Quantum mechanics in finite dimensional Hilbert space
de la Torre, A C
2002-01-01
The quantum mechanical formalism for position and momentum of a particle in a one dimensional cyclic lattice is constructively developed. Some mathematical features characteristic of the finite dimensional Hilbert space are compared with the infinite dimensional case. The construction of an unbiased basis for state determination is discussed.
Wavefunction controllability for finite-dimensional bilinear quantum systems
Energy Technology Data Exchange (ETDEWEB)
Turinici, Gabriel [INRIA Rocquencourt, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex (France); Rabitz, Herschel [Department of Chemistry, Princeton University, Princeton, NJ 08544-1009 (United States)
2003-03-14
We present controllability results for quantum systems interacting with lasers. Exact controllability for the wavefunction in these bilinear systems is proved in the finite-dimensional case under very natural hypotheses.
Optimal Control of Finite Dimensional Quantum Systems
Mendonca, Paulo E M F
2009-01-01
This thesis addresses the problem of developing a quantum counter-part of the well established classical theory of control. We dwell on the fundamental fact that quantum states are generally not perfectly distinguishable, and quantum measurements typically introduce noise in the system being measured. Because of these, it is generally not clear whether the central concept of the classical control theory -- that of observing the system and then applying feedback -- is always useful in the quantum setting. We center our investigations around the problem of transforming the state of a quantum system into a given target state, when the system can be prepared in different ways, and the target state depends on the choice of preparation. We call this the "quantum tracking problem" and show how it can be formulated as an optimization problem that can be approached both numerically and analytically. This problem provides a simple route to the characterization of the quantum trade-off between information gain and distu...
Quantum key distribution for composite dimensional finite systems
Shalaby, Mohamed; Kamal, Yasser
2017-06-01
The application of quantum mechanics contributes to the field of cryptography with very important advantage as it offers a mechanism for detecting the eavesdropper. The pioneering work of quantum key distribution uses mutually unbiased bases (MUBs) to prepare and measure qubits (or qudits). Weak mutually unbiased bases (WMUBs) have weaker properties than MUBs properties, however, unlike MUBs, a complete set of WMUBs can be constructed for systems with composite dimensions. In this paper, we study the use of weak mutually unbiased bases (WMUBs) in quantum key distribution for composite dimensional finite systems. We prove that the security analysis of using a complete set of WMUBs to prepare and measure the quantum states in the generalized BB84 protocol, gives better results than using the maximum number of MUBs that can be constructed, when they are analyzed against the intercept and resend attack.
Wigner distributions for finite dimensional quantum systems: An algebraic approach
Indian Academy of Sciences (India)
S Chaturvedi; E Ercolessi; G Marmo; G Morandi; N Mukunbda; R Simon
2005-12-01
We discuss questions pertaining to the definition of `momentum', `momentum space', `phase space' and `Wigner distributions'; for finite dimensional quantum systems. For such systems, where traditional concepts of `momenta' established for continuum situations offer little help, we propose a physically reasonable and mathematically tangible definition and use it for the purpose of setting up Wigner distributions in a purely algebraic manner. It is found that the point of view adopted here is limited to odd dimensional systems only. The mathematical reasons which force this situation are examined in detail.
Azam, Saeid; Yousofzadeh, Malihe
2011-01-01
We classify finite-dimensional irreducible highest weight modules of generalized quantum groups whose positive part is infinite dimensional and has a Kharchenko's PBW basis with an irreducible finite positive root system.
Grishanin, B A; Grishanin, Boris A.; Zadkov, Victor N.
2005-01-01
A concept of the generalized quantum measurement is introduced as the transformation, which establishes a correspondence between the initial states of the object system and final states of the object--measuring device (meter) system with the help of a classical informational index, unambiguously linked to the classically compatible set of states of the object--meter system. It is shown that the generalized measurement covers all the key known quantum measurement concepts--standard projective, entangling, fuzzy and the generalized measurement with the partial or complete destruction of the initial information contained in the object. A special class of partially-destructive measurements that map the continual set of the states in finite-dimensional quantum systems to that one of the infinite-dimensional quantum systems is considered. Their informational essence and some information characteristics are discussed in detail.
Finite-key analysis of a practical decoy-state high-dimensional quantum key distribution
Bao, Haize; Bao, Wansu; Wang, Yang; Zhou, Chun; Chen, Ruike
2016-05-01
Compared with two-level quantum key distribution (QKD), high-dimensional QKD enables two distant parties to share a secret key at a higher rate. We provide a finite-key security analysis for the recently proposed practical high-dimensional decoy-state QKD protocol based on time-energy entanglement. We employ two methods to estimate the statistical fluctuation of the postselection probability and give a tighter bound on the secure-key capacity. By numerical evaluation, we show the finite-key effect on the secure-key capacity in different conditions. Moreover, our approach could be used to optimize parameters in practical implementations of high-dimensional QKD.
Theory of finite-entanglement scaling at one-dimensional quantum critical points.
Pollmann, Frank; Mukerjee, Subroto; Turner, Ari M; Moore, Joel E
2009-06-26
Studies of entanglement in many-particle systems suggest that most quantum critical ground states have infinitely more entanglement than noncritical states. Standard algorithms for one-dimensional systems construct model states with limited entanglement, which are a worse approximation to quantum critical states than to others. We give a quantitative theory of previously observed scaling behavior resulting from finite entanglement at quantum criticality. Finite-entanglement scaling in one-dimensional systems is governed not by the scaling dimension of an operator but by the "central charge" of the critical point. An important ingredient is the universal distribution of density-matrix eigenvalues at a critical point [P. Calabrese and A. Lefevre, Phys. Rev. A 78, 032329 (2008)10.1103/PhysRevA.78.032329]. The parameter-free theory is checked against numerical scaling at several quantum critical points.
Energy Technology Data Exchange (ETDEWEB)
Marek-Crnjac, L. [Institute of Mathematics and Physics, University of Maribor (Slovenia)], E-mail: Leila.marek@guest.arnes.si; Iovane, G. [DIIMA - Universita di Salerno, Via Ponte don Melillo, 84084 Fisciano (Saudi Arabia) (Italy)], E-mail: iovane@diima.unisa.it; Nada, S.I. [Department of Mathematics, Faculty of Science, Qatar University (Qatar)], E-mail: snada@qu.edu.qa; Zhong, Ting [Department of Mathematics, Jishou University, 427000 Zhangjiajie, Hunan (China)], E-mail: zhongting_2005@126.com
2009-11-30
The present work gives first a review of the mathematical theory of finite and infinite dimensional topological spaces. Subsequently we connect the discussion with E-infinity theory and the theory of partially ordered sets. Finally, we contemplate the relevance of abstract results for quantum gravity.
Quantum-optical states in finite-dimensional Hilbert space; 1, General formalism
Miranowicz, A; Imoto, N; Miranowicz, Adam; Leonski, Wieslaw; Imoto, Nobuyuki
2001-01-01
The interest in quantum-optical states confined in finite-dimensional Hilbert spaces has recently been stimulated by the progress in quantum computing, quantum-optical state preparation and measurement techniques, in particular, by the development of the discrete quantum-state tomography. In the first part of our review we present two essentially different approaches to define harmonic oscillator states in the finite-dimensional Hilbert spaces. One of them is related to the truncation scheme of Pegg, Phillips and Barnett [Phys. Rev. Lett. 81, 1604 (1998)] -- the so-called quantum scissors device. The second method corresponds to the truncation scheme of Leo\\'nski and Tana\\'s [Phys. Rev. A 49, R20 (1994)]. We propose some new definitions of the states related to these truncation schemes and find their explicit forms in the Fock representation. We discuss finite-dimensional generalizations of coherent states, phase coherent states, displaced number states, Schr\\"odinger cats, and squeezed vacuum. We show some i...
Moretti, Valter
2016-01-01
This work concerns some issues about the interplay of standard and geometric (Hamiltonian) approaches to finite-dimensional quantum mechanics, formulated in the projective space. Our analysis relies upon the notion and the properties of so-called frame functions, introduced by A.M. Gleason to prove his celebrated theorem. In particular, the problem of associating quantum state with positive Liouville densities is tackled from an axiomatic point of view, proving a theorem classifying all possible correspondences. A similar result is established for classical observables representing quantum ones. These correspondences turn out to be encoded in a one-parameter class and, in both cases, the classical objects representing quantum ones result to be frame functions. The requirements of $U(n)$ covariance and (convex) linearity play a central r\\^ole in the proof of those theorems. A new characterization of classical observables describing quantum observables is presented, together with a geometric description of the ...
Ultraviolet finiteness of Chiral Perturbation Theory for two-dimensional Quantum Electrodynamics
Paston, S A; Franke, V A
2003-01-01
We consider the perturbation theory in the fermion mass (chiral perturbation theory) for the two-dimensional quantum electrodynamics. With this aim, we rewrite the theory in the equivalent bosonic form in which the interaction is exponential and the fermion mass becomes the coupling constant. We reformulate the bosonic perturbation theory in the superpropagator language and analyze its ultraviolet behavior. We show that the boson Green's functions without vacuum loops remain finite in all orders of the perturbation theory in the fermion mass.
A finite-dimensional representation of the quantum angular momentum operator
Campos, R G; Campos, Rafael G.
2000-01-01
A useful finite-dimensional matrix representation of the derivative of periodic functions is obtained by using some elementary facts of trigonometric interpolation. This NxN matrix becomes a projection of the angular derivative into polynomial subspaces of finite dimension and it can be interpreted as a generator of discrete rotations associated to the z-component of the projection of the angular momentum operator in such subspaces, inheriting thus some properties of the continuum operator. The group associated to these discrete rotations is the cyclic group of order N. Since the square of the quantum angular momentum L^2 is associated to a partial differential boundary value problem in the angular variables $\\theta$ and $\\phi$ whose solution is given in terms of the spherical harmonics, we can project such a differential equation to obtain an eigenvalue matrix problem of finite dimension by extending to several variables a projection technique for solving numerically two point boundary value problems and usi...
A complementarity-based approach to phase in finite-dimensional quantum systems
Energy Technology Data Exchange (ETDEWEB)
Klimov, A B [Departamento de Fisica, Universidad de Guadalajara, Revolucion 1500, 44420 Guadalajara, Jalisco (Mexico); Sanchez-Soto, L L [Departamento de Optica, Facultad de Fisica, Universidad Complutense, 28040 Madrid (Spain); Guise, H de [Department of Physics, Lakehead University, Thunder Bay, ON, P7B 5E1 (Canada)
2005-09-01
We develop a comprehensive theory of phase for finite-dimensional quantum systems. The only physical requirement we impose is that phase is complementary to amplitude. To implement this complementarity we use the notion of mutually unbiased bases, which exist for dimensions that are powers of a prime. For a d-dimensional system (qudit) we explicitly construct d+1 classes of maximally commuting operators, each one consisting of d-1 operators. One of these classes consists of diagonal operators that represent amplitudes (or inversions). By finite Fourier transformation, it is mapped onto ladder operators that can be appropriately interpreted as phase variables. We discuss examples of qubits and qutrits, and show how these results generalize previous approaches.
Czarnik, Piotr; Dziarmaga, Jacek; Oleś, Andrzej M.
2016-05-01
Progress in describing thermodynamic phase transitions in quantum systems is obtained by noticing that the Gibbs operator e-β H for a two-dimensional (2D) lattice system with a Hamiltonian H can be represented by a three-dimensional tensor network, the third dimension being the imaginary time (inverse temperature) β . Coarse graining the network along β results in a 2D projected entangled-pair operator (PEPO) with a finite bond dimension D . The coarse graining is performed by a tree tensor network of isometries. The isometries are optimized variationally, taking into account full tensor environment, to maximize the accuracy of the PEPO. The algorithm is applied to the isotropic quantum compass model on an infinite square lattice near a symmetry-breaking phase transition at finite temperature. From the linear susceptibility in the symmetric phase and the order parameter in the symmetry-broken phase, the critical temperature is estimated at Tc=0.0606 (4 ) J , where J is the isotropic coupling constant between S =1/2 pseudospins.
Finite-key analysis for time-energy high-dimensional quantum key distribution
Niu, Murphy Yuezhen; Xu, Feihu; Shapiro, Jeffrey H.; Furrer, Fabian
2016-11-01
Time-energy high-dimensional quantum key distribution (HD-QKD) leverages the high-dimensional nature of time-energy entangled biphotons and the loss tolerance of single-photon detection to achieve long-distance key distribution with high photon information efficiency. To date, the general-attack security of HD-QKD has only been proven in the asymptotic regime, while HD-QKD's finite-key security has only been established for a limited set of attacks. Here we fill this gap by providing a rigorous HD-QKD security proof for general attacks in the finite-key regime. Our proof relies on an entropic uncertainty relation that we derive for time and conjugate-time measurements that use dispersive optics, and our analysis includes an efficient decoy-state protocol in its parameter estimation. We present numerically evaluated secret-key rates illustrating the feasibility of secure and composable HD-QKD over metropolitan-area distances when the system is subjected to the most powerful eavesdropping attack.
Liu, Xi-Jing; Hu, Bing-Quan; Cho, Sam Young; Zhou, Huan-Qiang; Shi, Qian-Qian
2016-10-01
Recently, the finite-size corrections to the geometrical entanglement per lattice site in the spin-1/2 chain have been numerically shown to scale inversely with system size, and its prefactor b has been suggested to be possibly universal [Q-Q. Shi et al., New J. Phys. 12, 025008 (2010)]. As possible evidence of its universality, the numerical values of the prefactors have been confirmed analytically by using the Affleck-Ludwig boundary entropy with a Neumann boundary condition for a free compactified field [J-M. Stephan et al., Phys. Rev. B 82, 180406(R) (2010)]. However, the Affleck-Ludwig boundary entropy is not unique and does depend on conformally invariant boundary conditions. Here, we show that a unique Affleck-Ludwig boundary entropy corresponding to a finitesize correction to the geometrical entanglement per lattice site exists and show that the ratio of the prefactor b to the corresponding minimum groundstate degeneracy gmin for the Affleck- Ludwig boundary entropy is a constant for any critical region of the spin-1 XXZ system with the single-ion anisotropy, i.e., b/(2 log2 g min ) = -1. Previously studied spin-1/2 systems, including the quantum three-state Potts model, have verified the universal ratio. Hence, the inverse finite-size correction to the geometrical entanglement per lattice site and its prefactor b are universal for one-dimensional critical systems.
Radon Transform in Finite Dimensional Hilbert Space
Revzen, M.
2012-01-01
Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators are underpinned with finite geometry which provide intuitive perspective to the physical operators. The analysis emphasizes a central role for projectors of mutual unbiased bases (MUB) states, extending thereby their use in finite dimensional quantum mechani...
Chang, Weng-Long; Ren, Ting-Ting; Feng, Mang
2015-01-01
In this paper, it is shown that the proposed quantum algorithm for implementing Boolean circuits generated from the DNA-based algorithm solving the vertex-cover problem of any graph G with m edges and n vertices is the optimal quantum algorithm. Next, it is also demonstrated that mathematical solutions of the same biomolecular solutions are represented in terms of a unit vector in the finite-dimensional Hilbert space. Furthermore, for testing our theory, a nuclear magnetic resonance (NMR) experiment of three quantum bits to solve the simplest vertex-cover problem is completed.
Modesto, Leonardo
2013-01-01
We hereby present a class of multidimensional higher derivative theories of gravity that realizes an ultraviolet completion of Einstein general relativity. This class is marked by a "non-polynomal" entire function (form factor), which averts extra degrees of freedom (including ghosts) and improves the high energy behavior of the loop amplitudes. By power counting arguments, it is proved that the theory is super-renormalizable in any dimension, i.e. only one-loop divergences survive. Furthermore, in odd dimensions there are no counter terms for pure gravity and the theory turns out to be "finite." Finally, considering the infinite tower of massive states coming from dimensional reduction, quantum gravity is finite in even dimension as well.
Comment on "Quantum phase for an arbitrary system with finite-dimensional Hilbert space"
Hall, Michael J. W.; Pegg, David T.
2012-01-01
A construction of covariant quantum phase observables, for Hamiltonians with a finite number of energy eigenvalues, has been recently given by D. Arsenovic et al. [Phys. Rev. A 85, 044103 (2012)]. For Hamiltonians generating periodic evolution, we show that this construction is just a simple rescaling of the known canonical 'time' or 'age' observable, with the period T rescaled to 2\\pi. Further, for Hamiltonians generating quasiperiodic evolution, we note that the construction leads to a phas...
Quantum memories at finite temperature
Brown, Benjamin J.; Loss, Daniel; Pachos, Jiannis K.; Self, Chris N.; Wootton, James R.
2016-10-01
To use quantum systems for technological applications one first needs to preserve their coherence for macroscopic time scales, even at finite temperature. Quantum error correction has made it possible to actively correct errors that affect a quantum memory. An attractive scenario is the construction of passive storage of quantum information with minimal active support. Indeed, passive protection is the basis of robust and scalable classical technology, physically realized in the form of the transistor and the ferromagnetic hard disk. The discovery of an analogous quantum system is a challenging open problem, plagued with a variety of no-go theorems. Several approaches have been devised to overcome these theorems by taking advantage of their loopholes. The state-of-the-art developments in this field are reviewed in an informative and pedagogical way. The main principles of self-correcting quantum memories are given and several milestone examples from the literature of two-, three- and higher-dimensional quantum memories are analyzed.
Energy Technology Data Exchange (ETDEWEB)
Santhanam, Thalanayar S [Department of Physics Saint Louis University, Missouri, MO 63103 (United States); Santhanam, Balu [Department of Electrical and Computer Engineering, MSC01 1100 1, University of New Mexico Albuquerque, NM 87131-0001 (United States)], E-mail: santhats@slu.edu, E-mail: bsanthan@ece.unm.edu
2009-05-22
Quantum mechanics of a linear harmonic oscillator in a finite-dimensional Hilbert space satisfying the correct equations of motion is studied. The connections to Weyl's formulation of the algebra of bounded unitary operators in finite space as well as to a truncated quantized linear harmonic oscillator are discussed. It is pointed out that the discrete Fourier transformation (DFT) plays a central role in determining the actual form of the position, the momentum, the number and the Hamiltonian operators. The explicit form of these operators in different bases is exhibited for some low values of the dimension of the Hilbert space. In this formulation, it is shown that the Hamiltonian is indeed the logarithm of the DFT and that by modifying Weyl's framework to include position and momentum operators with non-uniformly spaced spectra the equations of motion are satisfied.
