on the symmetries of the Floquet drive and therefore can depend on the choice of origin of time. In the many-body localized phase the entanglement spectrum is also found to show level repulsion, following a semi-Poisson distribution (in contrast to the energy spectrum, which follows a Poisson distribution). This semi-Poisson distribution is found to come mainly from states at high entanglement energies. The observed level repulsion occurs only for interacting localized phases. We also demonstrate that equivalent results can be obtained by calculating with a single typical eigenstate or by averaging over a microcanonical energy window, a surprising result in the localized phase. This discovery of new structure in the pattern of entanglement of localized and thermalizing phases may open up new lines of attack on many-body localization, thermalization, and the localization transition.
Molecular dynamics simulation of interparticle spacing and many-body effect in gold supracrystals.
Liu, X P; Ni, Y; He, L H
2016-04-01
Interparticle spacing in supracrystals is a crucial parameter for photoelectric applications as it dominates the transport rates between neighboring nanoparticles (NPs). Based on large-scale molecular dynamics simulations, we calculate interparticle spacing in alkylthiol-stabilized gold supracrystals as a function of the NP size, ligand length and external pressure. The repulsive many-body interactions in the supracrystals are also quantified by comparing the interparticle spacing with that between two individual NPs at equilibrium. Our results are consistent with available experiments, and are expected to help precise control of interparticle spacing in supracrystal devices.
Dynamical Temperature of a One- Dimensional Many-Body Systerm in the Lennard-Jones Model
Institute of Scientific and Technical Information of China (English)
刘觉平; 袁保仑
2001-01-01
A new way to derive the formula of the dynamical temperature by using the invariance of the Liouville measure and the ergodicity hypothesis is presented, based on the invariance of the functional under the transformation of the measure. The obtained dynamical temperature is intrinsic to the underlying dynamics of the system. A molecular dynamical simulation of a one-dimensional many-body system in the Lennard-Jones model has been performed. The temperature calculated from the Hamiltonian for the stationary state of the system coincides with that determined with the thermodynamical method.
Atomistic formulas for local properties in systems with many-body interactions
Hardy, Robert J.
2016-11-01
Atomistic formulas are derived for the local densities and fluxes used in the continuum description of energy and momentum transport. Two general methods for the distribution of potential energy among a system's constituent particles are presented and analyzed. The resulting formulas for the heat flux and stress tensor and the equations for energy and momentum transport are exact consequences of the definitions of the densities and the equations of classical mechanics. The formulas and equations obtained are valid for systems with very general types of many-body interactions.
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.)
Ab initio many-body calculations of the 4He photo-absorption cross section
Schuster, Micah D; Johnson, Calvin W; Jurgenson, Eric D; Navratil, Petr
2013-01-01
A major goal of nuclear theory is to make quantitative calculations of low-energy nuclear observables starting from microscopic internucleon forces. Computationally, this is complicated by the large model spaces needed to reach convergence in many-body approaches, such as the no-core shell model (NCSM). In recent years, the similarity renormalization group (SRG) has provided a powerful and versatile means to soften interactions for ab initio structure calculations, thus leading to convergence within smaller model spaces. Here we compute the 4He total photo absorption cross section and study, for the first time, the consistency of the SRG approach in a continuum observable.
Band offsets at the Si/SiO2 interface from many-body perturbation theory.
Shaltaf, R; Rignanese, G-M; Gonze, X; Giustino, Feliciano; Pasquarello, Alfredo
2008-05-09
We use many-body perturbation theory, the state-of-the-art method for band-gap calculations, to compute the band offsets at the Si/SiO2 interface. We examine the adequacy of the usual approximations in this context. We show that (i) the separate treatment of band structure and potential lineup contributions, the latter being evaluated within density-functional theory, is justified, (ii) most plasmon-pole models lead to inaccuracies in the absolute quasiparticle corrections, (iii) vertex corrections can be neglected, and (iv) eigenenergy self-consistency is adequate. Our theoretical offsets agree with the experimental ones within 0.3 eV.
Bäcklund transformations for many-body systems related to KdV
Hone, A N W; Ragnisco, O
1999-01-01
We present Backlund transformations (BTs) with parameter for certain classical integrable n-body systems, namely the many-body generalised Henon-Heiles, Garnier and Neumann systems. Our construction makes use of the fact that all these systems may be obtained as particular reductions (stationary or restricted flows) of the KdV hierarchy; alternatively they may be considered as examples of the reduced sl(2) Gaudin magnet. The BTs provide exact time-discretizations of the original (continuous) systems, preserving the Lax matrix and hence all integrals of motion, and satisfy the spectrality property with respect to the Backlund parameter.
Center-of-mass corrections revisited a many-body expansion approach
Mihaila, B; Mihaila, Bogdan; Heisenberg, Jochen H.
1999-01-01
A many-body expansion for the computation of the charge form factor in the center-of-mass system is proposed. For convergence testing purposes, we apply our formalism to the case of the harmonic oscillator shell model, where an exact solution exists. We also work out the details of the calculation involving realistic nuclear wave functions. Results obtained for the Argonne $v$18 two-nucleon and Urbana-IX three-nucleon interactions are reported. No corrections due to the meson-exchange charge density are taken into account.
Center-of-mass corrections reexamined: A many-body expansion approach
Mihaila, Bogdan; Heisenberg, Jochen H.
1999-11-01
A many-body expansion for the computation of the charge form factor in the center-of-mass system is proposed. For convergence testing purposes, we apply our formalism to the case of the harmonic oscillator shell model, where an exact solution exists. We also work out the details of the calculation involving realistic nuclear wave functions. Results obtained for the Argonne v18 two-nucleon and Urbana-IX three-nucleon interactions are reported. No corrections due to the meson-exchange charge density are taken into account.
Many-body effects in doped graphene on a piezoelectric substrate
González, David G.; Zapata, Ivar; Schiefele, Jürgen; Sols, Fernando; Guinea, Francisco
2017-09-01
We investigate the many-body properties of graphene on top of a piezoelectric substrate, focusing on the interaction between graphene electrons and piezoelectric acoustic phonons. We calculate the electron and phonon self-energies as well as the electron mobility limited by the substrate phonons. We emphasize the importance of proper screening of the electron-phonon vertex, and we discuss the various limiting behaviors as a function of electron energy, temperature, and doping level. The effect of piezoelectric acoustic phonons on graphene electrons is compared with that of intrinsic deformation acoustic phonons. Substrate phonons tend to dominate over intrinsic ones for low doping levels at high and low temperatures.