Manos, T
2015-01-01
We study the quantum kicked rotator in the classically fully chaotic regime $K=10$ and for various values of the quantum parameter $k$ using Izrailev's $N$-dimensional model for various $N \\le 3000$, which in the limit $N \\rightarrow \\infty$ tends to the exact quantized kicked rotator. By numerically calculating the eigenfunctions in the basis of the angular momentum we find that the localization length ${\\cal L}$ for fixed parameter values has a certain distribution, in fact its inverse is Gaussian distributed, in analogy and in connection with the distribution of finite time Lyapunov exponents of Hamilton systems. However, unlike the case of the finite time Lyapunov exponents, this distribution is found to be independent of $N$, and thus survives the limit $N=\\infty$. This is different from the tight-binding model of Anderson localization. The reason is that the finite bandwidth approximation of the underlying Hamilton dynamical system in the Shepelyansky picture (D.L. Shepelyansky, {\\em Phys. Rev. Lett.} {...
Energy Technology Data Exchange (ETDEWEB)
Nakra Mohajer, Soukaina; El Harouny, El Hassan [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); Ibral, Asmaa [Equipe d’Optique et Electronique du Solide, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); Laboratoire d’Instrumentation, Mesure et Contrôle, Département de Physique, Faculté des Sciences, Université Chouaïb Doukkali, B. P. 20 El Jadida Principale, El Jadida (Morocco); El Khamkhami, Jamal [Laboratoire de Physique de la Matière Condensée, Département de Physique, Faculté des Sciences, Université Abdelmalek Essaadi, B.P. 2121 M’Hannech II, 93030 Tétouan (Morocco); and others
2016-09-15
Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.
Finite and profinite quantum systems
Vourdas, Apostolos
2017-01-01
This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and ...
Phase conjugate of quantum states in finite-dimensional Hilbert space
Zhou, X F; Guo, G C; Zhou, Xiang-Fa; Zhang, Yong-Sheng; Guo, Guang-Can
2006-01-01
We show that, for $N$ parallel input states, an anti-linear map with respect to a specific basis is essentially a classical operator. We also consider the information contained in phase-conjugate pairs $|\\phi > |\\phi^*>$, and prove that there is more information about a quantum state encoded in phase-conjugate pairs than in parallel pairs.
Numerical and algebraic studies for the control of finite-dimensional quantum systems
Energy Technology Data Exchange (ETDEWEB)
Sander, Uwe
2010-11-18
In this thesis, two aspects of control theory, namely controllability and optimal control, are applied to quantum systems. The presented results are based on group theoretical techniques and numerical studies. By Lie-algebraic analysis, the controllability properties of systems with an arbitrary topology are described and related to the symmetries existing in these systems. We find that symmetry precludes full controllability. Our work investigates well-known control systems and gives rules for the design of new systems. Furthermore, theoretical and numerical concepts are instrumental to studying quantum channels: Their capacities are optimised using gradient flows on the unitary group in order to find counterexamples to a long-established additivity conjecture. The last part of this thesis presents and benchmarks a modular optimal control algorithm known as GRAPE. Numerical tests show how the interplay of its modules can be optimised for higher performance, and how the algorithm performs in comparison to a Krotov-type optimal control algorithm. It is found that GRAPE performs particularly well when aiming for high qualities. (orig.)
Hypercontractivity in finite-dimensional matrix algebras
Energy Technology Data Exchange (ETDEWEB)
Junge, Marius, E-mail: junge@math.uiuc.edu [Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green St., Urbana, Illinois 61891 (United States); Palazuelos, Carlos, E-mail: carlospalazuelos@ucm.es [Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Universidad Complutense de Madrid, Facultad de Ciencias Matemáticas, Plaza de Ciencias s/n, 28040 Madrid (Spain); Parcet, Javier, E-mail: javier.parcet@icmat.es; Perrin, Mathilde, E-mail: mathilde.perrin@icmat.es [Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Nicolás Cabrera 13-15, 28049 Madrid (Spain)
2015-02-15
We obtain hypercontractivity estimates for a large class of semigroups defined on finite-dimensional matrix algebras M{sub n}. These semigroups arise from Poisson-like length functions ψ on ℤ{sub n} × ℤ{sub n} and provide new hypercontractive families of quantum channels when ψ is conditionally negative. We also study the optimality of our estimates.
Quantum Computing over Finite Fields
James, Roshan P; Sabry, Amr
2011-01-01
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a finite field instead of the field of complex numbers. This instantiation collapses much the structure of actual quantum mechanics but retains several of its distinguishing characteristics including the notions of superposition, interference, and entanglement. Furthermore, discrete quantum theory excludes local hidden variable models, has a no-cloning theorem, and can express natural counterparts of quantum information protocols such as superdense coding and teleportation. Our first result is to distill a model of discrete quantum computing from this quantum theory. The model is expressed using a monadic metalanguage built on top of a universal reversible language for finite computations, and hence is directly implementab...
Finite-temperature scaling close to Ising-nematic quantum critical points in two-dimensional metals
Punk, Matthias
2016-11-01
We study finite-temperature properties of metals close to an Ising-nematic quantum critical point in two spatial dimensions. In particular we show that at any finite temperature there is a regime where order parameter fluctuations are characterized by a dynamical critical exponent z =2 , in contrast to z =3 found at zero temperature. Our results are based on a simple Eliashberg-type approach, which gives rise to a boson self-energy proportional to Ω /γ (T ) at small momenta, where γ (T ) is the temperature dependent fermion scattering rate. These findings might shed some light on recent Monte Carlo simulations at finite temperature, where results consistent with z =2 were found.
An Application of Quantum Finite Automata to Interactive Proof Systems
Nishimura, H; Nishimura, Harumichi; Yamakami, Tomoyuki
2004-01-01
Quantum finite automata have been studied intensively since their introduction in late 1990s as a natural model of a quantum computer with finite-dimensional quantum memory space. This paper seeks their direct application to interactive proof systems in which a mighty quantum prover communicates with a quantum-automaton verifier through a common communication cell. Our quantum interactive proof systems are juxtaposed to Dwork-Stockmeyer's classical interactive proof systems whose verifiers are two-way probabilistic automata. We demonstrate strengths and weaknesses of our systems and further study how various restrictions on the behaviors of quantum-automaton verifiers affect the power of quantum interactive proof systems.
Finite-dimensional Hilbert space and frame quantization
Energy Technology Data Exchange (ETDEWEB)
Cotfas, Nicolae [Faculty of Physics, University of Bucharest, PO Box 76-54, Post Office 76, Bucharest (Romania); Gazeau, Jean Pierre [Laboratoire APC, Universite Paris Diderot, 10, rue A Domon et L Duquet, 75205 Paris Cedex 13 (France); Vourdas, Apostol, E-mail: ncotfas@yahoo.com, E-mail: gazeau@apc.univ-paris7.fr, E-mail: A.Vourdas@bradford.ac.uk [Department of Computing, University of Bradford, Bradford BD7 1DP (United Kingdom)
2011-04-29
The quantum observables used in the case of quantum systems with finite-dimensional Hilbert space are defined either algebraically in terms of an orthonormal basis and discrete Fourier transformation or by using a continuous system of coherent states. We present an alternative approach to these important quantum systems based on the finite frame quantization. Finite systems of coherent states, usually called finite tight frames, can be defined in a natural way in the case of finite quantum systems. Novel examples of such tight frames are presented. The quantum observables used in our approach are obtained by starting from certain classical observables described by functions defined on the discrete phase space corresponding to the system. They are obtained by using a finite frame and a Klauder-Berezin-Toeplitz-type quantization. Semi-classical aspects of tight frames are studied through lower symbols of basic classical observables.
On Finite $J$-Hermitian Quantum Mechanics
Lee, Sungwook
2014-01-01
In his recent paper arXiv:1312.7738, the author discussed $J$-Hermitian quantum mechanics and showed that $PT$-symmetric quantum mechanics is essentially $J$-Hermitian quantum mechanics. In this paper, the author discusses finite $J$-Hermitian quantum mechanics which is derived naturally from its continuum one and its relationship with finite $PT$-symmetric quantum mechanics.
Modesto, Leonardo; Piva, Marco; Rachwał, Lesław
2016-07-01
We explicitly compute the one-loop exact beta function for a nonlocal extension of the standard gauge theory, in particular, Yang-Mills and QED. The theory, made of a weakly nonlocal kinetic term and a local potential of the gauge field, is unitary (ghost-free) and perturbatively super-renormalizable. Moreover, in the action we can always choose the potential (consisting of one "killer operator") to make zero the beta function of the running gauge coupling constant. The outcome is a UV finite theory for any gauge interaction. Our calculations are done in D =4 , but the results can be generalized to even or odd spacetime dimensions. We compute the contribution to the beta function from two different killer operators by using two independent techniques, namely, the Feynman diagrams and the Barvinsky-Vilkovisky traces. By making the theories finite, we are able to solve also the Landau pole problems, in particular, in QED. Without any potential, the beta function of the one-loop super-renormalizable theory shows a universal Landau pole in the running coupling constant in the ultraviolet regime (UV), regardless of the specific higher-derivative structure. However, the dressed propagator shows neither the Landau pole in the UV nor the singularities in the infrared regime (IR).
Finite-dimensional (*)-serial algebras
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Let A be a finite-dimensional associative algebra with identity over a field k. In this paper we introduce the concept of (*)-serial algebras which is a generalization of serial algebras. We investigate the properties of (*)-serial algebras, and we obtain suficient and necessary conditions for an associative algebra to be (*)-serial.
Krovi, Hari; Russell, Alexander
2012-01-01
Knot and link invariants naturally arise from any braided Hopf algebra. We consider the computational complexity of the invariants arising from an elementary family of finite-dimensional Hopf algebras: quantum doubles of finite groups (denoted D(G), for a group G). Regarding algorithms for these invariants, we develop quantum circuits for the quantum Fourier transform over D(G); in general, we show that when one can uniformly and efficiently carry out the quantum Fourier transform over the ce...
Yakovenko, Victor M.; Goan, Hsi-Sheng
1996-12-01
This paper reviews recent developments in the theory of the quantum Hall effect (QHE) in the magnetic-field-induced spin-density-wave (FISDW) state of the quasi-one-dimensional organic conductors (TMTSF)2X. The origin and the basic features of the FISDW are reviewed. The QHE in the pinned FISDW state is derived in several simple, transparent ways, including the edge states formulation of the problem. The temperature dependence of the Hall conductivity is found to be the same as the temperature dependence of the Fröhlich current. It is shown that, when the FISDW is free to move, it produces an additional contribution to the Hall conductivity that nullifies the total Hall effect. The paper is written on mathematically simple level, emphasizes physical meaning over sophisticated mathematical technique, and uses inductive, rather than deductive, reasoning.
Energy Technology Data Exchange (ETDEWEB)
Ranade, Kedar S.
2009-02-04
This PhD thesis deals with quantum-cryptographic protocols which allow general finite-dimensional quantum systems (qudits) as carriers of information in contrast to the predominantly used two-dimensional quantum systems (qubits). The main focus of investigations is the maximum tolerable error rate of such protocols and its behaviour as a function of the dimension of the information carriers. For this purpose, several concepts are introduced which allow the treatment of this problem. In particular, protocols are presented which work up to a maximum tolerate error rate, and it is shown that a wide class of protocols cannot be used for higher error rates. Among other things, it turns out that the maximum tolerable error rate for two-basis protocols increases up to 50% for high dimensions. Apart from the above-mentioned main subjects of this thesis, some other results from the field of quantum information theory are given, which were achieved during this PhD project. (orig.)
Geometrical Underpinning of Finite Dimensional Hilbert space
Revzen, M
2011-01-01
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of Hilbert space operators that form mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among them revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.
Geometrical Underpinning of Finite Dimensional Hilbert space
Revzen, M.
2011-01-01
Finite geometry is employed to underpin operators in finite, d, dimensional Hilbert space. The central role of mutual unbiased bases (MUB) states projectors is exhibited. Interrelation among operators in Hilbert space, revealed through their (finite) dual affine plane geometry (DAPG) underpinning is studied. Transcription to (finite) affine plane geometry (APG) is given and utilized for their interpretation.
General finite-size effects for zero-entropy states in one-dimensional quantum integrable models
Eliëns, Sebas; Caux, Jean-Sébastien
2016-12-01
We present a general derivation of the spectrum of excitations for gapless states of zero entropy density in Bethe ansatz solvable models. Our formalism is valid for an arbitrary choice of bare energy function which is relevant to situations where the Hamiltonian for time evolution differs from the Hamiltonian in a (generalized) Gibbs ensemble, i.e. out of equilibrium. The energy of particle and hole excitations, as measured with the time-evolution Hamiltonian, is shown to include additional contributions stemming from the shifts of the Fermi points that may now have finite energy. The finite-size effects are also derived and the connection with conformal field theory discussed. The critical exponents can still be obtained from the finite-size spectrum, however the velocity occurring here differs from the one in the constant Casimir term. The derivation highlights the importance of the phase shifts at the Fermi points for the critical exponents of asymptotes of correlations. We generalize certain results known for the ground state and discuss the relation to the dressed charge (matrix). Finally, we discuss the finite-size corrections in the presence of an additional particle or hole, which are important for dynamical correlation functions.
Quantum channels with a finite memory
Bowen, G; Bowen, Garry; Mancini, Stefano
2004-01-01
In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted classical capacities it is shown that these bounds are attainable for certain classes of channel. Also, we show that the structure of any finite memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite-memory channel where no information is lost to the environment, the channel is asymptotically noiseless.
Higher dimensional loop quantum cosmology
Zhang, Xiangdong
2016-07-01
Loop quantum cosmology (LQC) is the symmetric sector of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogeneous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology.
Institute of Scientific and Technical Information of China (English)
王志华
2012-01-01
用初等的类似于量子群uq（sl2）上有限维单模的分类方法，给出了量子矩阵代数Mq（2）上有限维单模的一种分类。结果表明，当q不是单位根时，Mq（2）上有限维单模仅有1维单模，当q为r次单位根时（r为奇数），Mq（2）上所有单模都是有限维的，且仅有1维与r维单模。%Using elementary methods analogue to the classification of simple finite dimensional modules of quantum group uu ( sl2 ), all simple finite dimensional modules of quantum matrix algebra Mq ( 2 ) are classified. It turns out that when q is not a root of unity all simple finite dimensional modules are only with dimension 1, and when q is r-th root of unity with odd r all simple modules are finite with dimension 1 and r.
Quantum Phase Transitions in a Finite System
Leviatan, A
2006-01-01
A general procedure for studying finite-N effects in quantum phase transitions of finite systems is presented and applied to the critical-point dynamics of nuclei undergoing a shape-phase transition of second-order (continuous), and of first-order with an arbitrary barrier.
Measurement Uncertainty for Finite Quantum Observables
Directory of Open Access Journals (Sweden)
René Schwonnek
2016-06-01
Full Text Available Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method is semidefinite programming, which we apply to arbitrary finite collections of projective observables on a finite dimensional Hilbert space. The quantification of errors is based on an arbitrary cost function, which assigns a penalty to getting result x rather than y, for any pair ( x , y . This induces a notion of optimal transport cost for a pair of probability distributions, and we include an Appendix with a short summary of optimal transport theory as needed in our context. There are then different ways to form an overall figure of merit from the comparison of distributions. We consider three, which are related to different physical testing scenarios. The most thorough test compares the transport distances between the marginals of a joint measurement and the reference observables for every input state. Less demanding is a test just on the states for which a “true value” is known in the sense that the reference observable yields a definite outcome. Finally, we can measure a deviation as a single expectation value by comparing the two observables on the two parts of a maximally-entangled state. All three error quantities have the property that they vanish if and only if the tested observable is equal to the reference. The theory is illustrated with some characteristic examples.
Characterizations of 1-Way Quantum Finite Automata
Brodsky, A; Brodsky, Alex; Pippenger, Nicholas
1999-01-01
The 2-way quantum finite automaton introduced by Kondacs and Watrous can accept non-regular languages with bounded error in polynomial time. If we restrict the head of the automaton to moving classically and to moving only in one direction, the acceptance power of this 1-way quantum finite automaton is reduced to a proper subset of the regular languages. In this paper we study two different models of 1-way quantum finite automata. The first model, termed measure-once quantum finite automata, was introduced by Moore and Crutchfield, and the second model, termed measure-many quantum finite automata, was introduced by Kondacs and Watrous. We characterize the measure-once model when it is restricted to accepting with bounded error and show that, without that restriction, it can solve the word problem over the free group. We also show that it can be simulated by a probabilistic finite automaton and describe an algorithm that determines if two measure-once automata are equivalent. We prove several closure propertie...
Finite-dimensional division algebras over fields
Jacobson, Nathan
2009-01-01
Finite-Dimensional Division Algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called 'multiplication algebras of Riemann matrices'. The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of parti
Radon Transform for Finite Dimensional Hilbert Space
Revzen, M
2012-01-01
Finite dimensional, d, Hilbert space operators are underpinned with ?nite geometry. The analysis emphasizes a central role for mutual unbiased bases (MUB) states projectors. Interrelation among the Hilbert space operators revealed via their (?nite) dual a?ne plane geometry (DAPG) underpin- ning is studied and utilized in formulating a ?nite dimensional Radon transformation. The ?nite geometry required for our study is outlines.
Quantum channels with a finite memory
Bowen, Garry; Mancini, Stefano
2004-01-01
In this paper we study quantum communication channels with correlated noise effects, i.e., quantum channels with memory. We derive a model for correlated noise channels that includes a channel memory state. We examine the case where the memory is finite, and derive bounds on the classical and quantum capacities. For the entanglement-assisted and unassisted classical capacities it is shown that these bounds are attainable for certain classes of channel. Also, we show that the structure of any finite-memory state is unimportant in the asymptotic limit, and specifically, for a perfect finite-memory channel where no information is lost to the environment, achieving the upper bound implies that the channel is asymptotically noiseless.
Probabilistic and quantum finite automata with postselection
Yakaryilmaz, Abuzer
2011-01-01
We prove that endowing a real-time probabilistic or quantum computer with the ability of postselection increases its computational power. For this purpose, we provide a new model of finite automata with postselection, and compare it with the model of L\\={a}ce et al. We examine the related language classes, and also establish separations between the classical and quantum versions, and between the zero-error vs. bounded-error modes of recognition in this model.
An algebraic study of unitary one dimensional quantum cellular automata
Arrighi, P
2005-01-01
We provide algebraic characterizations of unitary one dimensional quantum cellular automata. We do so both by algebraizing existing decision procedures, and by adding constraints into the model which do not change the quantum cellular automata's computational power. The configurations we consider have finite but unbounded size.
Neutrix Calculus and Finite Quantum Field Theory
Ng, Y J
2004-01-01
In general, quantum field theories require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series in their interaction couplings. We propose to apply neutrix calculus, developed by van der Corput and Hadamard in connection with asymptotic series, to tackle divergent integrals, yielding finite renormalizations for the parameters in quantum field theories. We observe that quantum gravity theories are rendered more manageable, and that both renormalizable field theories and effective field theories can be accommodated in the framework of neutrix calculus.
Finite Dimensional KP \\tau-functions I. Finite Grassmannians
Balogh, F; Harnad, J
2014-01-01
We study \\tau-functions of the KP hierarchy in terms of abelian group actions on finite dimensional Grassmannians, viewed as subquotients of the Hilbert space Grassmannians of Sato, Segal and Wilson. A determinantal formula of Gekhtman and Kasman involving exponentials of finite dimensional matrices is shown to follow naturally from such reductions. All reduced flows of exponential type generated by matrices with arbitrary nondegenerate Jordan forms are derived, both in the Grassmannian setting and within the fermionic operator formalism. A slightly more general determinantal formula involving resolvents of the matrices generating the flow, valid on the big cell of the Grassmannian, is also derived. An explicit expression is deduced for the Pl\\"ucker coordinates appearing as coefficients in the Schur function expansion of the \\tau-function.
Finite-dimensional collisionless kinetic theory
Burby, J W
2016-01-01
A collisionless kinetic plasma model may often be cast as an infinite-dimensional noncanonical Hamiltonian system. I show that, when this is the case, the model can be discretized in space and particles while preserving its Hamiltonian structure, thereby producing a finite-dimensional Hamiltonian system that approximates the original kinetic model. I apply the general theory to two example systems: the relativistic Vlasov-Maxwell system with spin, and a gyrokinetic Vlasov-Maxwell system.
High resolution finite volume scheme for the quantum hydrodynamic equations
Lin, Chin-Tien; Yeh, Jia-Yi; Chen, Jiun-Yeu
2009-03-01
The theory of quantum fluid dynamics (QFD) helps nanotechnology engineers to understand the physical effect of quantum forces. Although the governing equations of quantum fluid dynamics and classical fluid mechanics have the same form, there are two numerical simulation problems must be solved in QFD. The first is that the quantum potential term becomes singular and causes a divergence in the numerical simulation when the probability density is very small and close to zero. The second is that the unitarity in the time evolution of the quantum wave packet is significant. Accurate numerical evaluations are critical to the simulations of the flow fields that are generated by various quantum fluid systems. A finite volume scheme is developed herein to solve the quantum hydrodynamic equations of motion, which significantly improve the accuracy and stability of this method. The QFD equation is numerically implemented within the Eulerian method. A third-order modified Osher-Chakravarthy (MOC) upwind-centered finite volume scheme was constructed for conservation law to evaluate the convective terms, and a second-order central finite volume scheme was used to map the quantum potential field. An explicit Runge-Kutta method is used to perform the time integration to achieve fast convergence of the proposed scheme. In order to meet the numerical result can conform to the physical phenomenon and avoid numerical divergence happening due to extremely low probability density, the minimum value setting of probability density must exceed zero and smaller than certain value. The optimal value was found in the proposed numerical approach to maintain a converging numerical simulation when the minimum probability density is 10 -5 to 10 -12. The normalization of the wave packet remains close to unity through a long numerical simulation and the deviations from 1.0 is about 10 -4. To check the QFD finite difference numerical computations, one- and two-dimensional particle motions were
Finite dimensional quadratic Lie superalgebras
Jarvis, Peter; Yates, Luke
2010-01-01
We consider a special class of Z_2-graded, polynomial algebras of degree 2, which we call quadratic Lie superalgebras. Starting from the formal definition, we discuss the generalised Jacobi relations in the context of the Koszul property, and give a proof of the PBW basis theorem. We give several concrete examples of quadratic Lie superalgebras for low dimensional cases, and discuss aspects of their structure constants for the `type I' class. Based on the factorisation of the enveloping algebra, we derive the Kac module construction for typical and atypical modules, and a related direct construction of irreducible modules due to Gould. We investigate the method for one specific case, the quadratic generalisation gl_2(n/1) of the Lie superalgebra sl(n/1). We formulate the general atypicality conditions at level 1, and present an analysis of zero-and one-step atypical modules for a certain family of Kac modules.
Quantum Finite Automata and Weighted Automata
Rao, M V P
2007-01-01
Quantum finite automata derive their strength by exploiting interference in complex valued probability amplitudes. Of particular interest is the 2-way model of Ambainis and Watrous that has both quantum and classical states (2QCFA) [A. Ambainis and J. Watrous, Two-way finite automata with quantum and classical state, Theoretical Computer Science, 287(1), pp. 299-311, 2002], since it combines the advantage of the power of interference in a constant-sized quantum system with a 2-way head. This paper is a step towards finding the least powerful model which is purely classical and can mimic the dynamics of quantum phase. We consider weighted automata with the Cortes-Mohri definition of language recognition [C. Cortes and M. Mohri, Context-Free Recognition with Weighted Automata, Grammars 3(2/3), pp. 133-150, 2000] as a candidate model for simulating 2QCFA. Given any 2QCFA that (i) uses the accept-reject-continue observable, (ii) recognizes a language with one-sided error and (iii) the entries of whose unitary mat...
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Finite Quantum Tomography and Semidefinite Programming
Mirzaee, M.; Rezaee, M.; Jafarizadeh, M. A.
2007-06-01
Using the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: truncated coherent states tomography, phase tomography and coherent spin state tomography, qudit tomography, N-qubit tomography, where that obtained results are in agreement with those of References (Buzek et al., Chaos, Solitons and Fractals 10 (1999) 981; Schack and Caves, Separable states of N quantum bits. In: Proceedings of the X. International Symposium on Theoretical Electrical Engineering, 73. W. Mathis and T. Schindler, eds. Otto-von-Guericke University of Magdeburg, Germany (1999); Pegg and Barnett Physical Review A 39 (1989) 1665; Barnett and Pegg Journal of Modern Optics 36 (1989) 7; St. Weigert Acta Physica Slov. 4 (1999) 613).
Finite de Finetti theorem for infinite-dimensional systems.
D'Cruz, Christian; Osborne, Tobias J; Schack, Rüdiger
2007-04-20
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state |Psi/Psi| chosen from a family of subsets {Cn} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give a second equivalent characterization of the family {Cn}.
A Finite de Finetti Theorem for Infinite-Dimensional Systems
D'Cruz, C; Schack, R; Cruz, Christian D'; Osborne, Tobias J.; Schack, Ruediger
2006-01-01
We formulate and prove a de Finetti representation theorem for finitely exchangeable states of a quantum system consisting of k infinite-dimensional subsystems. The theorem is valid for states that can be written as the partial trace of a pure state from a family of subspaces {S_n} of the full symmetric subspace for n subsystems. We show that such states become arbitrarily close to mixtures of pure power states as n increases. We give two simple equivalent characterizations of the family {S_n}.
Finite-key security analysis for multilevel quantum key distribution
Brádler, Kamil; Mirhosseini, Mohammad; Fickler, Robert; Broadbent, Anne; Boyd, Robert
2016-07-01
We present a detailed security analysis of a d-dimensional quantum key distribution protocol based on two and three mutually unbiased bases (MUBs) both in an asymptotic and finite-key-length scenario. The finite secret key rates (in bits per detected photon) are calculated as a function of the length of the sifted key by (i) generalizing the uncertainly relation-based insight from BB84 to any d-level 2-MUB QKD protocol and (ii) by adopting recent advances in the second-order asymptotics for finite block length quantum coding (for both d-level 2- and 3-MUB QKD protocols). Since the finite and asymptotic secret key rates increase with d and the number of MUBs (together with the tolerable threshold) such QKD schemes could in principle offer an important advantage over BB84. We discuss the possibility of an experimental realization of the 3-MUB QKD protocol with the orbital angular momentum degrees of freedom of photons.
A finite Zitterbewegung model for relativistic quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Noyes, H.P.
1990-02-19
Starting from steps of length h/mc and time intervals h/mc{sup 2}, which imply a quasi-local Zitterbewegung with velocity steps {plus minus}c, we employ discrimination between bit-strings of finite length to construct a necessary 3+1 dimensional event-space for relativistic quantum mechanics. By using the combinatorial hierarchy to label the strings, we provide a successful start on constructing the coupling constants and mass ratios implied by the scheme. Agreement with experiments is surprisingly accurate. 22 refs., 1 fig.
Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols
Directory of Open Access Journals (Sweden)
Simon J. Gay
2014-07-01
Full Text Available We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science. We have extended the quantum process calculus to describe d-dimensional quantum systems, which has not been done before. We summarise the necessary theory in the generalisation of quantum gates and Bell states and use the theory to apply the quantum process calculus CQP to quantum protocols, namely qudit teleportation and superdense coding.
The finite-dimensional Witsenhausen counterexample
Grover, Pulkit; Sahai, Anant
2010-01-01
Recently, a vector version of Witsenhausen's counterexample was considered and it was shown that in that limit of infinite vector length, certain quantization-based control strategies are provably within a constant factor of the optimal cost for all possible problem parameters. In this paper, finite vector lengths are considered with the dimension being viewed as an additional problem parameter. By applying a large-deviation "sphere-packing" philosophy, a lower bound to the optimal cost for the finite dimensional case is derived that uses appropriate shadows of the infinite-length bound. Using the new lower bound, we show that good lattice-based control strategies achieve within a constant factor of the optimal cost uniformly over all possible problem parameters, including the vector length. For Witsenhausen's original problem -- the scalar case -- the gap between regular lattice-based strategies and the lower bound is numerically never more than a factor of 8.
Two-dimensional quantum repeaters
Wallnöfer, J.; Zwerger, M.; Muschik, C.; Sangouard, N.; Dür, W.
2016-11-01
The endeavor to develop quantum networks gave rise to a rapidly developing field with far-reaching applications such as secure communication and the realization of distributed computing tasks. This ultimately calls for the creation of flexible multiuser structures that allow for quantum communication between arbitrary pairs of parties in the network and facilitate also multiuser applications. To address this challenge, we propose a two-dimensional quantum repeater architecture to establish long-distance entanglement shared between multiple communication partners in the presence of channel noise and imperfect local control operations. The scheme is based on the creation of self-similar multiqubit entanglement structures at growing scale, where variants of entanglement swapping and multiparty entanglement purification are combined to create high-fidelity entangled states. We show how such networks can be implemented using trapped ions in cavities.
Private algebras in quantum information and infinite-dimensional complementarity
Energy Technology Data Exchange (ETDEWEB)
Crann, Jason, E-mail: jason-crann@carleton.ca [School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6 (Canada); Laboratoire de Mathématiques Paul Painlevé–UMR CNRS 8524, UFR de Mathématiques, Université Lille 1–Sciences et Technologies, 59655 Villeneuve d’Ascq Cédex (France); Kribs, David W., E-mail: dkribs@uoguelph.ca [Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada); Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1 (Canada); Levene, Rupert H., E-mail: rupert.levene@ucd.ie [School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4 (Ireland); Todorov, Ivan G., E-mail: i.todorov@qub.ac.uk [Pure Mathematics Research Centre, Queen’s University Belfast, Belfast BT7 1NN (United Kingdom)
2016-01-15
We introduce a generalized framework for private quantum codes using von Neumann algebras and the structure of commutants. This leads naturally to a more general notion of complementary channel, which we use to establish a generalized complementarity theorem between private and correctable subalgebras that applies to both the finite and infinite-dimensional settings. Linear bosonic channels are considered and specific examples of Gaussian quantum channels are given to illustrate the new framework together with the complementarity theorem.
Finite dimensional quotients of commutative operator algebras
Meyer, R
1997-01-01
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital operator algebras. This allows to define invariant distances on the spectrum of commutative operator algebras analogous to the Caratheodory distance for complex manifolds. Moreover, unitizations of two-dimensional operator algebras with zero multiplication provide a rich class of counterexamples. Especially, several badly behaved quotients of function algebras are exhibited. Recently, Arveson has developed a model theory for d-contractions. Quotients of the operator algebra of the d-shift are much more well-behaved than quotients of function algebras. Completely isometric representations of these quotients are obtained explicitly. This provides a generalization of Nevanlinna-Pick theory. An important property of quotients of the d-shift algebra is that their quotients of finit...
Finite-size scaling at quantum transitions
Campostrini, Massimo; Pelissetto, Andrea; Vicari, Ettore
2014-03-01
We develop the finite-size scaling (FSS) theory at quantum transitions. We consider various boundary conditions, such as open and periodic boundary conditions, and characterize the corrections to the leading FSS behavior. Using renormalization-group (RG) theory, we generalize the classical scaling ansatz to describe FSS in the quantum case, classifying the different sources of scaling corrections. We identify nonanalytic corrections due to irrelevant (bulk and boundary) RG perturbations and analytic contributions due to regular backgrounds and analytic expansions of the nonlinear scaling fields. To check the general predictions, we consider the quantum XY chain in a transverse field. For this model exact or numerically accurate results can be obtained by exploiting its fermionic quadratic representation. We study the FSS of several observables, such as the free energy, the energy differences between low-energy levels, correlation functions of the order parameter, etc., confirming the general predictions in all cases. Moreover, we consider bipartite entanglement entropies, which are characterized by the presence of additional scaling corrections, as predicted by conformal field theory.
Higher (odd dimensional quantum Hall effect and extended dimensional hierarchy
Directory of Open Access Journals (Sweden)
Kazuki Hasebe
2017-07-01
Full Text Available We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S2k−1 in the SO(2k−1 monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S2k−1 to the one-dimension higher SO(2k gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah–Patodi–Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Higher (odd) dimensional quantum Hall effect and extended dimensional hierarchy
Hasebe, Kazuki
2017-07-01
We demonstrate dimensional ladder of higher dimensional quantum Hall effects by exploiting quantum Hall effects on arbitrary odd dimensional spheres. Non-relativistic and relativistic Landau models are analyzed on S 2 k - 1 in the SO (2 k - 1) monopole background. The total sub-band degeneracy of the odd dimensional lowest Landau level is shown to be equal to the winding number from the base-manifold S 2 k - 1 to the one-dimension higher SO (2 k) gauge group. Based on the chiral Hopf maps, we clarify the underlying quantum Nambu geometry for odd dimensional quantum Hall effect and the resulting quantum geometry is naturally embedded also in one-dimension higher quantum geometry. An origin of such dimensional ladder connecting even and odd dimensional quantum Hall effects is illuminated from a viewpoint of the spectral flow of Atiyah-Patodi-Singer index theorem in differential topology. We also present a BF topological field theory as an effective field theory in which membranes with different dimensions undergo non-trivial linking in odd dimensional space. Finally, an extended version of the dimensional hierarchy for higher dimensional quantum Hall liquids is proposed, and its relationship to quantum anomaly and D-brane physics is discussed.
Spacetime Singularities in (2+1)-Dimensional Quantum Gravity
Minassian, E A
2002-01-01
The effects of spacetime quantization on black hole and big bang/big crunch singularities can be studied using new tools from (2+1)-dimensional quantum gravity. I investigate effects of spacetime quantization on singularities of the (2+1)-dimensional BTZ black hole and the (2+1)-dimensional torus universe. Hosoya has considered the BTZ black hole, and using a ``quantum generalized affine parameter'' (QGAP), has shown that, for some specific paths, quantum effects ``smear'' the singularity. Using generic gaussian wave functions, I show that both BTZ black hole and the torus universe contain families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, further support this conclusion.
Spacetime singularities in (2 + 1)-dimensional quantum gravity
Minassian, Eric
2002-12-01
The effects of spacetime quantization on black-hole and big-bang/big-crunch singularities can be studied using new tools from (2 + 1)-dimensional quantum gravity. I investigate effects of spacetime quantization on the singularities of the (2 + 1)-dimensional BTZ black hole and the (2 + 1)-dimensional torus universe. Hosoya has considered the BTZ black hole, and using a 'quantum-generalized affine parameter' (QGAP), has shown that, for some specific paths, quantum effects 'smear' the singularity. Using generic Gaussian wavefunctions, I show that both the BTZ black hole and the torus universe contain families of paths that still reach the singularities with finite QGAPs, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular-invariant wavefunctions of Carlip and Nelson for the torus universe, further support this conclusion.
del Campo, Adolfo; Rams, Marek M; Zurek, Wojciech H
2012-09-14
The dynamics of a quantum phase transition is inextricably woven with the formation of excitations, as a result of critical slowing down in the neighborhood of the critical point. We design a transitionless quantum driving through a quantum critical point, allowing one to access the ground state of the broken-symmetry phase by a finite-rate quench of the control parameter. The method is illustrated in the one-dimensional quantum Ising model in a transverse field. Driving through the critical point is assisted by an auxiliary Hamiltonian, for which the interplay between the range of the interaction and the modes where excitations are suppressed is elucidated.
Quantum correlation and quantum phase transition in the one-dimensional extended Ising model
Zhang, Xi-Zheng; Guo, Jin-Liang
2017-09-01
Quantum phase transitions can be understood in terms of Landau's symmetry-breaking theory. Following the discovery of the quantum Hall effect, a new kind of quantum phase can be classified according to topological rather than local order parameters. Both phases coexist for a class of exactly solvable quantum Ising models, for which the ground state energy density corresponds to a loop in a two-dimensional auxiliary space. Motivated by this we study quantum correlations, measured by entanglement and quantum discord, and critical behavior seen in the one-dimensional extended Ising model with short-range interaction. We show that the quantum discord exhibits distinctive behaviors when the system experiences different topological quantum phases denoted by different topological numbers. Quantum discords capability to detect a topological quantum phase transition is more reliable than that of entanglement at both zero and finite temperatures. In addition, by analyzing the divergent behaviors of quantum discord at the critical points, we find that the quantum phase transitions driven by different parameters of the model can also display distinctive critical behaviors, which provides a scheme to detect the topological quantum phase transition in practice.