Many-body electronic structure calculations of Eu-doped ZnO
Lorke, M.; Frauenheim, T.; da Rosa, A. L.
2016-03-01
The formation energies and electronic structure of europium-doped zinc oxide has been determined using DFT and many-body G W methods. In the absence of intrisic defects, we find that the europium-f states are located in the ZnO band gap with europium possessing a formal charge of 2+. On the other hand, the presence of intrinsic defects in ZnO allows intraband f -f transitions otherwise forbidden in atomic europium. This result corroborates with recently observed photoluminescence in the visible red region S. Geburt et al. [Nano Lett. 14, 4523 (2014), 10.1021/nl5015553].
Absence of full many-body localization in the disordered Hubbard chain
Prelovšek, P.; Barišić, O. S.; Žnidarič, M.
2016-12-01
We present numerical results within the one-dimensional disordered Hubbard model for several characteristic indicators of the many-body localization (MBL). Considering traditionally studied charge disorder (i.e., the same disorder strength for both spin orientations) we find that even at strong disorder all signatures consistently show that while charge degree of freedom is nonergodic, the spin is delocalized and ergodic. This indicates the absence of the full MBL in the model that has been simulated in recent cold-atom experiments. Full localization can be restored if spin-dependent disorder is used instead.
Electro-optic and Many-body Effects on Optical Absorption of Twisted Bilayer Graphene
Lee, Kan-Heng; Huang, Lujie; Kim, Cheol-Joo; Park, Jiwoong
2015-03-01
In twisted bilayer graphene (tBLG), the interlayer rotation angle between the two graphene layers induces additional angle-dependent van Hove singularities (vHSs) in its band structure where the two Dirac cones from each layer intersect. These vHSs introduce extra angle-dependent absorption peaks in the optical absorption spectra of tBLG. Here, we experimentally investigate the effects of the overall doping and the interlayer potential on these interlayer absorption features at various angles. We independently tune the doping concentration of each layer with a newly-developed, optically transparent, dual-gate transistor geometry to perform simultaneous optical and electrical measurements. Our data show strong electro-optic phenomena in the optical absorption of tBLG: the peak energy and width of the interlayer resonance feature sensitively depends on the overall doping and interlayer potential. We explain our observation using a simple band picture as well as many-body effects. Our study provides a powerful experimental platform for studying more complicated structures such as rotated tri- and multi-layer graphene systems in the future. Moreover, the understanding of electro-optic and many-body effects in these materials opens up a way for novel electrochromic devices.
Regularities of many-body systems interacting by a two-body random ensemble
Energy Technology Data Exchange (ETDEWEB)
Zhao, Y.M. [Department of Physics, Shanghai Jiao-Tong University, Shanghai 200030 (China) and Cyclotron Center, Institute of Physical and Chemical Research - RIKEN, Hirosawa 2-1, Wako-shi, Saitama 351-0198 (Japan) and Department of Physics, Southeast University, Nanjing 210018 (China)]. E-mail: ymzhao@riken.jp; Arima, A. [Science Museum, Japan Science Foundation, 2-1 Kitanomaru-Koen, Chiyodaku, Tokyo 102-0091 (Japan); Yoshinaga, N. [Department of Physics, Saitama University, Saitama 338-0625 (Japan)
2004-10-01
The ground states of all even-even nuclei have angular momentum, I, equal to zero, I=0, and positive parity, {pi}=+. This feature was believed to be a consequence of the attractive short-range interaction between nucleons. However, in the presence of two-body random interactions, the predominance of I{pi}=0+ ground states (0 g.s.) was found to be robust both for bosons and for an even number of fermions. For simple systems, such as d bosons, sp bosons, sd bosons, and a few fermions in single-j shells for small j, there are a few approaches to predict and/or explain spin I ground state (I g.s.) probabilities. An empirical approach to predict I g.s. probabilities is available for general cases, such as fermions in a single-j (j>72) or many-j shells and various boson systems, but a more fundamental understanding of the robustness of 0 g.s. dominance is still out of reach. Further interesting results are also reviewed concerning other robust phenomena of many-body systems in the presence of random two-body interactions, such as the odd-even staggering of binding energies, generic collectivity, the behavior of average energies, correlations, and regularities of many-body systems interacting by a displaced two-body random ensemble.
Calibration of the Many-Body Dispersion Range-Separation Parameter
Markovich, Thomas; Rappoport, Dmitrij; Kim, Dasol; Aspuru-Guzik, Alán
2016-01-01
Recent work has shown that a fully many-body treatment of noncovalent interactions, such as that given by the method of many-body dispersion (MBD), is vital to accurately modeling the structure and energetics of many molecular systems with density functional theory (DFT). To avoid double counting the correlation contributions of DFT and the MBD correction, a single-parameter range-separation scheme is typically employed. Coupling the MBD correction to a given exchange-correlation functional therefore requires calibrating the range-separation parameter. We perform this calibration for 24 popular DFT functionals by optimizing against the S66x8 benchmark set. Additionally, we report a linear equation that predicts near optimal range-separation parameters, dependent only on the class of the exchange functional and the value of the gradient enhancement factor. When a calibrated MBD correction is employed, most of the exchange-correlation functionals considered are capable of achieving agreement with CCSD(T)/CBS in...
Signatures of many-body localization in the dynamics of two-site entanglement
Iemini, Fernando; Russomanno, Angelo; Rossini, Davide; Scardicchio, Antonello; Fazio, Rosario
2016-12-01
We are able to detect clear signatures of dephasing—a distinct trait of many-body localization (MBL)—via the dynamics of two-site entanglement, quantified through the concurrence. Using the protocol implemented by M. Schreiber et al. [Science 349, 842 (2015), 10.1126/science.aaa7432], we show that in the MBL phase the average two-site entanglement decays in time as a power law, while in the Anderson localized phase it tends to a plateau. The power-law exponent is not universal and displays a clear dependence on the interaction strength. This behavior is also qualitatively different from the ergodic phase, where the two-site entanglement decays exponentially. All the results are obtained by means of time-dependent density matrix renormalization-group simulations and further corroborated by analytical calculations on an effective model. Two-site entanglement has been measured in cold atoms: our analysis paves the way for the first direct experimental test of many-body dephasing in the MBL phase.