Finite Conformal Quantum Gravity and Nonsingular Spacetimes
Modesto, Leonardo
2016-01-01
We explicitly prove that a class of finite quantum gravitational theories (in odd as well as in even dimension) is actually a range of anomaly-free conformally invariant theories in the spontaneously broken phase of the conformal Weyl symmetry. At classical level we show how the Weyl conformal invariance is likely able to tame the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. This latter statement is rigorously proved by a singularity theorem that applies to a large class of weakly non-local theories. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions conformally equivalent to the Schwarzschild metric. Furthermore, we show that the FRW cosmological solutions and the Belinski, Khalatnikov, Lifshitz (BKL) spacetimes, which exactly solve the classical equations of motion, are conformally equivalent to regular spacetimes. Finally, we prove that the ...
Finite key analysis in quantum cryptography
Energy Technology Data Exchange (ETDEWEB)
Meyer, T.
2007-10-31
the obtainable key rate for any finite number of input signals, without making any approximations. As an application, we investigate the so-called ''Tomographic Protocol'', which is based on the Six-State Protocol and where Alice and Bob can obtain the additional information which quantum state they share after the distribution step of the protocol. We calculate the obtainable secret key rate under the assumption that the eavesdropper only conducts collective attacks and give a detailed analysis of the dependence of the key rate on various parameters: The number of input signals (the block size), the error rate in the sifted key (the QBER), and the security parameter. Furthermore, we study the influence of multi-photon events which naturally occur in a realistic implementation (orig.)
Deformed oscillator algebras for two dimensional quantum superintegrable systems
Bonatsos, Dennis; Kokkotas, K D; Bonatsos, Dennis
1994-01-01
Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable systema deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrodinger equation. The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.
Ultraviolet Finite Quantum Field Theory on Quantum Spacetime
Bahns, D; Fredenhagen, Klaus; Piacitelli, G
2003-01-01
We discuss a formulation of quantum field theory on quantum space time where the perturbation expansion of the S-matrix is term by term ultraviolet finite. The characteristic feature of our approach is a quantum version of the Wick product at coinciding points: the differences of coordinates q_j - q_k are not set equal to zero, which would violate the commutation relation between their components. We show that the optimal degree of approximate coincidence can be defined by the evaluation of a conditional expectation which replaces each function of q_j - q_k by its expectation value in optimally localized states, while leaving the mean coordinates (q_1 + ... + q_n)/n invariant. The resulting procedure is to a large extent unique, and is invariant under translations and rotations, but violates Lorentz invariance. Indeed, optimal localization refers to a specific Lorentz frame, where the electric and magnetic parts of the commutator of the coordinates have to coincide*). Employing an adiabatic switching, we show...
Fast-forward scaling in a finite-dimensional Hilbert space
TAKAHASHI, Kazutaka
2014-01-01
Time evolution of quantum systems is accelerated by the fast-forward scaling. We reformulate the method to study systems in a finite-dimensional Hilbert space. For several simple systems, we explicitly construct the acceleration potential. We also use our formulation to accelerate the adiabatic dynamics. Applying the method to the transitionless quantum driving, we find that the fast-forward potential can be understood as a counterdiabatic term.
Effects of symmetry breaking in finite quantum systems
Energy Technology Data Exchange (ETDEWEB)
Birman, J.L. [Department of Physics, City College, City University of New York, New York, NY 10031 (United States); Nazmitdinov, R.G. [Departament de Fisica, Universitat de les Illes Balears, Palma de Mallorca 07122 (Spain); Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 (Russian Federation); Yukalov, V.I., E-mail: yukalov@theor.jinr.ru [Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980 (Russian Federation)
2013-05-15
The review considers the peculiarities of symmetry breaking and symmetry transformations and the related physical effects in finite quantum systems. Some types of symmetry in finite systems can be broken only asymptotically. However, with a sufficiently large number of particles, crossover transitions become sharp, so that symmetry breaking happens similarly to that in macroscopic systems. This concerns, in particular, global gauge symmetry breaking, related to Bose–Einstein condensation and superconductivity, or isotropy breaking, related to the generation of quantum vortices, and the stratification in multicomponent mixtures. A special type of symmetry transformation, characteristic only for finite systems, is the change of shape symmetry. These phenomena are illustrated by the examples of several typical mesoscopic systems, such as trapped atoms, quantum dots, atomic nuclei, and metallic grains. The specific features of the review are: (i) the emphasis on the peculiarities of the symmetry breaking in finite mesoscopic systems; (ii) the analysis of common properties of physically different finite quantum systems; (iii) the manifestations of symmetry breaking in the spectra of collective excitations in finite quantum systems. The analysis of these features allows for the better understanding of the intimate relation between the type of symmetry and other physical properties of quantum systems. This also makes it possible to predict new effects by employing the analogies between finite quantum systems of different physical nature.
High-dimensional quantum cloning and applications to quantum hacking.
Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W; Karimi, Ebrahim
2017-02-01
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography.
High-dimensional quantum cloning and applications to quantum hacking
Bouchard, Frédéric; Fickler, Robert; Boyd, Robert W.; Karimi, Ebrahim
2017-01-01
Attempts at cloning a quantum system result in the introduction of imperfections in the state of the copies. This is a consequence of the no-cloning theorem, which is a fundamental law of quantum physics and the backbone of security for quantum communications. Although perfect copies are prohibited, a quantum state may be copied with maximal accuracy via various optimal cloning schemes. Optimal quantum cloning, which lies at the border of the physical limit imposed by the no-signaling theorem and the Heisenberg uncertainty principle, has been experimentally realized for low-dimensional photonic states. However, an increase in the dimensionality of quantum systems is greatly beneficial to quantum computation and communication protocols. Nonetheless, no experimental demonstration of optimal cloning machines has hitherto been shown for high-dimensional quantum systems. We perform optimal cloning of high-dimensional photonic states by means of the symmetrization method. We show the universality of our technique by conducting cloning of numerous arbitrary input states and fully characterize our cloning machine by performing quantum state tomography on cloned photons. In addition, a cloning attack on a Bennett and Brassard (BB84) quantum key distribution protocol is experimentally demonstrated to reveal the robustness of high-dimensional states in quantum cryptography. PMID:28168219
Universal order parameters and quantum phase transitions: a finite-size approach.
Shi, Qian-Qian; Zhou, Huan-Qiang; Batchelor, Murray T
2015-01-08
We propose a method to construct universal order parameters for quantum phase transitions in many-body lattice systems. The method exploits the H-orthogonality of a few near-degenerate lowest states of the Hamiltonian describing a given finite-size system, which makes it possible to perform finite-size scaling and take full advantage of currently available numerical algorithms. An explicit connection is established between the fidelity per site between two H-orthogonal states and the energy gap between the ground state and low-lying excited states in the finite-size system. The physical information encoded in this gap arising from finite-size fluctuations clarifies the origin of the universal order parameter. We demonstrate the procedure for the one-dimensional quantum formulation of the q-state Potts model, for q = 2, 3, 4 and 5, as prototypical examples, using finite-size data obtained from the density matrix renormalization group algorithm.
Measuring finite quantum geometries via quasi-coherent states
Schneiderbauer, Lukas; Steinacker, Harold C.
2016-07-01
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or ‘fuzzy’ geometries realized by a set of finite-dimensional Hermitian matrices. The method is designed to recover the semi-classical limit of quantized symplectic spaces embedded in {{{R}}}d including the well-known examples of fuzzy spaces, but it applies much more generally. The central tool is provided by quasi-coherent states, which are defined as ground states of Laplace- or Dirac operators corresponding to localized point branes in target space. The displacement energy of these quasi-coherent states is used to extract the local dimension and tangent space of the semi-classical geometry, and provides a measure for the quality and self-consistency of the semi-classical approximation. The method is discussed and tested with various examples, and implemented in an open-source Mathematica package.
Measuring finite Quantum Geometries via Quasi-Coherent States
Schneiderbauer, Lukas
2016-01-01
We develop a systematic approach to determine and measure numerically the geometry of generic quantum or "fuzzy" geometries realized by a set of finite-dimensional hermitian matrices. The method is designed to recover the semi-classical limit of quantized symplectic spaces embedded in $\\mathbb{R}^d$ including the well-known examples of fuzzy spaces, but it applies much more generally. The central tool is provided by quasi-coherent states, which are defined as ground states of Laplace- or Dirac operators corresponding to localized point branes in target space. The displacement energy of these quasi-coherent states is used to extract the local dimension and tangent space of the semi-classical geometry, and provides a measure for the quality and self-consistency of the semi-classical approximation. The method is discussed and tested with various examples, and implemented in an open-source Mathematica package.
Quantum codes from linear codes over finite chain rings
Liu, Xiusheng; Liu, Hualu
2017-10-01
In this paper, we provide two methods of constructing quantum codes from linear codes over finite chain rings. The first one is derived from the Calderbank-Shor-Steane (CSS) construction applied to self-dual codes over finite chain rings. The second construction is derived from the CSS construction applied to Gray images of the linear codes over finite chain ring {\\mathbb {F}}_{p^{2m}}+u{\\mathbb {F}}_{p^{2m}}. The good parameters of quantum codes from cyclic codes over finite chain rings are obtained.
Finiteness of cominuscule quantum K-theory
Buch, Anders; Mihalcea, Leonardo C; Perrin, Nicolas
2010-01-01
The product of two Schubert classes in the quantum K-theory ring of a homogeneous space X = G/P is a formal power series with coefficients in the Grothendieck ring of algebraic vector bundles on X. We show that if X is cominuscule, then this power series has only finitely many non-zero terms. The proof is based on a geometric study of boundary Gromov-Witten varieties in the Kontsevich moduli space, consisting of stable maps to X that take the marked points to general Schubert varieties and whose domains are reducible curves of genus zero. We show that all such varieties have rational singularities, and that boundary Gromov-Witten varieties defined by two Schubert varieties are either empty or unirational. We also prove a relative Kleiman-Bertini theorem for rational singularities, which is of independent interest. A key result is that when X is cominuscule, all boundary Gromov-Witten varieties defined by three single points in X are rationally connected.
Computations in finite-dimensional Lie algebras
Directory of Open Access Journals (Sweden)
A. M. Cohen
1997-12-01
Full Text Available This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System, within the computer algebra package GAP. A first sketch of the package can be found in Cohen and de Graaf[1]. Since then, in a collaborative effort with G. Ivanyos, the authors have continued to develop algorithms which were implemented in ELIAS by the second author. These activities are part of a bigger project, called ACELA and financed by STW, the Dutch Technology Foundation, which aims at an interactive book on Lie algebras (cf. Cohen and Meertens [2]. This paper gives a global description of the main ways in which to present Lie algebras on a computer. We focus on the transition from a Lie algebra abstractly given by an array of structure constants to a Lie algebra presented as a subalgebra of the Lie algebra of n×n matrices. We describe an algorithm typical of the structure analysis of a finite-dimensional Lie algebra: finding a Levi subalgebra of a Lie algebra.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Fodor, Z; Katz, S D; Lellouch, L; Portelli, A; Szabo, K K; Toth, B C
2015-01-01
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Energy Technology Data Exchange (ETDEWEB)
Fodor, Z. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich (Germany); Institute for Theoretical Physics, Eötvös University, H-1117 Budapest (Hungary); Hoelbling, C. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Katz, S.D. [Institute for Theoretical Physics, Eötvös University, H-1117 Budapest (Hungary); MTA-ELTE Lendület Lattice Gauge Theory Research Group, H-1117 Budapest (Hungary); Lellouch, L., E-mail: lellouch@cpt.univ-mrs.fr [CNRS, Aix-Marseille U., U. de Toulon, CPT, UMR 7332, F-13288, Marseille (France); Portelli, A. [School of Physics & Astronomy, University of Southampton, SO17 1BJ (United Kingdom); Szabo, K.K. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany); Jülich Supercomputing Centre, Forschungszentrum Jülich, D-52428 Jülich (Germany); Toth, B.C. [Department of Physics, University of Wuppertal, D-42119 Wuppertal (Germany)
2016-04-10
Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Quantum electrodynamics in finite volume and nonrelativistic effective field theories
Directory of Open Access Journals (Sweden)
Z. Fodor
2016-04-01
Full Text Available Electromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume.
Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
Directory of Open Access Journals (Sweden)
Alexander A. Andrianov
2009-06-01
Full Text Available When several inequivalent supercharges form a closed superalgebra in Quantum Mechanics it entails the appearance of hidden symmetries of a Super-Hamiltonian. We examine this problem in one-dimensional QM for the case of periodic potentials and potentials with finite number of bound states. After the survey of the results existing in the subject the algebraic and analytic properties of hidden-symmetry differential operators are rigorously elaborated in the Theorems and illuminated by several examples.
Examples of bosonic de Finetti states over finite dimensional Hilbert spaces
Gottlieb, A D
2005-01-01
According to the Quantum de Finetti Theorem, locally normal infinite particle states with Bose-Einstein symmetry can be represented as mixtures of infinite tensor powers of vector states. This note presents examples of infinite-particle states with Bose-Einstein symmetry that arise as limits of Gibbs ensembles on finite dimensional spaces, and displays their de Finetti representations. We consider Gibbs ensembles for systems of bosons in a finite dimensional setting and discover limits as the number of particles tends to infinity, provided the temperature is scaled in proportion to particle number.
The Quantum Consistency of the Ten-Dimensional Heterotic String Effective Action
Institute of Scientific and Technical Information of China (English)
Simon Davis
2011-01-01
The finiteness of superstring theory at each order in perturbation theory is considered with respect to the ten-dimensional effective action. The quantum consistency of the ten-dimensional superstring effective action is confirmed with an analysis of the perturbative expansion of the quartic sector. It is found to be compatible with the finiteness of reduced four-dimensional theory. Furthermore, implications for the validity of superstring perturbation theory at lower energies is considered.
Quantum Shape-Phase Transitions in Finite Nuclei
Leviatan, A
2007-01-01
Quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Critical-point Hamiltonians for first- and second-order transitions are identified by resolving them into intrinsic and collective parts. Suitable wave functions and finite-N estimates for observables at the critical-points are derived.
Quantum Shape-Phase Transitions in Finite Nuclei
Energy Technology Data Exchange (ETDEWEB)
Leviatan, A. [Racah Institute of Physics, Hebrew University, Jerusalem 91904 (Israel)
2007-05-15
Quantum shape-phase transitions in finite nuclei are considered in the framework of the interacting boson model. Critical-point Hamiltonians for first- and second-order transitions are identified by resolving them into intrinsic and collective parts. Suitable wave functions and finite-N estimates for observables at the critical-points are derived.
Conductance of a Finite Quantum Wire Connected to Reservoirs
Liu, Yu-Liang
1997-01-01
We study a finite quantum wire connected to external leads, and show that the conductance of the system significantly depends upon the length of the quantum wire and the position of the impurity in it. For a very long quantum wire and the impurity far away from its two ends, the conductance has the same behavior as that for an infinity quantum wire above some very little energy scale. However, for a very short quantum wire, the conductance is independent of the electron-electron interactions ...
Entropic Barriers for Two-Dimensional Quantum Memories
Brown, Benjamin J.; Al-Shimary, Abbas; Pachos, Jiannis K.
2014-03-01
Comprehensive no-go theorems show that information encoded over local two-dimensional topologically ordered systems cannot support macroscopic energy barriers, and hence will not maintain stable quantum information at finite temperatures for macroscopic time scales. However, it is still well motivated to study low-dimensional quantum memories due to their experimental amenability. Here we introduce a grid of defect lines to Kitaev's quantum double model where different anyonic excitations carry different masses. This setting produces a complex energy landscape which entropically suppresses the diffusion of excitations that cause logical errors. We show numerically that entropically suppressed errors give rise to superexponential inverse temperature scaling and polynomial system size scaling for small system sizes over a low-temperature regime. Curiously, these entropic effects are not present below a certain low temperature. We show that we can vary the system to modify this bound and potentially extend the described effects to zero temperature.
The finite-dimensional Freeman thesis.
Rudolph, Lee
2008-06-01
I suggest a modification--and mathematization--of Freeman's thesis on the relations among "perception", "the finite brain", and "the world", based on my recent proposal that the theory of finite topological spaces is both an adequate and a natural mathematical foundation for human psychology.
-Boundedness and -Compactness in Finite Dimensional Probabilistic Normed Spaces
Indian Academy of Sciences (India)
Reza Saadati; Massoud Amini
2005-11-01
In this paper, we prove that in a finite dimensional probabilistic normed space, every two probabilistic norms are equivalent and we study the notion of -compactness and -boundedness in probabilistic normed spaces.
Electronic states in crystals of finite size quantum confinement of bloch waves
Ren, Shang Yuan
2017-01-01
This book presents an analytical theory of the electronic states in ideal low dimensional systems and finite crystals based on a differential equation theory approach. It provides precise and fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and offers new insights into some of the basic problems in low-dimensional systems, such as the surface states and quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community. Many previous predictions have been confirmed in subsequent investigations by other authors on various relevant problems. In this new edition, the theory is further extended to one-dimensional photonic crystals and phononic crystals, and a general theoretical formalism for investigating the existence and properties of surface states/modes in semi-infinite one-dimensional crystals is developed. In addition, there are various revisions and improvements, including us...
Operator spaces and residually finite-dimensional $C^{*}$-algebras
Pestov, V G
1993-01-01
For every operator space $X$ the $C^\\ast$-algebra containing it in a universal way is residually finite-dimensional (that is, has a separating family of finite-dimensional representations). In particular, the free $C^\\ast$-algebra on any normed space so is. This is an extension of an earlier result by Goodearl and Menal, and our short proof is based on a criterion due to Exel and Loring.
Few quantum particles on one dimensional lattices
Energy Technology Data Exchange (ETDEWEB)
Valiente Cifuentes, Manuel
2010-06-18
extended Hubbard models; it is found that the latter can show resonant scattering behavior. A new theorem, which characterizes all two-body bound states on a one-dimensional lattice with arbitrary finite range interactions, is proven here. The methods used for the simplest Hubbard models are then generalized to obtain exact results for arbitrary interactions and particle statistics. The problem of binding and scattering of three identical bosons is studied in detail, finding new types of bound states with no continuous space counterparts. The physics of these trimers is revealed by an effective model which is then applied to ''dimer''-''monomer'' scattering on the lattice. Stationary states of other lattice systems are also considered. First, the problems of binding and scattering of a single particle on a superlattice off a static impurity are analytically solved. Among the results obtained, the presence of a second bound state for any lattice and interaction strengths is highlighted. Second, a model of the harmonic oscillator on the lattice, preserving most of the properties of its continuous space analog, is presented and analytically solved. Two different models, being formally equivalent to the aforementioned lattice oscillator, are then constructed and solved exactly. Quantum transport of a a single particle and a bound particle pair on a onedimensional lattice superimposed with a weak trap is investigated. Based on the knowledge of the results obtained for stationary states, coherent, non-dispersive transport of one and two particles can be achieved. A surprising fact - repulsively bound pairs are tighter bound than those with attractive interaction - is found and physically explained in a simple way. (orig.)
Quantum computation with two-dimensional graphene quantum dots
Institute of Scientific and Technical Information of China (English)
Li Jie-Sen; Li Zhi-Bing; Yao Dao-Xin
2012-01-01
We study an array of graphene nano sheets that form a two-dimensional S =1/2 Kagome spin lattice used for quantum computation.The edge states of the graphene nano sheets axe used to form quantum dots to confine electrons and perform the computation.We propose two schemes of bang-bang control to combat decoherence and realize gate operations on this array of quantum dots.It is shown that both schemes contain a great amount of information for quantum computation.The corresponding gate operations are also proposed.
Dimension and dimensional reduction in quantum gravity
Carlip, S.
2017-10-01
A number of very different approaches to quantum gravity contain a common thread, a hint that spacetime at very short distances becomes effectively two dimensional. I review this evidence, starting with a discussion of the physical meaning of ‘dimension’ and concluding with some speculative ideas of what dimensional reduction might mean for physics.
A construction of full qed using finite dimensional Hilbert space
Francis, Charles
2006-01-01
While causal perturbation theory and lattice regularisation allow treatment of the ultraviolet divergences in qed, they do not resolve the issues of constructive field theory, or show the validity of qed except as a perturbation theory. I present a rigorous construction of quantum and classical electrodynamics from fundamental principles of quantum theory. Hilbert space of dimension N is justified from statements about measurements with finite range and resolution. Using linear combinations o...
On Quantum Estimation, Quantum Cloning and Finite Quantum de Finetti Theorems
Chiribella, Giulio
This paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measure-and-prepare channel that uses optimal estimation to convert M copies into k approximate copies of an unknown pure state and we show that this channel is equal to a random loss of all but s particles followed by cloning from s to k copies. When the number k of output copies is large with respect to the number M of input copies the measure-and-prepare channel converges in diamond norm to the optimal universal cloning. In the opposite case, when M is large compared to k, the estimation becomes almost perfect and the measure-and-prepare channel converges in diamond norm to the partial trace over all but k systems. This result is then used to derive de Finetti-type results for quantum states and for symmetric broadcast channels, that is, channels that distribute quantum information to many receivers in a permutationally invariant fashion. Applications of the finite de Finetti theorem for symmetric broadcast channels include the derivation of diamond-norm bounds on the asymptotic convergence of quantum cloning to state estimation and the derivation of bounds on the amount of quantum information that can be jointly decoded by a group of k receivers at the output of a symmetric broadcast channel.
Contraction of the Finite One-Dimensional Oscillator
Atakishiyev, Natig M.; Pogosyan, George S.; Wolf, Kurt Bernardo
The finite oscillator model of 2j + 1 points has the dynamical algebra u(2), consisting of position, momentum and mode number. It is a paradigm of finite quantum mechanics where a sequence of finite unitary models contract to the well-known continuum theory. We examine its contraction as the number and density of points increase. This is done on the level of the dynamical algebra, of the Schrödinger difference equation, the (Kravchuk) wave functions, and the Fourier-Kravchuk transformation between position and momentum representations.
QED multi-dimensional vacuum polarization finite-difference solver
Carneiro, Pedro; Grismayer, Thomas; Silva, Luís; Fonseca, Ricardo
2015-11-01
The Extreme Light Infrastructure (ELI) is expected to deliver peak intensities of 1023 - 1024 W/cm2 allowing to probe nonlinear Quantum Electrodynamics (QED) phenomena in an unprecedented regime. Within the framework of QED, the second order process of photon-photon scattering leads to a set of extended Maxwell's equations [W. Heisenberg and H. Euler, Z. Physik 98, 714] effectively creating nonlinear polarization and magnetization terms that account for the nonlinear response of the vacuum. To model this in a self-consistent way, we present a multi dimensional generalized Maxwell equation finite difference solver with significantly enhanced dispersive properties, which was implemented in the OSIRIS particle-in-cell code [R.A. Fonseca et al. LNCS 2331, pp. 342-351, 2002]. We present a detailed numerical analysis of this electromagnetic solver. As an illustration of the properties of the solver, we explore several examples in extreme conditions. We confirm the theoretical prediction of vacuum birefringence of a pulse propagating in the presence of an intense static background field [arXiv:1301.4918 [quant-ph
Quantum gases finite temperature and non-equilibrium dynamics
Szymanska, Marzena; Davis, Matthew; Gardiner, Simon
2013-01-01
The 1995 observation of Bose-Einstein condensation in dilute atomic vapours spawned the field of ultracold, degenerate quantum gases. Unprecedented developments in experimental design and precision control have led to quantum gases becoming the preferred playground for designer quantum many-body systems. This self-contained volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose-Einstein condensates, degenerate Fermi gases, and the more recently realised exciton-polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics. Thematically organised chapters on different methodologies, contributed by key researchers using a unified notation, provide the first integrated view of the relative merits of individual approaches, aided by pertinent introductory chapters and the guidance of ed...
Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements
Planat, M R P; Perrine, S; Saniga, M; Planat, Michel R. P.; Rosu, Haret; Perrine, Serge; Saniga, Metod
2004-01-01
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of important mathematical concepts like, e.g., Fourier transforms, Galois fields and rings, finite and related projective geometries, and entanglement, to mention a few. Some applications of the theory to quantum information tasks are also mentioned.
Detecting dimensional crossover and finite Hilbert space through entanglement entropies
Garagiola, Mariano; Cuestas, Eloisa; Pont, Federico M.; Serra, Pablo; Osenda, Omar
2016-01-01
The information content of the two-particle one- and two-dimensional Calogero model is studied using the von Neumann and R\\'enyi entropies. The one-dimensional model is shown to have non-monotonic entropies with finite values in the large interaction strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confine...
Transport through a Finite One-Dimensional Crystal
Kouwenhoven, L.P.; Hekking, F.W.J.; Wees, B.J. van; Harmans, C.J.P.M.; Timmering, C.E.; Foxon, C.T.
1990-01-01
We have studied the magnetotransport properties of an artificial one-dimensional crystal. The crystal consists of a sequence of fifteen quantum dots, defined in the two-dimensional electron gas of a GaAs/AlGaAs heterostructure by means of a split-gate technique. At a fixed magnetic field of 2 T, two
Finite dimensional quotients of commutative operator algebras
Meyer, Ralf
1997-01-01
The matrix normed structure of the unitization of a (non-selfadjoint) operator algebra is determined by that of the original operator algebra. This yields a classification up to completely isometric isomorphism of two-dimensional unital operator algebras. This allows to define invariant distances on the spectrum of commutative operator algebras analogous to the Caratheodory distance for complex manifolds. Moreover, unitizations of two-dimensional operator algebras with zero multiplication pro...
A de Finetti representation for finite symmetric quantum states
König, R; Koenig, Robert; Renner, Renato
2004-01-01
Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.
A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras
Koç, Ayten; Güloğlu, Ismail; Kanuni, Müge; Koc, Ayten; Esin, Songul; Guloglu, Ismail; Kanuni, Muge
2012-01-01
Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings. In this paper we will consider the special case where all division rings are exactly the field K. All such finite dimensional semisimple algebras arise as a finite dimensional Leavitt path algebra. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely detemined specific graph - which we name as a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant {\\kappa}(A) for A and count the number of isomorphism classes of Leavitt path algebras with {\\kappa}(A)=n. Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras of possible trees with a given number of vertices and determine the number of distinct Leavitt path algebras of a line graph with a given number of vertices.
Finite quantum electrodynamics the causal approach
Scharf, Günter
2014-01-01
In this classic text for advanced undergraduates and graduate students of physics, author Günter Scharf carefully analyzes the role of causality in quantum electrodynamics. His approach offers full proofs and detailed calculations of scattering processes in a mathematically rigorous manner. This third edition contains Scharf's revisions and corrections plus a brief new Epilogue on gauge invariance of quantum electrodynamics to all orders. The book begins with Dirac's theory, followed by the quantum theory of free fields and causal perturbation theory, a powerful method that avoids ultraviolet divergences and solves the infrared problem by means of the adiabatic limit. Successive chapters explore properties of the S-matrix — such as renormalizability, gauge invariance, and unitarity — the renormalization group, and interactive fields. Additional topics include electromagnetic couplings and the extension of the methods to non-abelian gauge theories. Each chapter is supplemented with problems, and four appe...
Finite temperature simulations from quantum field dynamics?
Energy Technology Data Exchange (ETDEWEB)
Salle, Mischa; Smit, Jan; Vink, Jeroen C
2001-03-01
We describe a Hartree ensemble method to approximately solve the Heisenberg equations for the phi (cursive,open) Greek{sup 4} model in 1 + 1 dimensions. We compute the energies and number densities of the quantum particles described by the phi (cursive,open) Greek field and find that the particles initially thermalize with a Bose-Einstein distribution for the particle density. Gradually, however, the distribution changes towards classical equipartition. Using suitable initial conditions quantum thermalization is achieved much faster than the onset of this undesirable equipartition. We also show how the numerical efficiency of our method can be significantly improved.
Exact stabilization of entangled states in finite time by dissipative quantum circuits
Johnson, Peter D.; Ticozzi, Francesco; Viola, Lorenza
2017-07-01
Open quantum systems evolving according to discrete-time dynamics are capable, unlike continuous-time counterparts, to converge to a stable equilibrium in finite time with zero error. We consider dissipative quantum circuits consisting of sequences of quantum channels subject to specified quasi-locality constraints, and determine conditions under which stabilization of a pure multipartite entangled state of interest may be exactly achieved in finite time. Special emphasis is devoted to characterizing scenarios where finite-time stabilization may be achieved robustly with respect to the order of the applied quantum maps, as suitable for unsupervised control architectures. We show that if a decomposition of the physical Hilbert space into virtual subsystems is found, which is compatible with the locality constraint and relative to which the target state factorizes, then robust stabilization may be achieved by independently cooling each component. We further show that if the same condition holds for a scalable class of pure states, a continuous-time quasi-local Markov semigroup ensuring rapid mixing can be obtained. Somewhat surprisingly, we find that the commutativity of the canonical parent Hamiltonian one may associate to the target state does not directly relate to its finite-time stabilizability properties, although in all cases where we can guarantee robust stabilization, a (possibly noncanonical) commuting parent Hamiltonian may be found. Aside from graph states, quantum states amenable to finite-time robust stabilization include a class of universal resource states displaying two-dimensional symmetry-protected topological order, along with tensor network states obtained by generalizing a construction due to Bravyi and Vyalyi [Quantum Inf. Comput. 5, 187 (2005)]. Extensions to representative classes of mixed graph-product and thermal states are also discussed.
The Socle and Finite Dimensionality of some Banach Algebras
Indian Academy of Sciences (India)
Ali Ghaffari; Ali Reza Medghalchi
2005-08-01
The purpose of this note is to describe some algebraic conditions on a Banach algebra which force it to be finite dimensional. One of the main results in Theorem 2 which states that for a locally compact group , is compact if there exists a measure in $\\mathrm{Soc} (L^1(G))$ such that () ≠ 0. We also prove that is finite if $\\mathrm{Soc}(M(G))$ is closed and every nonzero left ideal in () contains a minimal left ideal.
Quantum information processing with finite resources mathematical foundations
Tomamichel, Marco
2016-01-01
This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigation possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rényi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rényi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. F...
Fidelity of states in infinite dimensional quantum systems
Hou, Jinchuan
2011-01-01
In this paper we discuss the fidelity of states in infinite dimensional systems, give an elementary proof of the infinite dimensional version of Uhlmann's theorem, and then, apply it to generalize several properties of the fidelity from finite dimensional case to infinite dimensional case. Some of them are somewhat different from those for finite dimensional case.
Finite-Dimensional Representations for Controlled Diffusions with Delay
Energy Technology Data Exchange (ETDEWEB)
Federico, Salvatore, E-mail: salvatore.federico@unimi.it [Università di Milano, Dipartimento di Economia, Management e Metodi Quantitativi (Italy); Tankov, Peter, E-mail: tankov@math.univ-paris-diderot.fr [Université Paris Diderot, Laboratoire de Probabilités et Modèles Aléatoires (France)
2015-02-15
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which the solution of the SDDE and a linear path functional of it admit a finite-dimensional Markovian representation. As a second contribution, we show how approximate finite-dimensional Markovian representations may be constructed when these conditions are not satisfied, and provide an estimate of the error corresponding to these approximations. These results are applied to optimal control and optimal stopping problems for stochastic systems with delay.
Finite-dimensional representations of twisted hyper loop algebras
Bianchi, Angelo
2012-01-01
We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the classification of the irreducible modules, the definition of the universal highest-weight modules, called the Weyl modules, and, under a certain mild restriction on the characteristic of the ground field, a proof that the simple modules and the Weyl modules for the twisted hyper loop algebras are isomorphic to appropriate simple and Weyl modules for the non-twisted hyper loop algebras, respectively, via restriction of the action.
Effects of finite laser pulse width on two-dimensional electronic spectroscopy
Leng, Xuan; Yue, Shuai; Weng, Yu-Xiang; Song, Kai; Shi, Qiang
2017-01-01
We combine the hierarchical equations of motion method and the equation-of-motion phase-matching approach to calculate two-dimensional electronic spectra of model systems. When the laser pulse is short enough, the current method reproduces the results based on third-order response function calculations in the impulsive limit. Finite laser pulse width is found to affect both the peak positions and shapes, as well as the time evolution of diagonal and cross peaks. Simulations of the two-color two-dimensional electronic spectra also show that, to observe quantum beats in the diagonal and cross peaks, it is necessary to excite the related excitonic states simultaneously.
Quantum Simulations of One-Dimensional Nanostructures under Arbitrary Deformations
Koskinen, Pekka
2016-09-01
A powerful technique is introduced for simulating mechanical and electromechanical properties of one-dimensional nanostructures under arbitrary combinations of bending, twisting, and stretching. The technique is based on an unconventional control of periodic symmetry which eliminates artifacts due to deformation constraints and quantum finite-size effects and allows transparent electronic-structure analysis. Via density-functional tight-binding implementation, the technique demonstrates its utility by predicting nonlinear electromechanical properties in carbon nanotubes and abrupt behavior in the structural yielding of Au7 and Mo6 S6 nanowires. The technique drives simulations markedly closer to the realistic modeling of these slender nanostructures under experimental conditions.
On quantum estimation, quantum cloning and finite quantum de Finetti theorems
Chiribella, Giulio
2010-01-01
This paper presents a series of results on the interplay between quantum estimation, cloning and finite de Finetti theorems. First, we consider the measure-and-prepare channel that uses optimal estimation to convert M copies into k approximate copies of an unknown pure state, and we show that for k < M the channel is equal to a random loss of all but s particles followed by cloning from s to k copies. When the number M of input copies is large compared to the number k of output copies, the estimation becomes almost perfect and the measure-and-prepare channel converges in diamond norm to the partial trace over all but k systems. This result is then used to derive de Finetti-type results for quantum states and for symmetric broadcast channels, that is, channels that distribute quantum information to many receivers in a permutationally invariant fashion. Applications of the finite de Finetti theorem for symmetric broadcast channels include the derivation of diamond-norm bounds on the asymptotic convergence of...
Orthogonal apartments in Hilbert Grassmannians. Finite-dimensional case
Pankov, Mark
2015-01-01
Let $H$ be a complex Hilbert space of finite dimension $n\\ge 3$. Denote by ${\\mathcal G}_{k}(H)$ the Grassmannian consisting of $k$-dimensional subspaces of $H$. Every orthogonal apartment of ${\\mathcal G}_{k}(H)$ is defined by a certain orthogonal base of $H$ and consists of all $k$-dimensional subspaces spanned by subsets of this base. For $n\
Digital calculus and finite groups in quantum mechanics
Garcia-Morales, Vladimir
2015-01-01
By means of a digit function that has been introduced in a recent formulation of classical and quantum mechanics, we provide a new construction of some infinite families of finite groups, both abelian and nonabelian, of importance for theoretical, atomic and molecular physics. Our construction is not based on algebraic relationships satisfied by generators, but in establishing the appropriate law of composition that induces the group structure on a finite set of nonnegative integers (the cardinal of the set being equal to the order of the group) thus making computations with finite groups quite straightforward. We establish the abstract laws of composition for infinite families of finite groups including all cyclic groups (and any direct sums of them), dihedral, dicyclic and other metacyclic groups, the symmetric groups of permutations of $p$ symbols and the alternating groups of even permutations. Specific examples are given to illustrate the expressions for the law of composition obtained in each case.
A Remark on the Unitary Group of a Tensor Product of Finite-Dimensional Hilbert Spaces
Indian Academy of Sciences (India)
K R Parthasarathy
2003-02-01
Let $H_i, 1 ≤ i ≤ n$ be complex finite-dimensional Hilbert spaces of dimension $d_i, 1 ≤ i ≤ n$ respectively with $d_i ≥ 2$ for every . By using the method of quantum circuits in the theory of quantum computing as outlined in Nielsen and Chuang [2] and using a key lemma of Jaikumar [1] we show that every unitary operator on the tensor product $H = H_1 \\otimes H_2 \\otimes\\ldots \\otimes H_n$ can be expressed as a composition of a finite number of unitary operators living on pair products $H_i \\otimes H_j, 1 ≤ i, j ≤ n$. An estimate of the number of operators appearing in such a composition is obtained.