Finite-temperature second-order many-body perturbation theory revisited
Santra, Robin
2016-01-01
We present an algebraic, nondiagrammatic derivation of finite-temperature second-order many-body perturbation theory [FT-MBPT(2)], using techniques and concepts accessible to theoretical chemical physicists. We give explicit expressions not just for the grand potential but particularly for the mean energy of an interacting many-electron system. The framework presented is suitable for computing the energy of a finite or infinite system in contact with a heat and particle bath at finite temperature and chemical potential. FT-MBPT(2) may be applied if the system, at zero temperature, may be described using standard (i.e., zero-temperature) second-order many-body perturbation theory [ZT-MBPT(2)] for the energy. We point out that in such a situation, FT-MBPT(2) reproduces, in the zero-temperature limit, the energy computed within ZT-MBPT(2). In other words, the difficulty that has been referred to as the Kohn--Luttinger conundrum, does not occur. We comment, in this context, on a "renormalization" scheme recently ...
Many-body approach to proton emission and the role of spectroscopic factors
Al-Khalili, J S; Escher, J; Jennings, B K; Sparenberg, J M; Al-Khalili, Jim; Barbieri, Carlo; Escher, Jutta; Jennings, Byron K.; Sparenberg, Jean-Marc
2003-01-01
The process of proton emission from nuclei is studied by utilizing the two-potential approach of Gurvitz and Kalbermann in the context of the full many-body problem. A time-dependent approach is used for calculating the decay width. Starting from an initial many-body quasi-stationary state, we employ the Feshbach projection operator approach and reduce the formalism to an effective one-body problem. We show that the decay width can be expressed in terms of a one-body matrix element multiplied by a normalization factor. We demonstrate that the traditional interpretation of this normalization as the square root of a spectroscopic factor is only valid for one particular choice of projection operator. This causes no problem for the calculation of the decay width in a consistent microscopic approach, but it leads to ambiguities in the interpretation of experimental results. In particular, spectroscopic factors extracted from a comparison of the measured decay width with a calculated single-particle width may be af...
A Relativistic Many-Body Analysis of the Electric Dipole Moment of $^{223}$Rn
Sahoo, B K; Das, B P
2014-01-01
We report the results of our {\\it ab initio} relativistic many-body calculations of the electric dipole moment (EDM) $d_A$ arising from the electron-nucleus tensor-pseudotensor (T-PT) interaction, the interaction of the nuclear Schiff moment (NSM) with the atomic electrons and the electric dipole polarizability $\\alpha_d$ for $^{223}$Rn. Our relativistic random-phase approximation (RPA) results are substantially larger than those of lower-order relativistic many-body perturbation theory (MBPT) and the results based on the relativistic coupled-cluster (RCC) method with single and double excitations (CCSD) are the most accurate to date for all the three properties that we have considered. We obtain $d_A = 4.85(6) \\times 10^{-20} C_T \\ |e| \\ cm$ from T-PT interaction, $d_A=2.89(4) \\times 10^{-17} {S/(|e|\\ fm^3)}$ from NSM interaction and $\\alpha_d=35.27(9) \\ ea_0^3$. The former two results in combination with the measured value of $^{223}$Rn EDM, when it becomes available, could yield the best limits for the T-...
Long-range interacting many-body systems with alkaline-earth-metal atoms
Olmos, B; Singh, Y; Schreck, F; Bongs, K; Lesanovsky, I
2012-01-01
Alkaline-earth-metal atoms exhibit long-range dipolar interactions, which are generated via the coherent exchange of photons on the 3P_0-3D_1-transition of the triplet manifold. In case of bosonic strontium, which we discuss here, this transition has a wavelength of 2.7 \\mu m and a dipole moment of 2.46 Debye, and there exists a magic wavelength permitting the creation of optical lattices that are identical for the states 3P_0 and 3D_1. This interaction enables the realization and study of mixtures of hard-core lattice bosons featuring long-range hopping, with tuneable disorder and anisotropy. We derive the many-body Master equation, investigate the dynamics of excitation transport and analyze spectroscopic signatures stemming from coherent long-range interactions and collective dissipation. Our results show that lattice gases of alkaline-earth-metal atoms permit the creation of long-lived collective atomic states and constitute a simple and versatile platform for the exploration of many-body systems with lon...
Many-body expansion of the Fock matrix in the fragment molecular orbital method
Fedorov, Dmitri G.; Kitaura, Kazuo
2017-09-01
A many-body expansion of the Fock matrix in the fragment molecular orbital method is derived up to three-body terms for restricted Hartree-Fock and density functional theory in the atomic orbital basis and compared to the expansion in the basis of fragment molecular orbitals (MOs). The physical nature of many-body corrections is revealed in terms of charge transfer terms. An improvement of the fragment MO expansion is proposed by adding exchange to the embedding. The accuracy of all developed methods is demonstrated in comparison to unfragmented results for polyalanines, a water cluster, Trp-cage (PDB: 1L2Y) and crambin (PDB: 1CRN) proteins, a zeolite cluster, a Si nano-wire, and a boron nitride ribbon. The physical nature of metallicity is discussed, and it is shown what kinds of metallic systems can be treated by fragment-based methods. The density of states is calculated for a fully closed and a partially open nano-ring of boron nitride with a diameter of 105 nm.
Aromatic molecules on low-index coinage metal surfaces: Many-body dispersion effects
Jiang, Yingda; Yang, Sha; Li, Shuang; Liu, Wei
2016-12-01
Understanding the binding mechanism for aromatic molecules on transition-metal surfaces in atomic scale is a major challenge in designing functional interfaces for to (opto)electronic devices. Here, we employ the state-of-the-art many-body dispersion (MBD) approach, coupled with density functional theory methods, to study the interactions of benzene with low-index coinage metal surfaces. The many-body effects contribute mostly to the (111) surface, and leastly to the (110) surface. This corresponds to the same sequence of planar atomic density of face-centered-cubic lattices, i.e., (111) > (100) > (110). The binding energy for benzene/Au(110) is even stronger than that for benzene/Ag(110), due to a larger broadening of molecular orbitals in the former case. On the other hand, our calculations show almost identical binding energies for benzene on Ag(111) and Au(111), which contradicts the classic d-band center theory that could well predict the trend in chemisorption energies for various small molecules on a number of metal surfaces. Our results provide important insight into the benchmark adsorption systems with opener surfaces, which could help in designing more complex functional interfaces.