Confined two-dimensional fermions at finite density
De Francia, M; Loewe, M; Santangelo, E M; De Francia, M; Falomir, H; Loewe, M; Santangelo, E M
1995-01-01
We introduce the chemical potential in a system of two-dimensional massless fermions, confined to a finite region, by imposing twisted boundary conditions in the Euclidean time direction. We explore in this simple model the application of functional techniques which could be used in more complicated situations.
Characterizations of one-way general quantum finite automata
Li, Lvzhou; Zou, Xiangfu; Li, Lvjun; Wu, Lihua
2009-01-01
In this paper we study a generalized model named one-way general quantum finite automata} (1gQFA), in which each symbol in the input alphabet induces a trace-preserving quantum operation, instead of a unitary transformation. Two different kinds of 1gQFA will be studied: measure-once one-way general quantum finite automata} (MO-1gQFA), and measure-many one-way general quantum finite automata (MM-1gQFA). We prove that MO-1gQFA can recognize all regular languages but only regular languages with bounded error. We prove that MM-1gQFA also recognize only regular languages with bounded error. Thus, MM-1gQFA and MO-1gQFA have the same language recognition power, which is greatly different from the conventional case in which the times of measurement performed in the computation generally affect the language recognition power of one-way QFA. Finally, we present a sufficient and necessary condition for two MM-1gQFA to be equivalent.
Bloch-Like Oscillations in Finite Quantum Structures
DEFF Research Database (Denmark)
Duggen, Lars; Willatzen, Morten; Lassen, Benny;
Inspired by several attempts to generate Bloch-like oscillations in different fields of physics [1,2], we examine a multitude of oscillator systems and interactions that lead to Bloch oscillations in finite quantum structures. A general requirement is the existence of a common period in the time...... of individual quantum wells and changing the coupling strength as a function of position. It is, furthermore, demonstrated that the application of a magnetic field to a structure of quantum wells may lead to the observation of Bloch oscillations (similar to Bloch oscillations stemming from the Stark effect......) and derive rather general mathematical relations between quantum systems that allow the existence of Bloch oscillations. References: [1]: G. Corrielli, A. Crespi, G. Della Valle, S. Longhi, and R. Osellame, Nature Communications 4, 1555 (2013) [2]: H. Sanchis-Alepuz, Y. A. Kosevich, and J. Sanchez...
Regularization independence of finite states in four dimensional quantized gravity
Ita, Eyo
2009-01-01
This is one of a series of works designed to address a major criticism concerning the mathematical rigor of the generalized Kodama states. The present paper analyzes the criterion for finiteness due to cancellation of the ultraviolet divergences stemming from the quantum Hamiltonian constraint, in the full theory. We argue that any reliable state must be independent of the regulating functions and parameters utilized to extract finite results. Using point-splitting regularization, we show that the results, typically regarded either as being purely formal or meaningless, are indeed mathematically rigorous and consistent with the axioms of field theory and regulator independence. Our analysis is carried out at the level of the quantum constraint solutions, and does not consider the algebra of constraints.
Extra-dimensional confinement of quantum particles
Hedin, Eric R
2016-01-01
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and 5th spatial component. A higher-dimensional simple harmonic oscillator confining potential localizes particles into 3-d space, characterizing the brane tension which confines Standard Model particles to the sub-manifold. Quantum effects allow a non-zero probability for a particle's evanescent existence in the higher dimensions, and suggest an experimental test for the validity of this model via particles being temporarily excited into the first excited state of the extra-dimensional potential well, in which their probability of existing in 3-d space transiently drops to zero. Several consistency checks of the outcomes of this extra-dimensional model are included in this paper. Among the outcomes of this model are: a match with the quantum phenomenon of zitterbewegung; the pr...
Finite quantum corrections to the tribimaximal neutrino mixing
Energy Technology Data Exchange (ETDEWEB)
Araki, Takeshi, E-mail: araki@ihep.ac.c [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Geng, Chao-Qiang, E-mail: geng@phys.nthu.edu.t [Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwan (China); Xing Zhizhong, E-mail: xingzz@ihep.ac.c [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China)
2011-05-16
We calculate finite quantum corrections to the tribimaximal neutrino mixing pattern V{sub TB} in three generic classes of neutrino mass models. We show that three flavor mixing angles can all depart from their tree-level results described by V{sub TB}, among which {theta}{sub 12} is most sensitive to such quantum effects, and the Dirac CP-violating phase can radiatively arise from two Majorana CP-violating phases. This theoretical scheme offers a new way to understand why {theta}{sub 13} is naturally small and how three CP-violating phases are presumably correlated.
The quantum Ising model: finite sums and hyperbolic functions
Damski, Bogdan
2015-10-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn and Ryzhik Table of Integrals, Series, and Products.
The quantum Ising model: finite sums and hyperbolic functions
Bogdan Damski
2015-01-01
We derive exact closed-form expressions for several sums leading to hyperbolic functions and discuss their applicability for studies of finite-size Ising spin chains. We show how they immediately lead to closed-form expressions for both fidelity susceptibility characterizing the quantum critical point and the coefficients of the counterdiabatic Hamiltonian enabling arbitrarily quick adiabatic driving of the system. Our results generalize and extend the sums presented in the popular Gradshteyn...
Finite dimensional thermo-mechanical systems and second order constraints
Cendra, Hernán; Amaya, Maximiliano Palacios
2016-01-01
In this paper we study a class of physical systems that combine a finite number of mechanical and thermodynamic observables. We call them finite dimensional thermo-mechanical systems. We introduce these systems by means of simple examples. The evolution equations of the involved observables are obtained in each example by using, essentially, the Newton's law and the First Law of Thermodynamics only. We show that such equations are similar to those defining certain mechanical systems with higher order constraints. Moreover, we show that all of the given examples can be described in a variational formalism in terms of second order constrained systems.
Quantum electrodynamic effects in finite space
Dobiasch, P.; Walther, H.
The modifications of various quantum properties due to a discrete structure of the modes of the vacuum electromagnetic field are discussed. In contrast to the usual case of a continuous spectrum of the free space fluctuations, we consider physical systems in a resonator or in a wave guide. It is shown that the relaxation time of the system can be increased ot decreased, by increasing or decreasing the density of modes with respect to the case of unperturbed vacuum. On the other hand, we predict level shifts due to the reduced mass of the electron and deviations from the Lambshift for hydrogen in a wave guide, which can be detected with the presently feasible high resolution spectroscopy. We propose an experimental set-up. Nous discutons les modifications de diverses propriétés quantiques sous l'influence d'une structure de modes discrets du champ électromagnétique dans le vide. En comparaison du cas habituel d'un spectre continu des fluctuations du vide dans l'espace libre, nous considérons ici des systèmes physiques dans un résonateur ou un guide d'ondes. Il est démontré que le temps de relaxation du système peut être prolongé ou raccourci, ceci en augmentant ou diminuant la densité des modes par rapport à sa valeur dans le vide non-perturbé. D'autre part, nous prédisons des déplacements de niveau dus à la masse réduite de l'électron et des déviations du Lamb shift pour des atomes d'hydrogène dans un guide d'ondes, qui peuvent être détectées grâce à la haute résolution accessible actuellement en spectroscopie. Nous présentons un dispositif expérimental.
Perturbative algebraic quantum field theory at finite temperature
Energy Technology Data Exchange (ETDEWEB)
Lindner, Falk
2013-08-15
We present the algebraic approach to perturbative quantum field theory for the real scalar field in Minkowski spacetime. In this work we put a special emphasis on the inherent state-independence of the framework and provide a detailed analysis of the state space. The dynamics of the interacting system is constructed in a novel way by virtue of the time-slice axiom in causal perturbation theory. This method sheds new light in the connection between quantum statistical dynamics and perturbative quantum field theory. In particular it allows the explicit construction of the KMS and vacuum state for the interacting, massive Klein-Gordon field which implies the absence of infrared divergences of the interacting theory at finite temperature, in particular for the interacting Wightman and time-ordered functions.
Momentum Dynamics of One Dimensional Quantum Walks
Fuss, I; Sherman, P J; Naguleswaran, S; Fuss, Ian; White, langord B.; Sherman, Peter J.; Naguleswaran, Sanjeev
2006-01-01
We derive the momentum space dynamic equations and state functions for one dimensional quantum walks by using linear systems and Lie group theory. The momentum space provides an analytic capability similar to that contributed by the z transform in discrete systems theory. The state functions at each time step are expressed as a simple sum of three Chebyshev polynomials. The functions provide an analytic expression for the development of the walks with time.
Finite dimensional semigroup quadratic algebras with minimal number of relations
Iyudu, Natalia
2011-01-01
A quadratic semigroup algebra is an algebra over a field given by the generators $x_1,...,x_n$ and a finite set of quadratic relations each of which either has the shape $x_jx_k=0$ or the shape $x_jx_k=x_lx_m$. We prove that a quadratic semigroup algebra given by $n$ generators and $d\\leq \\frac{n^2+n}{4}$ relations is always infinite dimensional. This strengthens the Golod--Shafarevich estimate for the above class of algebras. Our main result however is that for every $n$, there is a finite dimensional quadratic semigroup algebra with $n$ generators and $\\delta_n$ generators, where $\\delta_n$ is the first integer greater than $\\frac{n^2+n}{4}$. This shows that the above Golod-Shafarevich type estimate for semigroup algebras is sharp.
How to derive Feynman diagrams for finite-dimensional integrals directly from the BV formalism
Gwilliam, Owen
2012-01-01
The Batalin-Vilkovisky formalism in quantum field theory was originally invented to avoid the difficult problem of finding diagrammatic descriptions of oscillating integrals with degenerate critical points. But since then, BV algebras have become interesting objects of study in their own right, and mathematicians sometimes have good understanding of the homological aspects of the story without any access to the diagrammatics. In this note we reverse the usual direction of argument: we begin by asking for an explicit calculation of the homology of a BV algebra, and from it derive Wick's Theorem and the other Feynman rules for finite-dimensional integrals.
Optimal state estimation for d-dimensional quantum systems
Bruss, D
1999-01-01
We establish a connection between optimal quantum cloning and optimal state estimation for d-dimensional quantum systems. In this way we derive an upper limit on the fidelity of state estimation for d-dimensional pure quantum states and, furthermore, for generalized inputs supported on the symmetric subspace.
Form factors of the finite quantum XY-chain
Energy Technology Data Exchange (ETDEWEB)
Iorgov, Nikolai, E-mail: iorgov@bitp.kiev.ua [Bogolyubov Institute for Theoretical Physics, Kiev 03680 (Ukraine)
2011-08-19
Explicit factorized formulas for the matrix elements (form factors) of the spin operators {sigma}{sup x} and {sigma}{sup y} between the eigenvectors of the Hamiltonian of the finite quantum periodic XY-chain in a transverse field were derived. The derivation is based on the relations between three models: the model of quantum XY-chain, Ising model on 2D lattice and N = 2 Baxter-Bazhanov-Stroganov {tau}{sup (2)}-model. Due to these relations we transfer the formulas for the form factors of the latter model recently obtained by the use of separation of variables method to the model of quantum XY-chain. Hopefully, the formulas for the form factors will help in analysis of multipoint dynamic correlation functions at a finite temperature. As an example, we re-derive the asymptotics of the two-point correlation function in the disordered phase without the use of the Toeplitz determinants and the Wiener-Hopf factorization method.
Finite temperature quantum correlations in su(2)(c) quark states and quantum spin models
Hamieh, S; Tawfik, A
2005-01-01
The entanglement at finite temperatures is analyzed by using thermal models for colored quarks making tip the hadron physical states. We have found that these quantum correlations entirely vanish at T-c >= m(q)/ln(1.5). For temperatures larger than T-c the correlations are classical. We have also wo
Wenzel, Sandro; Bogacz, Leszek; Janke, Wolfhard
2008-09-19
The two-dimensional J-J' dimerized quantum Heisenberg model is studied on the square lattice by means of (stochastic series expansion) quantum Monte Carlo simulations as a function of the coupling ratio alpha=J'/J. The critical point of the order-disorder quantum phase transition in the J-J' model is determined as alpha_c=2.5196(2) by finite-size scaling for up to approximately 10 000 quantum spins. By comparing six dimerized models we show, contrary to the current belief, that the critical exponents of the J-J' model are not in agreement with the three-dimensional classical Heisenberg universality class. This lends support to the notion of nontrivial critical excitations at the quantum critical point.
Transport through Zero-Dimensional States in a Quantum Dot
Kouwenhoven, Leo P.; Wees, Bart J. van; Harmans, Kees J.P.M.; Williamson, John G.
1990-01-01
We have studied the electron transport through zero-dimensional (0D) states. 0D states are formed when one-dimensional edge channels are confined in a quantum dot. The quantum dot is defined in a two-dimensional electron gas with a split gate technique. To allow electronic transport, connection to
Finite-dimensional attractors for the Kirchhoff models
Zhijian, Yang
2010-09-01
The paper studies the existence of the finite-dimensional global attractor and exponential attractor for the dynamical system associated with the Kirchhoff models arising in elasto-plastic flow utt-div{|∇u|m -1∇u}-Δut+Δ2u+h(ut)+g(u)=f(x). By using the method of ℓ-trajectories and the operator technique, it proves that under subcritical case, 1≤m
Towards quantum turbulence in finite temperature Bose-Einstein condensates
Energy Technology Data Exchange (ETDEWEB)
Lan, Shanquan [Department of Physics, Beijing Normal University,Beijing, 100875 (China); Tian, Yu [School of Physics, University of Chinese Academy of Sciences,Beijing, 100049 (China); Shanghai Key Laboratory of High Temperature Superconductors,Shanghai, 200444 (China); Zhang, Hongbao [Department of Physics, Beijing Normal University,Beijing, 100875 (China); Theoretische Natuurkunde, Vrije Universiteit Brussel, andThe International Solvay Institutes,Pleinlaan 2, Brussels, B-1050 (Belgium)
2016-07-19
Motivated by the various indications that holographic superfluid is BCS like at the standard quantization but BEC like at the alternative quantization, we have implemented the alternative quantization in the dynamical holographic superfluid for the first time. With this accomplishment, we further initiate the detailed investigation of quantum turbulence in finite temperature BEC by a long time stable numerical simulation of bulk dynamics, which includes the two body decay of vortex number caused by vortex pair annihilation, the onset of superfluid turbulence signaled by Kolmogorov scaling law, and a direct energy cascade demonstrated by injecting energy to the turbulent superfluid. All of these results share the same patterns as the holographic superfluid at the standard quantization, thus suggest that these should be universal features for quantum turbulence at temperatures order of the critical temperature.
Towards quantum turbulence in finite temperature Bose-Einstein condensates
Lan, Shanquan; Tian, Yu; Zhang, Hongbao
2016-07-01
Motivated by the various indications that holographic superfluid is BCS like at the standard quantization but BEC like at the alternative quantization, we have implemented the alternative quantization in the dynamical holographic superfluid for the first time. With this accomplishment, we further initiate the detailed investigation of quantum turbulence in finite temperature BEC by a long time stable numerical simulation of bulk dynamics, which includes the two body decay of vortex number caused by vortex pair annihilation, the onset of superfluid turbulence signaled by Kolmogorov scaling law, and a direct energy cascade demonstrated by injecting energy to the turbulent superfluid. All of these results share the same patterns as the holographic superfluid at the standard quantization, thus suggest that these should be universal features for quantum turbulence at temperatures order of the critical temperature.
Towards Quantum Turbulence in Finite Temperature Bose-Einstein Condensates
Lan, Shanquan; Zhang, Hongbao
2016-01-01
Motivated by the various indications that holographic superfluid is BCS like at the standard quantization but BEC like at the alternative quantization, we have implemented the alternative quantization in the dynamical holographic superfluid for the first time. With this accomplishment, we further initiate the detailed investigation of quantum turbulence in finite temperature BEC by a long time stable numerical simulation of bulk dynamics, which includes the two body decay of vortex number caused by vortex pair annihilation, the onset of superfluid turbulence signaled by Kolmogorov scaling law, and a direct energy cascade demonstrated by injecting energy to the turbulent superfluid. All of these results share the same patterns as the holographic superfluid at the standard quantization, thus suggest that these should be universal features for quantum turbulence at temperatures order of the critical temperature.
Finite quantum corrections to the tribimaximal neutrino mixing
Araki, Takeshi; Xing, Zhi-zhong
2010-01-01
We calculate finite quantum corrections to the tribimaximal neutrino mixing pattern V_TB in three generic classes of neutrino mass models. We show that three flavor mixing angles can all depart from their tree-level results described by V_TB, and the Dirac CP-violating phase can radiatively arise from two Majorana CP-violating phases. This theoretical scheme offers a new way to understand why one neutrino mixing angle is naturally small and how three CP-violating phases are presumably correlated.
Quantum tunneling from high dimensional G\\"odel black hole
Li, Hui-Ling; Zu, Xiao-Tao
2014-01-01
Considering quantum gravity effect, we investigate the quantum tunneling from high dimensional Kerr-G\\"odel black hole using generalized Dirac equation. As a result, revised tunneling probability is obtained, and the corrected Hawking temperature is also presented.
Finite Element Analysis to Two-Dimensional Nonlinear Sloshing Problems
Institute of Scientific and Technical Information of China (English)
严承华; 王赤忠; 程尔升
2001-01-01
A two-dimensional nonlinear sloshing problem is analyzed by means of the fully nonlinear theory and time domainsecond order theory of water waves. Liquid sloshing in a rectangular container subjected to a horizontal excitation is sim-ulated by the finite element method. Comparisons between the two theories are made based on their numerical results. Itis found that good agreement is obtained for the case of small amplitude oscillation and obvious differences occur forlarge amplitude excitation. Even though, the second order solution can still exhibit typical nonlinear features ofnonlinear wave and can be used instead of the fully nonlinear theory.
Complete controllability of finite quantum systems with twofold energy level degeneracy
Energy Technology Data Exchange (ETDEWEB)
Zhang Zhedong; Fu, H C, E-mail: hcfu@szu.edu.c [School of Physical Sciences and Technology, Shenzhen University, Shenzhen 518060 (China)
2010-05-28
Complete controllability of finite-dimensional quantum systems with energy level degeneracy is investigated using two different approaches. One approach is to apply a weak constant field to eliminate the degeneracy and then control it using techniques developed for non-degenerate quantum systems. Conditions for the elimination of degeneracy are found and the issues of influence of relaxation time of a constant external field on the target state are addressed through the fidelity. Another approach is to control the degenerate system by a single control field directly. It is found that the system with twofold degenerate excited states and non-degenerate ground state is completely controllable except for the two-level system. Conditions of complete controllability are found for both systems with different energy gaps and with equal energy gaps.
Double quantum dot Cooper-pair splitter at finite couplings
Hussein, Robert; Jaurigue, Lina; Governale, Michele; Braggio, Alessandro
2016-12-01
We consider the subgap physics of a hybrid double-quantum dot Cooper-pair splitter with large single-level spacings, in the presence of tunneling between the dots and finite Coulomb intra- and interdot Coulomb repulsion. In the limit of a large superconducting gap, we treat the coupling of the dots to the superconductor exactly. We employ a generalized master-equation method, which easily yields currents, noise, and cross-correlators. In particular, for finite inter- and intradot Coulomb interaction, we investigate how the transport properties are determined by the interplay between local and nonlocal tunneling processes between the superconductor and the dots. We examine the effect of interdot tunneling on the particle-hole symmetry of the currents with and without spin-orbit interaction. We show that spin-orbit interaction in combination with finite Coulomb energy opens the possibility to control the nonlocal entanglement and its symmetry (singlet/triplet). We demonstrate that the generation of nonlocal entanglement can be achieved even without any direct nonlocal coupling to the superconducting lead.
On the Maximal Dimension of a Completely Entangled Subspace for Finite Level Quantum Systems
Indian Academy of Sciences (India)
K R Parthasarathy
2004-11-01
Let $\\mathcal{H}_i$ be a finite dimensional complex Hilbert space of dimension $d_i$ associated with a finite level quantum system $A_i$ for $i=1, 2,\\ldots,k$. A subspace $S\\subset\\mathcal{H} = \\mathcal{H}_{A_1 A_2\\ldots A_k} = \\mathcal{H}_1 \\otimes \\mathcal{H}_2 \\otimes\\cdots\\otimes \\mathcal{H}_k$ is said to be completely entangled if it has no non-zero product vector of the form $u_1 \\otimes u_2 \\otimes\\cdots\\otimes u_k$ with $u_i$ in $\\mathcal{H}_i$ for each . Using the methods of elementary linear algebra and the intersection theorem for projective varieties in basic algebraic geometry we prove that $$\\max\\limits_{S\\in\\mathcal{E}}\\dim S=d_1 d_2\\ldots d_k-(d_1+\\cdots +d_k)+k-1,$$ where $\\mathcal{E}$ is the collection of all completely entangled subspaces. When $\\mathcal{H}_1 = \\mathcal{H}_2$ and $k = 2$ an explicit orthonormal basis of a maximal completely entangled subspace of $\\mathcal{H}_1 \\otimes \\mathcal{H}_2$ is given. We also introduce a more delicate notion of a perfectly entangled subspace for a multipartite quantum system, construct an example using the theory of stabilizer quantum codes and pose a problem.
Three-dimensional finite element analysis of platform switched implant
2017-01-01
PURPOSE The purpose of this study was to analyze the influence of the platform switching concept on an implant system and peri-implant bone using three-dimensional finite element analysis. MATERIALS AND METHODS Two three-dimensional finite element models for wide platform and platform switching were created. In the wide platform model, a wide platform abutment was connected to a wide platform implant. In the platform switching model, the wide platform abutment of the wide platform model was replaced by a regular platform abutment. A contact condition was set between the implant components. A vertical load of 300 N was applied to the crown. The maximum von Mises stress values and displacements of the two models were compared to analyze the biomechanical behavior of the models. RESULTS In the two models, the stress was mainly concentrated at the bottom of the abutment and the top surface of the implant in both models. However, the von Mises stress values were much higher in the platform switching model in most of the components, except for the bone. The highest von Mises values and stress distribution pattern of the bone were similar in the two models. The components of the platform switching model showed greater displacement than those of the wide platform model. CONCLUSION Due to the stress concentration generated in the implant and the prosthodontic components of the platform switched implant, the mechanical complications might occur when platform switching concept is used. PMID:28243389
Super-renormalizable or finite Lee-Wick quantum gravity
Modesto, Leonardo
2016-08-01
We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2 = 0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee-Wick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named ;anti-gravitons; because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-renormalizable or finite Lee-Wick standard model of particle physics.
Super-renormalizable or finite Lee–Wick quantum gravity
Directory of Open Access Journals (Sweden)
Leonardo Modesto
2016-08-01
Full Text Available We propose a class of multidimensional higher derivative theories of gravity without extra real degrees of freedom besides the graviton field. The propagator shows up the usual real graviton pole in k2=0 and extra complex conjugates poles that do not contribute to the absorptive part of the physical scattering amplitudes. Indeed, they may consistently be excluded from the asymptotic observable states of the theory making use of the Lee–Wick and Cutkosky, Landshoff, Olive and Polkinghorne prescription for the construction of a unitary S-matrix. Therefore, the spectrum consists of the graviton and short lived elementary unstable particles that we named “anti-gravitons” because of their repulsive contribution to the gravitational potential at short distance. However, another interpretation of the complex conjugate pairs is proposed based on the Calmet's suggestion, i.e. they could be understood as black hole precursors long established in the classical theory. Since the theory is CPT invariant, the conjugate complex of the micro black hole precursor can be interpreted as a white hole precursor consistently with the 't Hooft complementarity principle. It is proved that the quantum theory is super-renormalizable in even dimension, i.e. only a finite number of divergent diagrams survive, and finite in odd dimension. Furthermore, turning on a local potential of the Riemann tensor we can make the theory finite in any dimension. The singularity-free Newtonian gravitational potential is explicitly computed for a range of higher derivative theories. Finally, we propose a new super-renormalizable or finite Lee–Wick standard model of particle physics.
Bouchoule, I.; Szigeti, S. S.; Davis, M. J.; Kheruntsyan, K. V.
2016-11-01
We develop a finite-temperature hydrodynamic approach for a harmonically trapped one-dimensional quasicondensate and apply it to describe the phenomenon of frequency doubling in the breathing-mode oscillations of the quasicondensate momentum distribution. The doubling here refers to the oscillation frequency relative to the oscillations of the real-space density distribution, invoked by a sudden confinement quench. By constructing a nonequilibrium phase diagram that characterizes the regime of frequency doubling and its gradual disappearance, we find that this crossover is governed by the quench strength and the initial temperature rather than by the equilibrium-state crossover from the quasicondensate to the ideal Bose gas regime. The hydrodynamic predictions are supported by the results of numerical simulations based on a finite-temperature c -field approach and extend the utility of the hydrodynamic theory for low-dimensional quantum gases to the description of finite-temperature systems and their dynamics in momentum space.
Strain distributions and electronic structure of three-dimensional InAs/GaAs quantum rings
Institute of Scientific and Technical Information of China (English)
Liu Yu-Min; Yu Zhong-Yuan; Jia Bo-Yong; Xu Zi-Huan; Yao Wen-Jie; Chen Zhi-Hui; Lu Peng-Fei
2009-01-01
This paper presents a finite element calculation for the electronic structure and strain distribution of self-organized InAs/GaAs quantum rings, The strain distribution calculations are based on the continuum elastic theory. An ideal three-dimensional circular quantum ring model is adopted in this work. The electron and heavy-hole energy levels of the InAs/GaAs quantum rings are calculated by solving the three-dimensional effective mass Schrodinger equation including the deformation potential and piezoelectric potential up to the second order induced by the strain. The calculated results show the importance of strain and piezoelectric effects, and these effects should be taken into consideration in analysis of the optoelectronic characteristics of strain quantum rings.
Quantum dynamics at finite temperature: Time-dependent quantum Monte Carlo study
Energy Technology Data Exchange (ETDEWEB)
Christov, Ivan P., E-mail: ivan.christov@phys.uni-sofia.bg
2016-08-15
In this work we investigate the ground state and the dissipative quantum dynamics of interacting charged particles in an external potential at finite temperature. The recently devised time-dependent quantum Monte Carlo (TDQMC) method allows a self-consistent treatment of the system of particles together with bath oscillators first for imaginary-time propagation of Schrödinger type of equations where both the system and the bath converge to their finite temperature ground state, and next for real time calculation where the dissipative dynamics is demonstrated. In that context the application of TDQMC appears as promising alternative to the path-integral related techniques where the real time propagation can be a challenge.
Quantum-corrected finite entropy of noncommutative acoustic black holes
Anacleto, M A; Luna, G C; Passos, E; Spinelly, J
2015-01-01
In this paper we consider the generalized uncertainty principle in the tunneling formalism via Hamilton-Jacobi method to determine the quantum-corrected Hawking temperature and entropy for 2+1-dimensional noncommutative acoustic black holes. In our results we obtain an area entropy, a correction logarithmic in leading order, a correction term in subleading order proportional to the radiation temperature associated with the noncommutative acoustic black holes and an extra term that depends on a conserved charge. Thus, as in the gravitational case, there is no need to introduce the ultraviolet cut-off and divergences are eliminated.
Optimal eavesdropping in cryptography with three-dimensional quantum states.
Bruss, D; Macchiavello, C
2002-03-25
We study optimal eavesdropping in quantum cryptography with three-dimensional systems, and show that this scheme is more secure against symmetric attacks than protocols using two-dimensional states. We generalize the according eavesdropping transformation to arbitrary dimensions, and discuss the connection with optimal quantum cloning.
Song, Huimin
In the aerospace and automotive industries, many finite element analyses use lower-dimensional finite elements such as beams, plates and shells, to simplify the modeling. These simplified models can greatly reduce the computation time and cost; however, reduced-dimensional models may introduce inaccuracies, particularly near boundaries and near portions of the structure where reduced-dimensional models may not apply. Another factor in creation of such models is that beam-like structures frequently have complex geometry, boundaries and loading conditions, which may make them unsuitable for modeling with single type of element. The goal of this dissertation is to develop a method that can accurately and efficiently capture the response of a structure by rigorous combination of a reduced-dimensional beam finite element model with a model based on full two-dimensional (2D) or three-dimensional (3D) finite elements. The first chapter of the thesis gives the background of the present work and some related previous work. The second chapter is focused on formulating a system of equations that govern the joining of a 2D model with a beam model for planar deformation. The essential aspect of this formulation is to find the transformation matrices to achieve deflection and load continuity on the interface. Three approaches are provided to obtain the transformation matrices. An example based on joining a beam to a 2D finite element model is examined, and the accuracy of the analysis is studied by comparing joint results with the full 2D analysis. The third chapter is focused on formulating the system of equations for joining a beam to a 3D finite element model for static and free-vibration problems. The transition between the 3D elements and beam elements is achieved by use of the stress recovery technique of the variational-asymptotic method as implemented in VABS (the Variational Asymptotic Beam Section analysis). The formulations for an interface transformation matrix and
Frehner, Marcel; Schmalholz, Stefan M.; Saenger, Erik H.; Steeb, Holger
2008-01-01
Two-dimensional scattering of elastic waves in a medium containing a circular heterogeneity is investigated with an analytical solution and numerical wave propagation simulations. Different combinations of finite difference methods (FDM) and finite element methods (FEM) are used to numerically solve
Frehner, Marcel; Schmalholz, Stefan M.; Saenger, Erik H.; Steeb, Holger Karl
2008-01-01
Two-dimensional scattering of elastic waves in a medium containing a circular heterogeneity is investigated with an analytical solution and numerical wave propagation simulations. Different combinations of finite difference methods (FDM) and finite element methods (FEM) are used to numerically solve
Decay Process of Quantum Open System at Finite Temperatures
Institute of Scientific and Technical Information of China (English)
肖骁; 高一波
2012-01-01
Starting from the formal solution to the Heisenberg equation, we revisit an universal model for a quantum open system with a harmonic oscillator linearly coupled to a boson bath. The analysis of the decay process for a Fock state and a coherent state demonstrate that this method is very useful in dealing with the problems in decay process of the open system. For finite temperatures, the calculations of the reduced density matrix and the mean excitation number for the open system show that an initiaJ coherent state will evolve into a temperature-dependant coherent state after tracing over the bath variables. Also in short-time limit, a temperature-dependant effective Hamiltonian for the open system characterizes the decay process of the open system.
Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots
Energy Technology Data Exchange (ETDEWEB)
Cundiff, Steven T. [Univ. of Colorado, Boulder, CO (United States)
2016-05-03
This final report describes the activities undertaken under grant "Optical Two-Dimensional Spectroscopy of Disordered Semiconductor Quantum Wells and Quantum Dots". The goal of this program was to implement optical 2-dimensional Fourier transform spectroscopy and apply it to electronic excitations, including excitons, in semiconductors. Specifically of interest are quantum wells that exhibit disorder due to well width fluctuations and quantum dots. In both cases, 2-D spectroscopy will provide information regarding coupling among excitonic localization sites.
Continuous variable quantum teleportation with a finite-basis entanglement resource
Kurzeja, S I J
2002-01-01
Entanglement is a crucial resource in quantum information theory. We investigate the use of different forms of entangled states in continuous variable quantum teleportation, specifically the use of a finite-basis entanglement resource. We also consider the continuous variable teleportation of finite-basis states, such as qubits, and present results that point to the possibility of an efficient conditional scheme for continuous variable teleportation of such states with near-unit fidelity using finite-basis entanglement.
Effect of finite phosphor thickness on detective quantum efficiency
Energy Technology Data Exchange (ETDEWEB)
Nishikawa, R.M.; Yaffe, M.J.; Holmes, R.B. (Univ. of Toronto (Canada))
1989-09-01
In this paper we describe theoretically the relationship between the finite thickness of a phosphor screen and its spatial-frequency-dependent detective quantum efficiency DQE(f-). The finite thickness of the screen causes a variation in both the total number of light quanta emitted from the screen in a burst from a given x-ray interaction and in the spatial distribution of the quanta within the light burst (i.e., shape or point spread function (PSF) of the light burst). The variation in magnitude of the burst gives rise to a spatial-frequency-independent reduction in DQE, characterized by the scintillation efficiency As. The variation in PSF causes a roll off in DQE with increasing spatial frequency which we have characterized by the function Rc(f). Both As and Rc(f) can be determined from the moments of the distribution of the spatial Fourier spectrum of light bursts emitted from the phosphor and thus they are related: As is a scaling factor for Rc(f). Our theory predicts that it is necessary for all light bursts which appear at the output to have the same magnitude to maximize As and the same shape to maximize Rc(f). These requirements can lead to the result that the fluorescent screen with the highest modulation transfer function will not necessarily have the highest DQE(f) even at high spatial frequencies.
Sifting attacks in finite-size quantum key distribution
Pfister, Corsin; Lütkenhaus, Norbert; Wehner, Stephanie; Coles, Patrick J.
2016-05-01
A central assumption in quantum key distribution (QKD) is that Eve has no knowledge about which rounds will be used for parameter estimation or key distillation. Here we show that this assumption is violated for iterative sifting, a sifting procedure that has been employed in some (but not all) of the recently suggested QKD protocols in order to increase their efficiency. We show that iterative sifting leads to two security issues: (1) some rounds are more likely to be key rounds than others, (2) the public communication of past measurement choices changes this bias round by round. We analyze these two previously unnoticed problems, present eavesdropping strategies that exploit them, and find that the two problems are independent. We discuss some sifting protocols in the literature that are immune to these problems. While some of these would be inefficient replacements for iterative sifting, we find that the sifting subroutine of an asymptotically secure protocol suggested by Lo et al (2005 J. Cryptol. 18 133-65), which we call LCA sifting, has an efficiency on par with that of iterative sifting. One of our main results is to show that LCA sifting can be adapted to achieve secure sifting in the finite-key regime. More precisely, we combine LCA sifting with a certain parameter estimation protocol, and we prove the finite-key security of this combination. Hence we propose that LCA sifting should replace iterative sifting in future QKD implementations. More generally, we present two formal criteria for a sifting protocol that guarantee its finite-key security. Our criteria may guide the design of future protocols and inspire a more rigorous QKD analysis, which has neglected sifting-related attacks so far.
Information Tradeoff Relations for Finite-Strength Quantum Measurements
Fuchs, C; Fuchs, Christopher A.; Jacobs, Kurt
2001-01-01
In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a two-state quantum system. The question we address is to what extent one observer can, by measurement, increase the purity of his density operator without affecting the purity of the other observer's. If there were no restrictions on the first observer's measurements, then he could carry this out trivially by measuring the initial density operator's eigenbasis. If, however, the allowed measurements are those of finite strength---i.e., those measurements strictly within the interior of the convex set of all measurements---then the issue becomes significantly more complex. We find that for a large class of such measurements the first observer's purity increases the most precisely when there is some loss of purity for the second observer. More generally the tradeoff between the two pur...
Quantum entanglement in a two-dimensional ion trap
Institute of Scientific and Technical Information of China (English)
王成志; 方卯发
2003-01-01
In this paper, we investigate the quantum entanglement in a two-dimensional ion trap system. We discuss the quantum entanglement between the ion and phonons by using reduced entropy, and that between two degrees of freedom of the vibrational motion along x and y directions by using quantum relative entropy. We discuss also the influence of initial state of the system on the quantum entanglement and the relation between two entanglements in the trapped ion system.
Quantum entanglement in a two—dimensional ion trap
Institute of Scientific and Technical Information of China (English)
王成志; 方卯发
2003-01-01
In this paper,we investigate the quantum entanglement in a two-dimensional ion trap system.we discuss the quantum entanglement between the ion and phonons by using reduced entropy,and that between two degrees of freedom of the vibrational motion along x and y directions by using quantum relative entropy.We discuss also the influence of initial state of the system on the quantum entanglement and the relation between two entanglements in the trapped ion system.
Discrete coherent states and probability distributions in finite-dimensional spaces
Energy Technology Data Exchange (ETDEWEB)
Galetti, D.; Marchiolli, M.A.
1995-06-01
Operator bases are discussed in connection with the construction of phase space representatives of operators in finite-dimensional spaces and their properties are presented. It is also shown how these operator bases allow for the construction of a finite harmonic oscillator-like coherent state. Creation and annihilation operators for the Fock finite-dimensional space are discussed and their expressions in terms of the operator bases are explicitly written. The relevant finite-dimensional probability distributions are obtained and their limiting behavior for an infinite-dimensional space are calculated which agree with the well know results. (author). 20 refs, 2 figs.