Theory of the Many-Body Localization Transition in One-Dimensional Systems
Directory of Open Access Journals (Sweden)
Ronen Vosk
2015-09-01
Full Text Available We formulate a theory of the many-body localization transition based on a novel real-space renormalization group (RG approach. The results of this theory are corroborated and intuitively explained with a phenomenological effective description of the critical point and of the “badly conducting” state found near the critical point on the delocalized side. The theory leads to the following sharp predictions: (i The delocalized state established near the transition is a Griffiths phase, which exhibits subdiffusive transport of conserved quantities and sub-ballistic spreading of entanglement. The anomalous diffusion exponent α<1/2 vanishes continuously at the critical point. The system does thermalize in this Griffiths phase. (ii The many-body localization transition is controlled by a new kind of infinite-randomness RG fixed point, where the broadly distributed scaling variable is closely related to the eigenstate entanglement entropy. Dynamically, the entanglement grows as ∼logt at the critical point, as it does in the localized phase. (iii In the vicinity of the critical point, the ratio of the entanglement entropy to the thermal entropy and its variance (and, in fact, all moments are scaling functions of L/ξ, where L is the length of the system and ξ is the correlation length, which has a power-law divergence at the critical point.
Many-body localization in one dimension as a dynamical renormalization group fixed point.
Vosk, Ronen; Altman, Ehud
2013-02-08
We formulate a dynamical real space renormalization group (RG) approach to describe the time evolution of a random spin-1/2 chain, or interacting fermions, initialized in a state with fixed particle positions. Within this approach we identify a many-body localized state of the chain as a dynamical infinite randomness fixed point. Near this fixed point our method becomes asymptotically exact, allowing analytic calculation of time dependent quantities. In particular, we explain the striking universal features in the growth of the entanglement seen in recent numerical simulations: unbounded logarithmic growth delayed by a time inversely proportional to the interaction strength. This is in striking contrast to the much slower entropy growth as loglogt found for noninteracting fermions with bond disorder. Nonetheless, even the interacting system does not thermalize in the long time limit. We attribute this to an infinite set of approximate integrals of motion revealed in the course of the RG flow, which become asymptotically exact conservation laws at the fixed point. Hence we identify the many-body localized state with an emergent generalized Gibbs ensemble.
Griffiths effects and slow dynamics in nearly many-body localized systems
Gopalakrishnan, Sarang; Agarwal, Kartiek; Demler, Eugene A.; Huse, David A.; Knap, Michael
2016-04-01
The low-frequency response of systems near a many-body localization transition can be dominated by rare regions that are locally critical or "in the other phase." It is known that in one dimension, these rare regions can cause the dc conductivity and diffusion constant to vanish even inside the delocalized thermal phase. Here, we present a general analysis of such Griffiths effects in the thermal phase near the many-body localization transition: we consider both one-dimensional and higher-dimensional systems, subject to quenched randomness, and discuss both linear response (including the frequency- and wave-vector-dependent conductivity) and more general dynamics. In all the regimes we consider, we identify observables that are dominated by rare-region effects. In some cases (one-dimensional systems and Floquet systems with no extensive conserved quantities), essentially all long-time local observables are dominated by rare-region effects; in others, generic observables are instead dominated by hydrodynamic long-time tails throughout the thermal phase, and one must look at specific probes, such as spin echo, to see Griffiths behavior.
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.
Code C# for chaos analysis of relativistic many-body systems with reactions
Grossu, I. V.; Besliu, C.; Jipa, Al.; Stan, E.; Esanu, T.; Felea, D.; Bordeianu, C. C.
2012-04-01
In this work we present a reaction module for “Chaos Many-Body Engine” (Grossu et al., 2010 [1]). Following our goal of creating a customizable, object oriented code library, the list of all possible reactions, including the corresponding properties (particle types, probability, cross section, particle lifetime, etc.), could be supplied as parameter, using a specific XML input file. Inspired by the Poincaré section, we propose also the “Clusterization Map”, as a new intuitive analysis method of many-body systems. For exemplification, we implemented a numerical toy-model for nuclear relativistic collisions at 4.5 A GeV/c (the SKM200 Collaboration). An encouraging agreement with experimental data was obtained for momentum, energy, rapidity, and angular π distributions. Catalogue identifier: AEGH_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGH_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 184 628 No. of bytes in distributed program, including test data, etc.: 7 905 425 Distribution format: tar.gz Programming language: Visual C#.NET 2005 Computer: PC Operating system: Net Framework 2.0 running on MS Windows Has the code been vectorized or parallelized?: Each many-body system is simulated on a separate execution thread. One processor used for each many-body system. RAM: 128 Megabytes Classification: 6.2, 6.5 Catalogue identifier of previous version: AEGH_v1_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 1464 External routines: Net Framework 2.0 Library Does the new version supersede the previous version?: Yes Nature of problem: Chaos analysis of three-dimensional, relativistic many-body systems with reactions. Solution method: Second order Runge-Kutta algorithm for simulating relativistic many-body systems with reactions
Scale-adaptive tensor algebra for local many-body methods of electronic structure theory
Energy Technology Data Exchange (ETDEWEB)
Liakh, Dmitry I [ORNL
2014-01-01
While the formalism of multiresolution analysis (MRA), based on wavelets and adaptive integral representations of operators, is actively progressing in electronic structure theory (mostly on the independent-particle level and, recently, second-order perturbation theory), the concepts of multiresolution and adaptivity can also be utilized within the traditional formulation of correlated (many-particle) theory which is based on second quantization and the corresponding (generally nonorthogonal) tensor algebra. In this paper, we present a formalism called scale-adaptive tensor algebra (SATA) which exploits an adaptive representation of tensors of many-body operators via the local adjustment of the basis set quality. Given a series of locally supported fragment bases of a progressively lower quality, we formulate the explicit rules for tensor algebra operations dealing with adaptively resolved tensor operands. The formalism suggested is expected to enhance the applicability and reliability of local correlated many-body methods of electronic structure theory, especially those directly based on atomic orbitals (or any other localized basis functions).
Relativistic many-body analysis of the electric dipole moment of 223Rn
Sahoo, B. K.; Singh, Yashpal; Das, B. P.
2014-11-01
We report the results of our ab initio relativistic many-body calculations of the electric dipole moment (EDM) dA arising from the electron-nucleus tensor-pseudotensor (T-PT) interaction, the interaction of the nuclear Schiff moment (NSM) with the atomic electrons and the electric dipole polarizability αd for 223Rn . Our relativistic random-phase approximation results are substantially larger than those of lower-order relativistic many-body perturbation theory and the results based on the relativistic coupled-cluster method with single and double excitations are highly accurate for all three properties that we have considered. We obtain dA=4.85 (6 ) ×10-20 CT|e | cm from T-PT interaction, dA=2.89 (4 ) ×10-17S /(|e |fm3) from NSM interaction, and αd=35.27 (9 ) e a03 . The former two results in combination with the measured value of 223Rn EDM, when it becomes available, could yield the best limits for the T-PT coupling constant, EDMs, and chromo-EDMs of quarks and θQCD parameter, and would thereby shed light on leptoquark and supersymmetric models that predict C P violation.
Energy Technology Data Exchange (ETDEWEB)
Sahu, Biswajit, E-mail: biswajit-sahu@yahoo.co.in [Department of Mathematics, West Bengal State University, Barasat, Kolkata 700126 (India); Sinha, Anjana, E-mail: sinha.anjana@gmail.com [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Roychoudhury, Rajkumar, E-mail: rroychoudhury123@gmail.com [Department of Mathematics, Visva-Bharati, Santiniketan - 731 204, India and Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700 075 (India)
2015-09-15
A numerical study is presented of the nonlinear dynamics of a magnetized, cold, non-relativistic plasma, in the presence of electron-ion collisions. The ions are considered to be immobile while the electrons move with non-relativistic velocities. The primary interest is to study the effects of the collision parameter, external magnetic field strength, and the initial electromagnetic polarization on the evolution of the plasma system.
2016-06-03
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Understanding the many-body expansion for large systems. II. Accuracy considerations
Lao, Ka Un; Liu, Kuan-Yu; Richard, Ryan M.; Herbert, John M.
2016-04-01
To complement our study of the role of finite precision in electronic structure calculations based on a truncated many-body expansion (MBE, or "n-body expansion"), we examine the accuracy of such methods in the present work. Accuracy may be defined either with respect to a supersystem calculation computed at the same level of theory as the n-body calculations, or alternatively with respect to high-quality benchmarks. Both metrics are considered here. In applications to a sequence of water clusters, (H2O)N=6-55 described at the B3LYP/cc-pVDZ level, we obtain mean absolute errors (MAEs) per H2O monomer of ˜1.0 kcal/mol for two-body expansions, where the benchmark is a B3LYP/cc-pVDZ calculation on the entire cluster. Three- and four-body expansions exhibit MAEs of 0.5 and 0.1 kcal/mol/monomer, respectively, without resort to charge embedding. A generalized many-body expansion truncated at two-body terms [GMBE(2)], using 3-4 H2O molecules per fragment, outperforms all of these methods and affords a MAE of ˜0.02 kcal/mol/monomer, also without charge embedding. GMBE(2) requires significantly fewer (although somewhat larger) subsystem calculations as compared to MBE(4), reducing problems associated with floating-point roundoff errors. When compared to high-quality benchmarks, we find that error cancellation often plays a critical role in the success of MBE(n) calculations, even at the four-body level, as basis-set superposition error can compensate for higher-order polarization interactions. A many-body counterpoise correction is introduced for the GMBE, and its two-body truncation [GMBCP(2)] is found to afford good results without error cancellation. Together with a method such as ωB97X-V/aug-cc-pVTZ that can describe both covalent and non-covalent interactions, the GMBE(2)+GMBCP(2) approach provides an accurate, stable, and tractable approach for large systems.
Krishtal, Alisa; Sinha, Debalina; Genova, Alessandro; Pavanello, Michele
2015-05-01
Subsystem density-functional theory (DFT) is an emerging technique for calculating the electronic structure of complex molecular and condensed phase systems. In this topical review, we focus on some recent advances in this field related to the computation of condensed phase systems, their excited states, and the evaluation of many-body interactions between the subsystems. As subsystem DFT is in principle an exact theory, any advance in this field can have a dual role. One is the possible applicability of a resulting method in practical calculations. The other is the possibility of shedding light on some quantum-mechanical phenomenon which is more easily treated by subdividing a supersystem into subsystems. An example of the latter is many-body interactions. In the discussion, we present some recent work from our research group as well as some new results, casting them in the current state-of-the-art in this review as comprehensively as possible.
Ripoche, J.; Lacroix, D.; Gambacurta, D.; Ebran, J.-P.; Duguet, T.
2017-01-01
Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei. In their best current level of implementation, their accuracy is of the order of a few percent error on the ground-state correlation energy. Recently implemented variants of these methods are operating a breakthrough in the description of medium-mass open-shell nuclei at a polynomial computational cost while putting state-of-the-art models of internucleon interactions to the test. Purpose: As progress in the design of internucleon interactions is made, and as questions one wishes to answer are refined in connection with increasingly available experimental data, further efforts must be made to tailor many-body methods that can reach an even higher precision for an even larger number of observable quantum states or nuclei. The objective of the present work is to contribute to such a quest by designing and testing a new many-body scheme. Methods: We formulate a truncated configuration-interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N -body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two- and four-quasiparticle excitations. Furthermore, the extent by which the underlying BCS state breaks U(1 ) symmetry is optimized in the presence of the projected two- and four-quasiparticle excitations. This constitutes an extension of the so-called restricted variation after projection method in use within the frame of multireference energy density functional calculations. The quality of the newly designed method is tested against exact solutions of the so-called attractive pairing Hamiltonian problem. Results: By construction, the method reproduces exact results for N =2 and N =4 . For N =(8 ,16 ,20 ) , the error in the ground-state correlation energy is less than (0.006%, 0.1%, 0.15%) across the entire range of
Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics
Freeman, Walter J
2008-01-01
Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body physics by using tools that physicists have devised to analyze comparable hierarchies in other fields of science. We focus on a mesoscopic level that offers a multi-step pathway between the microscopic functions of neurons and the macroscopic functions of brain systems revealed by hemodynamic imaging. We use electroencephalographic (EEG) records collected from high-density electrode arrays fixed on the epidural surfaces of primary sensory and limbic areas in rabbits and cats trained to discriminate conditioned stimuli (CS) in the various modalities. High temporal resolution of EEG signals with the Hilbert transform gives evidence for diverse intermittent spatial patterns of amplitude (AM) and phase modulations (PM) of carrier waves that repeatedly re-synchronize in the beta and g...
Regularizing the molecular potential in electronic structure calculations. II. Many-body methods
Energy Technology Data Exchange (ETDEWEB)
Bischoff, Florian A., E-mail: florian.bischoff@hu-berlin.de [Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin (Germany)
2014-11-14
In Paper I of this series [F. A. Bischoff, “Regularizing the molecular potential in electronic structure calculations. I. SCF methods,” J. Chem. Phys. 141, 184105 (2014)] a regularized molecular Hamilton operator for electronic structure calculations was derived and its properties in SCF calculations were studied. The regularization was achieved using a correlation factor that models the electron-nuclear cusp. In the present study we extend the regularization to correlated methods, in particular the exact solution of the two-electron problem, as well as second-order many body perturbation theory. The nuclear and electronic correlation factors lead to computations with a smaller memory footprint because the singularities are removed from the working equations, which allows coarser grid resolution while maintaining the precision. Numerical examples are given.
Interaction-Induced Characteristic Length in Strongly Many-Body Localized Systems
He, Rong-Qiang
2016-01-01
We propose a numerical method for explicitly constructing a complete set of local integrals of motion (LIOM) and definitely show the existence of LIOM for strongly many-body localized systems. The method starts with a complete set of maximally localized guessed LIOM, gradually deforms it into a complete set of true LIOM. By using this method we find that for strongly disordered and weakly interacting systems, there are two characteristic lengths in the LIOM. The first one is governed by disorder and is of Anderson-localization nature. The second one is induced by interaction but independent of the strength of interaction, showing a nonperturbative nature. We prove that the entanglement and correlation in any eigenstate extend not longer than twice the second length.
On the construction of a new solvable model and validity of many-body approximation methods
Zettili, Nouredine; Villars, Felix M. H.
1987-07-01
This work deals both with the construction of a new analytically solvable model and with the quantitative test of the time-dependent Hartree-Fock (TDHF) method. First, we construct a new analytically solvable model, which serves as a testing ground for the various many-body approximation methods. The construction is based on two vector operators that are the generators of a Lie algebra. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. The model has a simple analytic energy spectrum. Second, we use this model to test the validity of the TDHF approximation. Exact eigenvalues are compared with the corresponding solutions of the TDHF method. The TDHF approximation is shown to be reasonably accurate in the description of the system's eigenstates.
On the construction of a new solvable model and validity of many-body approximation methods
Energy Technology Data Exchange (ETDEWEB)
Zettili, N.; Villars, F.M.H.
1987-07-20
This work deals both with the construction of a new analytically solvable model and with the quantitative test of the time-dependent Hartree-Fock (TDHF) method. First, we construct a new analytically solvable model, which serves as a testing ground for the various many-body approximation methods. The construction is based on two vector operators that are the generators of a Lie algebra. The model consists of a one-dimensional system of two distinguishable sets of fermions interacting via a schematic two-body force. The model has a simple analytic energy spectrum. Second, we use this model to test the validity of the TDHF approximation. Exact eigenvalues are compared with the corresponding solutions of the TDHF method. The TDHF approximation is shown to be reasonably accurate in the description of the system's eigenstates.
A charge optimized many-body potential for titanium nitride (TiN).
Cheng, Y-T; Liang, T; Martinez, J A; Phillpot, S R; Sinnott, S B
2014-07-01
This work presents a new empirical, variable charge potential for TiN systems in the charge-optimized many-body potential framework. The potential parameters were determined by fitting them to experimental data for the enthalpy of formation, lattice parameters, and elastic constants of rocksalt structured TiN. The potential does a good job of describing the fundamental physical properties (defect formation and surface energies) of TiN relative to the predictions of first-principles calculations. This potential is used in classical molecular dynamics simulations to examine the interface of fcc-Ti(0 0 1)/TiN(0 0 1) and to characterize the adsorption of oxygen atoms and molecules on the TiN(0 0 1) surface. The results indicate that the potential is well suited to model TiN thin films and to explore the chemistry associated with their oxidation.
Periodically driven interacting electrons in one dimension: Many-body Floquet approach
Puviani, M.; Manghi, F.
2016-10-01
We propose a method to study the time evolution of correlated electrons driven by a harmonic perturbation. Combining Floquet formalism to include the time-dependent field and cluster perturbation theory to solve the many-body problem in the presence of short-range correlations, we treat the electron double dressing, by photons and by e -e interactions, on the same footing. We apply the method to an extended Hubbard chain at half occupation, and we show that in the regime of small field frequency and for given values of field strength, the zero-mode Floquet band is no longer gapped and the system recovers a metallic state. Our results are indicative of an omnipresent mechanism for insulator-to-metal transitions in one-dimensional systems.
How Many-Body Correlations and α Clustering Shape 6He
Romero-Redondo, Carolina; Quaglioni, Sofia; Navrátil, Petr; Hupin, Guillaume
2016-11-01
The Borromean 6He nucleus is an exotic system characterized by two halo neutrons orbiting around a compact 4He (or α ) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for ab initio theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with 4He +n +n cluster degrees of freedom largely solves this issue. We analyze the role played by α clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.
How many-body correlations and $\\alpha$-clustering shape $^6$He
Romero-Redondo, Carolina; Navratil, Petr; Hupin, Guillaume
2016-01-01
The Borromean $^6$He nucleus is an exotic system characterized by two `halo' neutrons orbiting around a compact $^4$He (or $\\alpha$) core, in which the binary subsystems are unbound. The simultaneous reproduction of its small binding energy and extended matter and point-proton radii has been a challenge for {\\em ab initio} theoretical calculations based on traditional bound-state methods. Using soft nucleon-nucleon interactions based on chiral effective field theory potentials, we show that supplementing the model space with $^4$He+$n$+$n$ cluster degrees of freedom largely solves this issue. We analyze the role played by the $\\alpha$-clustering and many-body correlations, and study the dependence of the energy spectrum on the resolution scale of the interaction.
Many-Body Coarse-Grained Interactions using Gaussian Approximation Potentials
John, S T
2016-01-01
This thesis introduces a framework that is able to describe general many-body coarse-grained interactions. We make use of this to describe the free energy surface as a cluster expansion in terms of monomer, dimer, and trimer terms. The contributions to the free energy due to these terms are inferred from MD results of the underlying all-atom model using Gaussian Approximation Potentials, a type of machine-learning potential based on Gaussian process regression. This provides CG interactions that are much more accurate than is possible with site-based pair potentials. While slower than these, it can still be faster than all-atom simulations for solvent-free CG models of systems with a large amount of solvent, as is common in biomolecular simulations.
Many-body correlations in Semiclassical Molecular Dynamics and Skyrme interaction
Papa, Massimo
2012-01-01
Constraint Molecular dynamics CoMD calculations have been performed for asymmetric nuclear matter (NM) by using a simple effective interactions of the Skyrme type. The set of parameter values reproducing common accepted saturation properties of nuclear matter have been obtained for different degree of stiffness characterizing the iso-vectorial potential density dependence. A comparison with results obtained in the limit of the Semi-Classical Mean Field approximation using the same kind of interaction put in evidence the role played by the many-body correlations in to explain the noticeable differences obtained in the parameter values in the two cases. Even if from a numerical point of view the obtained results are strictly valid for the CoMD model, some rather general feature of the discussed correlations can give a wider meaning to the obtained differences being strongly related to the spacial correlations generated in the semiclassical wave packets dynamics.
An approximate many-body calculation for trapped bosons with attractive interaction
Energy Technology Data Exchange (ETDEWEB)
Kundu, Anasuya [Department of Physics, University of Calcutta, 92 A P C Road, Calcutta-700 009 (India); Chakrabarti, Barnali [Department of Physics, Lady Brabourne College, P1/2 Surawardi Avenue, Calcutta-700 017 (India); Das, Tapan Kumar [Department of Physics, University of Calcutta, 92 A P C Road, Calcutta-700 009 (India); Canut, Sylvio [Instituto de Fisica, Universidade de Sao Paulo, CP 66318, 05315-970, Sao Paulo, SP (Brazil)
2007-06-28
The stability of trapped interacting bosons with attractive interactions is studied using an approximate many-body calculation. Instead of using the traditional hyperspherical harmonics expansion method we prescribe a potential harmonics expansion method (PHEM). The justification of the use of PHEM in connection with dilute condensates is presented. The choice of a correlation function is justified as it correctly reproduces the short-range two-body correlation in the wavefunction as also the correct value of the s-wave scattering length (a{sub s}). Applications to {sup 7}Li and {sup 85}Rb condensates with the realistic van der Waals interaction give good agreement with the Rice and JILA experiments, respectively. The JILA experiment used controlled collapse of the {sup 85}Rb condensate for different values of a{sub s}. Our calculations agree with the experimental results within the experimental error bars.
Charge-Transfer Excited States in Aqueous DNA: Insights from Many-Body Green's Function Theory
Yin, Huabing; Ma, Yuchen; Mu, Jinglin; Liu, Chengbu; Rohlfing, Michael
2014-06-01
Charge-transfer (CT) excited states play an important role in the excited-state dynamics of DNA in aqueous solution. However, there is still much controversy on their energies. By ab initio many-body Green's function theory, together with classical molecular dynamics simulations, we confirm the existence of CT states at the lower energy side of the optical absorption maximum in aqueous DNA as observed in experiments. We find that the hydration shell can exert strong effects (˜1 eV) on both the electronic structure and CT states of DNA molecules through dipole electric fields. In this case, the solvent cannot be simply regarded as a macroscopic screening medium as usual. The influence of base stacking and base pairing on the CT states is also discussed.
Zhang, Liangsheng; Zhao, Bo; Devakul, Trithep; Huse, David A.
2016-06-01
We present a simplified strong-randomness renormalization group (RG) that captures some aspects of the many-body localization (MBL) phase transition in generic disordered one-dimensional systems. This RG can be formulated analytically and is mathematically equivalent to a domain coarsening model that has been previously solved. The critical fixed-point distribution and critical exponents (that satisfy the Chayes inequality) are thus obtained analytically or to numerical precision. This reproduces some, but not all, of the qualitative features of the MBL phase transition that are indicated by previous numerical work and approximate RG studies: our RG might serve as a "zeroth-order" approximation for future RG studies. One interesting feature that we highlight is that the rare Griffiths regions are fractal. For thermal Griffiths regions within the MBL phase, this feature might be qualitatively correctly captured by our RG. If this is correct beyond our approximations, then these Griffiths effects are stronger than has been previously assumed.
Image method for induced surface charge from many-body system of dielectric spheres
Qin, Jian; de Pablo, Juan J.; Freed, Karl F.
2016-09-01
Charged dielectric spheres embedded in a dielectric medium provide the simplest model for many-body systems of polarizable ions and charged colloidal particles. We provide a multiple scattering formulation for the total electrostatic energy for such systems and demonstrate that the polarization energy can be rapidly evaluated by an image method that generalizes the image methods for conducting spheres. Individual contributions to the total electrostatic energy are ordered according to the number of polarized surfaces involved, and each additional surface polarization reduces the energy by a factor of (a/R)3ɛ, where a is the sphere radius, R the average inter-sphere separation, and ɛ the relevant dielectric mismatch at the interface. Explicit expressions are provided for both the energy and the forces acting on individual spheres, which can be readily implemented in Monte Carlo and molecular dynamics simulations of polarizable charged spheres, thereby avoiding costly computational techniques that introduce a surface charge distribution that requires numerical solution.
Retardation and many-body effects in multilayer-film adsorption
Cheng, E.; Cole, Milton W.
1988-07-01
A discussion is presented of the relation between the film thickness d and the coexisting vapor pressure P for a physisorbed film. The theory of Dzyaloshinskii, Lifshitz, and Pitaevskii (DLP) is used to calculate the chemical potential Δμ≡-γ(d)d-3 relative to the value for bulk liquid. The relation is established between the DLP theory and a many-body expansion, of which the Frenkel-Halsey-Hill (FHH) theory is a first approximation to the nonretarded limit. Numerical calculations are performed for the cases of 4He, Ne, H2, N2, Ar, O2, CH4, Kr, and Xe films on glass, gold, graphite, Si, quartz, and Al. Typically, the effect of retardation is to reduce the thickness by 20% for d~200 Å. The function γ(d) is shown to have a universal retardation behavior with a thickness scale (d1/2) depending on both adsorbate and substrate characteristic frequencies.
Particle-hole configuration interaction and many-body perturbation theory: application to Hg+
Berengut, J C
2016-01-01
The combination of configuration interaction and many-body perturbation theory methods (CI+MBPT) is extended to non-perturbatively include configurations with electron holes below the designated Fermi level, allowing us to treat systems where holes play an important role. For example, the method can treat valence-hole systems like Ir$^{17+}$, particle-hole excitations in noble gases, and difficult transitions such as the $6s \\rightarrow 5d^{-1}6s^2$ optical clock transition in Hg$^+$. We take the latter system as our test case for the method and obtain very good accuracy (~1%) for the low-lying transition energies. The $\\alpha$-dependence of these transitions is calculated and used to reinterpret the existing best laboratory limits on the time-dependence of the fine-structure constant.
Many-body effects in the van der Waals-Casimir interaction between graphene layers
Sarabadani, Jalal; Naji, Ali; Asgari, Reza; Podgornik, Rudolf
2011-10-01
Van der Waals-Casimir dispersion interactions between two apposed graphene layers, a graphene layer and a substrate, and in a multilamellar graphene system are analyzed within the framework of the Lifshitz theory. This formulation hinges on a known form of the dielectric response function of an undoped or doped graphene sheet, assumed to be of a random-phase-approximation form. In the geometry of two apposed layers, the separation dependence of the van der Waals-Casimir interaction for both types of graphene sheets is determined and critically compared with some well-known limiting cases. In a multilamellar array, the many-body effects are quantified and shown to increase the magnitude of the van der Waals-Casimir interactions.
Derivation of many-body potential among charged particles in the S-matrix method
Ohta, Tadayuki; Kimura, Toshiei
1992-06-01
A general method of deriving a classical potential from the S-matrix element of particle scattering in the theory of quantized fields is applied to electrodynamics to the post-post-Coulombian approximation. To obtain the many-body potential, a consistent prescription is implemented in subtracting the contributions of the repetition of lower-order potential from the S-matrix elements of the higher-order diagrams. The result shows that the four-body potential between charged particles has a characteristic feature at a large distance and the two-body potential is identical with that given in the reduced Hamiltonian of Wheeler-Feynman electrodynamics. The advantage of the S-matrix method over the canonical formalism is to give the potential directly, without complicated treatment of the interaction with higher derivatives by a method of constrained dynamics.
Non-equilibrium 1D many-body problems and asymptotic properties of Toeplitz determinants
Energy Technology Data Exchange (ETDEWEB)
Gutman, D B [Department of Physics, Bar Ilan University, Ramat Gan 52900 (Israel); Gefen, Yuval [Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100 (Israel); Mirlin, A D [Institut fuer Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe (Germany)
2011-04-22
Non-equilibrium bosonization technique facilitates the solution of a number of important many-body problems out of equilibrium, including the Fermi-edge singularity, the tunneling spectroscopy and full counting statistics of interacting fermions forming a Luttinger liquid. We generalize the method to non-equilibrium hard-core bosons (Tonks-Girardeau gas) and establish interrelations between all these problems. The results can be expressed in terms of Fredholm determinants of the Toeplitz type. We analyze the long time asymptotics of such determinants, using Szego and Fisher-Hartwig theorems. Our analysis yields dephasing rates as well as power-law scaling behavior, with exponents depending not only on the interaction strength but also on the non-equilibrium state of the system.
Hypervirial approach to calculating expectation values of the many-body Hamiltonian
Adam, R. M.; Fiedeldey, H.
1995-05-01
We present a new method, based on the hypervirial operator, for calculating expectation values of many-body Hamiltonians for local velocity-independent potentials. Our approach enables us to calculate the contributions of different components of an interaction [e.g., tensor, one pion exchange part (OPEP)] to the binding energy when all components are acting. In particular, using the integro-differential equation approach we investigate the contributions of different components of realistic nucleon-nucleon potentials to the triton and α particle ground-state binding energies. Although the tensor force contributes the most to the expectation value of the potential energy, we find that its overall contribution to the binding energy is much reduced by its large contribution to the expectation value of the kinetic energy.
Monserrat, Bartomeu
2016-03-01
A method is proposed for the inclusion of electron correlation in the calculation of the temperature dependence of band structures arising from electron-phonon coupling. It relies on an efficient exploration of the vibrational phase space along the recently introduced thermal lines. Using the G0W0 approximation, the temperature dependence of the direct gaps of diamond, silicon, lithium fluoride, magnesium oxide, and titanium dioxide is calculated. Within the proposed formalism, a single calculation at each temperature of interest is sufficient to obtain results of the same accuracy as in alternative, more expensive methods. It is shown that many-body contributions beyond semilocal density functional theory modify the electron-phonon coupling strength by almost 50 % in diamond, silicon, and titanium dioxide, but by less than 5 % in lithium flouride and magnesium oxide. The results reveal a complex picture regarding the validity of semilocal functionals for the description of electron-phonon coupling.
Accessing Rydberg-dressed interactions using many-body Ramsey dynamics
Mukherjee, Rick; Killian, Thomas C.; Hazzard, Kaden R. A.
2016-11-01
We demonstrate that Ramsey spectroscopy can be used to observe Rydberg-dressed interactions in a many-body system well within experimentally measured lifetimes, in contrast to previous research, which either focused on interactions near Förster resonances or on few-atom systems. We build a spin-1/2 from one level that is Rydberg-dressed and another that is not. These levels may be hyperfine or long-lived electronic states. An Ising spin model governs the Ramsey dynamics, which we demonstrate can be used to characterize the Rydberg-dressed interactions. Furthermore, the dynamics can differ significantly from that observed in other spin systems. As one example, spin echo can increase the rate at which coherence decays. The results also apply to bare (undressed) Rydberg states as a special case, for which we quantitatively reproduce recent ultrafast experiments without fitting.
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...
Screened test-charge - electron interaction including many-body effects in two and three dimensions
Gold, A.; Ghazali, A.
1997-05-01
Bound states of a negatively charged test particle and an electron are studied by incorporating many-body effects (exchange and correlation) in the screening function of an interacting electron gas via the local-field correction. Using a variational method and a matrix-diagonalization method we determine the energies and the wave functions of the ground state and the excited states as functions of the electron density for three-dimensional and two-dimensional systems. For high electron density no bound states are found. Below a critical density the number and the energy of the bound states increase with decreasing electron density. We also present results for bound-state energies of a positively charged test particle with an electron, and compare them with results obtained within the random-phase approximation where the local-field correction is ignored.