Finite Dimensional Integrable Systems Related to Generalized Schr(o)dinger Equations
Institute of Scientific and Technical Information of China (English)
施齐焉
2003-01-01
The binary nonlinearization method is applied to a 4×4 matrix eigenvalue problem. The typical system of the corresponding soliton hierarchy associated with this eigenvalue problem is the multi-component generalization of the nonlinear Schrodinger equation. With this method, Lax pairs and adjoint Lax pairs of the soliton hierarchy are reduced to two classes of finite dimensional Hamiltonian systems: a spatial finite dimensional Hamiltonian system and a hierarchy of temporal finite dimensional Hamiltonian systems. These finite dimensional Hamiltonian systems are commutative and Liouville integrable.
Two-Dimensional Nonlinear Finite Element Analysis of CMC Microstructures
Mital, Subodh K.; Goldberg, Robert K.; Bonacuse, Peter J.
2012-01-01
A research program has been developed to quantify the effects of the microstructure of a woven ceramic matrix composite and its variability on the effective properties and response of the material. In order to characterize and quantify the variations in the microstructure of a five harness satin weave, chemical vapor infiltrated (CVI) SiC/SiC composite material, specimens were serially sectioned and polished to capture images that detailed the fiber tows, matrix, and porosity. Open source quantitative image analysis tools were then used to isolate the constituents, from which two dimensional finite element models were generated which approximated the actual specimen section geometry. A simplified elastic-plastic model, wherein all stress above yield is redistributed to lower stress regions, is used to approximate the progressive damage behavior for each of the composite constituents. Finite element analyses under in-plane tensile loading were performed to examine how the variability in the local microstructure affected the macroscopic stress-strain response of the material as well as the local initiation and progression of damage. The macroscopic stress-strain response appeared to be minimally affected by the variation in local microstructure, but the locations where damage initiated and propagated appeared to be linked to specific aspects of the local microstructure.
Three dimensional quantum geometry and deformed symmetry
Joung, E.; Mourad, J.; Noui, K.
2009-05-01
We study a three dimensional noncommutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)). We generalize to the deformed case the construction of E3 as the quotient of its isometry group ISU(2) by SU(2). We show that the algebra of functions on E3 becomes the noncommutative algebra of SU(2) distributions, C(SU(2))∗, endowed with the convolution product. This construction gives the action of ISU(2) on the algebra and allows the determination of plane waves and coordinate functions. In particular, we show the following: (i) plane waves have bounded momenta; (ii) to a given momentum are associated several SU(2) elements leading to an effective description of ϕ ɛC(SU(2))∗ in terms of several physical scalar fields on E3; (iii) their product leads to a deformed addition rule of momenta consistent with the bound on the spectrum. We generalize to the noncommutative setting the "local" action for a scalar field. Finally, we obtain, using harmonic analysis, another useful description of the algebra as the direct sum of the algebra of matrices. The algebra of matrices inherits the action of ISU(2): rotations leave the order of the matrices invariant, whereas translations change the order in a way we explicitly determine.
Quantum computing and polynomial equations over the finite field Z_2
Dawson, C M; Hines, A P; Mortimer, D; Nielsen, M A; Osborne, T J; Dawson, Christopher M.; Haselgrove, Henry L.; Hines, Andrew P.; Mortimer, Duncan; Nielsen, Michael A.; Osborne, Tobias J.
2004-01-01
What is the computational power of a quantum computer? We show that determining the output of a quantum computation is equivalent to counting the number of solutions to an easily computed set of polynomials defined over the finite field Z_2. This connection allows simple proofs to be given for two known relationships between quantum and classical complexity classes.
Quantum Monte Carlo simulation of a two-dimensional Majorana lattice model
Hayata, Tomoya; Yamamoto, Arata
2017-07-01
We study interacting Majorana fermions in two dimensions as a low-energy effective model of a vortex lattice in two-dimensional time-reversal-invariant topological superconductors. For that purpose, we implement ab initio quantum Monte Carlo simulation to the Majorana fermion system in which the path-integral measure is given by a semipositive Pfaffian. We discuss spontaneous breaking of time-reversal symmetry at finite temperatures.
Krönke, Sven; Knörzer, Johannes; Schmelcher, Peter
2015-05-01
We explore the correlated quantum dynamics of a single atom, regarded as an open system, with a spatio-temporally localized coupling to a finite bosonic environment. The single atom, initially prepared in a coherent state of low energy, oscillates in a one-dimensional harmonic trap and thereby periodically penetrates an interacting ensemble of NA bosons held in a displaced trap. We show that the inter-species energy transfer accelerates with increasing NA and becomes less complete at the same time. System-environment correlations prove to be significant except for times when the excess energy distribution among the subsystems is highly imbalanced. These correlations result in incoherent energy transfer processes, which accelerate the early energy donation of the single atom and stochastically favour certain energy transfer channels, depending on the instantaneous direction of transfer. Concerning the subsystem states, the energy transfer is mediated by non-coherent states of the single atom and manifests itself in singlet and doublet excitations in the finite bosonic environment. These comprehensive insights into the non-equilibrium quantum dynamics of an open system are gained by ab initio simulations of the total system with the recently developed multi-layer multi-configuration time-dependent Hartree method for bosons.
Finite-Temperature Properties of Three-Dimensional Chiral Helimagnets
Shinozaki, Misako; Hoshino, Shintaro; Masaki, Yusuke; Kishine, Jun-ichiro; Kato, Yusuke
2016-07-01
We study a three-dimensional (3d) classical chiral helimagnet at finite temperatures through analysis of a spin Hamiltonian, which is defined on a simple cubic lattice and consists of the Heisenberg exchange, monoaxial Dzyaloshinskii-Moriya interactions, and the Zeeman energy due to a magnetic field applied in the plane perpendicular to the helical axis. We take account of the quasi-two-dimensionality of the known monoaxial chiral helimagnet CrNb3S6 and we adopt three methods: (i) a conventional mean-field (MF) analysis, which we call the 3dMF method, (ii) a hybrid method called the 2dMC-1dMF method, which is composed of a classical Monte Carlo (MC) simulation and a MF approximation applied respectively to the intra- and interlayer interactions, and (iii) a simple-MC simulation (3dMC) at zero field. The temperature dependence of the magnetization calculated by the 3dMF method shows a cusp-like structure similar to that observed in experiments. In the absence of a magnetic field, both 2dMC-1dMF and 3dMC yield similar values of the transition temperature. The 2dMC-1dMF method provides a quantitative description of the thermodynamic properties, even under an external field, at an accessible numerical cost.
Quantum phase transitions in low-dimensional optical lattices
Di Liberto, M.F.
2015-01-01
In this thesis, we discuss quantum phase transitions in low-dimensional optical lattices, namely one- and two-dimensional lattices. The dimensional confinement is realized in experiments by suppressing the hopping in the extra dimensions through a deep potential barrier that prevents the atoms to tu
Device-independent certification of high-dimensional quantum systems.
D'Ambrosio, Vincenzo; Bisesto, Fabrizio; Sciarrino, Fabio; Barra, Johanna F; Lima, Gustavo; Cabello, Adán
2014-04-11
An important problem in quantum information processing is the certification of the dimension of quantum systems without making assumptions about the devices used to prepare and measure them, that is, in a device-independent manner. A crucial question is whether such certification is experimentally feasible for high-dimensional quantum systems. Here we experimentally witness in a device-independent manner the generation of six-dimensional quantum systems encoded in the orbital angular momentum of single photons and show that the same method can be scaled, at least, up to dimension 13.
Unconventional critical activated scaling of two-dimensional quantum spin glasses
Matoz-Fernandez, D. A.; Romá, F.
2016-07-01
We study the critical behavior of two-dimensional short-range quantum spin glasses by numerical simulations. Using a parallel tempering algorithm, we calculate the Binder cumulant for the Ising spin glass in a transverse magnetic field with two different short-range bond distributions, the bimodal and the Gaussian ones. Through an exhaustive finite-size analysis, we show that the cumulant probably follows an unconventional activated scaling, which we interpret as new evidence supporting the hypothesis that the quantum critical behavior is governed by an infinite randomness fixed point.
Gu, Yingfei; Lee, Ching Hua; Wen, Xueda; Cho, Gil Young; Ryu, Shinsei; Qi, Xiao-Liang
2016-09-01
In this paper, we study (2 +1 ) -dimensional quantum anomalous Hall states, i.e., band insulators with quantized Hall conductance, using exact holographic mapping. Exact holographic mapping is an approach to holographic duality which maps the quantum anomalous Hall state to a different state living in (3 +1 ) -dimensional hyperbolic space. By studying topological response properties and the entanglement spectrum, we demonstrate that the holographic dual theory of a quantum anomalous Hall state is a (3 +1 ) -dimensional topological insulator. The dual description enables a characterization of topological properties of a system by the quantum entanglement between degrees of freedom at different length scales.
Nussinov, Zohar; Johnson, Patrick; Graf, Matthias J.; Balatsky, Alexander V.
2013-05-01
Many electronic systems (e.g., the cuprate superconductors and heavy fermions) exhibit striking features in their dynamical response over a prominent range of experimental parameters. While there are some empirical suggestions of particular increasing length scales that accompany such transitions in some cases, this identification is not universal and in numerous instances no large correlation length is evident. To better understand, as a matter of principle, such behavior in quantum systems, we extend a known mapping (earlier studied in stochastic or supersymmetric quantum mechanics) between finite temperature classical Fokker-Planck systems and related quantum systems at zero temperature to include general nonequilibrium dynamics. Unlike Feynman mappings or stochastic quantization methods in field theories (as well as more recent holographic type dualities), the classical systems that we consider and their quantum duals reside in the same number of space-time dimensions. The upshot of our very broad and rigorous result is that a Wick rotation exactly relates (i) the dynamics in general finite temperature classical dissipative systems to (ii) zero temperature dynamics in the corresponding dual many-body quantum systems. Using this correspondence, we illustrate that, even in the absence of imposed disorder, many continuum quantum fluid systems (and possible lattice counterparts) may exhibit a zero-point “quantum dynamical heterogeneity” wherein the dynamics, at a given instant, is spatially nonuniform. While the static length scales accompanying this phenomenon do not seem to exhibit a clear divergence in standard correlation functions, the length scale of the dynamical heterogeneities can increase dramatically. We further study “quantum jamming” and illustrate how a hard-core bosonic system can undergo a zero temperature quantum critical metal-to-insulator-type transition with an extremely large effective dynamical exponent z>4 that is consistent with
无限维系统中的量子纠错定理%Theory of Quantum Error-Correction in Infinite-Dimensional Quantum System
Institute of Scientific and Technical Information of China (English)
2015-01-01
Information is often affected by noise during transmission .In order to avoid the effect of noise ,it is needed to correct the quantum information .The current quantum error‐correc‐tion theory gives the sufficient and necessary conditions for the error‐correction of quantum chan‐nel in finite dimensional quantum systems .In this paper ,the quantum error‐correction theory in infinite dimensional quantum systems was studied ,and the necessary and sufficient conditions were given for the error‐correction of quantum channel with finite dimensional error correcting codes .%信息在传输过程中，经常会受到噪声的影响。为了避免噪声的影响，就需要对量子信息进行纠错。量子纠错定理描述量子信道可纠错的充分必要条件。但目前的纠错定理基于有限维量子系统给出。本文研究无限维量子纠错定理，给出量子信道具有有限维纠错码的充要条件。
A two-dimensional spin liquid in quantum kagome ice.
Carrasquilla, Juan; Hao, Zhihao; Melko, Roger G
2015-06-22
Actively sought since the turn of the century, two-dimensional quantum spin liquids (QSLs) are exotic phases of matter where magnetic moments remain disordered even at zero temperature. Despite ongoing searches, QSLs remain elusive, due to a lack of concrete knowledge of the microscopic mechanisms that inhibit magnetic order in materials. Here we study a model for a broad class of frustrated magnetic rare-earth pyrochlore materials called quantum spin ices. When subject to an external magnetic field along the [111] crystallographic direction, the resulting interactions contain a mix of geometric frustration and quantum fluctuations in decoupled two-dimensional kagome planes. Using quantum Monte Carlo simulations, we identify a set of interactions sufficient to promote a groundstate with no magnetic long-range order, and a gap to excitations, consistent with a Z2 spin liquid phase. This suggests an experimental procedure to search for two-dimensional QSLs within a class of pyrochlore quantum spin ice materials.
Holographic Relaxation of Finite Size Isolated Quantum Systems
Abajo-Arrastia, Javier; Lopez, Esperanza; Mas, Javier; Serantes, Alexandre
2014-01-01
We study holographically the out of equilibrium dynamics of a finite size closed quantum system in 2+1 dimensions, modelled by the collapse of a shell of a massless scalar field in AdS4. In global coordinates there exists a variety of evolutions towards final black hole formation which we relate with different patterns of relaxation in the dual field theory. For large scalar initial data rapid thermalization is achieved as a priori expected. Interesting phenomena appear for small enough amplitudes. Such shells do not generate a black hole by direct collapse, but quite generically an apparent horizon emerges after enough bounces off the AdS boundary. We relate this bulk evolution with relaxation processes at strong coupling which delay in reaching an ergodic stage. Besides the dynamics of bulk fields, we monitor the entanglement entropy, finding that it oscillates quasi-periodically before final equilibration. The radial position of the traveling shell is brought into correspondence with the evolution of the e...
Entanglement Concentration for Higher-Dimensional Quantum Systems
Institute of Scientific and Technical Information of China (English)
姚春梅; 顾永建; 叶柳; 郭光灿
2002-01-01
Using local operations and classicalcommunication, we present two schemes for realizing entanglement concentration from pure entangled pairs of qutrits. These methods can be easily generalized to d-dimensional (d ＞ 3)quantum systems.
Fate of classical solitons in one-dimensional quantum systems.
Energy Technology Data Exchange (ETDEWEB)
Pustilnik, M.; Matveev, K. A.
2015-11-23
We study one-dimensional quantum systems near the classical limit described by the Korteweg-de Vries (KdV) equation. The excitations near this limit are the well-known solitons and phonons. The classical description breaks down at long wavelengths, where quantum effects become dominant. Focusing on the spectra of the elementary excitations, we describe analytically the entire classical-to-quantum crossover. We show that the ultimate quantum fate of the classical KdV excitations is to become fermionic quasiparticles and quasiholes. We discuss in detail two exactly solvable models exhibiting such crossover, the Lieb-Liniger model of bosons with weak contact repulsion and the quantum Toda model, and argue that the results obtained for these models are universally applicable to all quantum one-dimensional systems with a well-defined classical limit described by the KdV equation.
A quantum router for high-dimensional entanglement
Erhard, Manuel; Malik, Mehul; Zeilinger, Anton
2017-03-01
In addition to being a workhorse for modern quantum technologies, entanglement plays a key role in fundamental tests of quantum mechanics. The entanglement of photons in multiple levels, or dimensions, explores the limits of how large an entangled state can be, while also greatly expanding its applications in quantum information. Here we show how a high-dimensional quantum state of two photons entangled in their orbital angular momentum can be split into two entangled states with a smaller dimensionality structure. Our work demonstrates that entanglement is a quantum property that can be subdivided into spatially separated parts. In addition, our technique has vast potential applications in quantum as well as classical communication systems.
K1 Group of Finite Dimensional Path Algebra
Institute of Scientific and Technical Information of China (English)
Xue Jun GUO; Li Bin LI
2001-01-01
In this paper, by calculating the commutator subgroup of the unit group of finite pathalgebra κ/△ and the unit group abelianized, we explicitly characterize the K1 group of finite dimensionalpath algebra over an arbitrary field.
The Quantum Socket: Three-Dimensional Wiring for Extensible Quantum Computing
Béjanin, J H; Rinehart, J R; Earnest, C T; McRae, C R H; Shiri, D; Bateman, J D; Rohanizadegan, Y; Penava, B; Breul, P; Royak, S; Zapatka, M; Fowler, A G; Mariantoni, M
2016-01-01
Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: The quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum ...
Quantum quenches to the attractive one-dimensional Bose gas: exact results
Directory of Open Access Journals (Sweden)
Lorenzo Piroli, Pasquale Calabrese, Fabian H. L. Essler
2016-09-01
Full Text Available We study quantum quenches to the one-dimensional Bose gas with attractive interactions in the case when the initial state is an ideal one-dimensional Bose condensate. We focus on properties of the stationary state reached at late times after the quench. This displays a finite density of multi-particle bound states, whose rapidity distribution is determined exactly by means of the quench action method. We discuss the relevance of the multi-particle bound states for the physical properties of the system, computing in particular the stationary value of the local pair correlation function $g_2$.
Quantum Probability, Renormalization and Infinite-Dimensional *-Lie Algebras
Directory of Open Access Journals (Sweden)
Luigi Accardi
2009-05-01
Full Text Available The present paper reviews some intriguing connections which link together a new renormalization technique, the theory of *-representations of infinite dimensional *-Lie algebras, quantum probability, white noise and stochastic calculus and the theory of classical and quantum infinitely divisible processes.
Quantum transport in strongly interacting one-dimensional nanostructures
Agundez, R. R.
2015-01-01
In this thesis we study quantum transport in several one-dimensional systems with strong electronic interactions. The first chapter contains an introduction to the concepts treated throughout this thesis, such as the Aharonov-Bohm effect, the Kondo effect, the Fano effect and quantum state transfer.
Quantum Fluctuation of a Mesoscopic Inductance Coupling Circuit at Finite Temperature
Institute of Scientific and Technical Information of China (English)
SONG Tong-Qiang; ZHU Yue-Jin
2003-01-01
We study the quantization of mesoscopic inductance coupling circuit and discuss its time evolution. Bymeans of the thermal field dynamics theory we study the quantum fluctuation of the system at finite temperature.
Constraints on RG Flow for Four Dimensional Quantum Field Theories
Jack, I
2013-01-01
The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve $a$, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered. Previous consistency conditions for the anomalous terms, which implicitly define a metric $G$ on the space of couplings and give rise to gradient flow like equations for $a$, are derived taking into account the role of lower dimension operators. The results for infinitesimal Weyl rescaling are integrated to finite rescalings $e^{2\\sigma}$ to a form which involves running couplings $g_\\sigma$ and which interpolates between IR and UV fixed points. The results are also restricted to flat space where they give rise to broken conformal Ward identities. Expressions for the three loop Yukawa $\\beta$-functions for a general scalar/fermion theory are obtained and the three loop contribution to the metric $G$ for this theory are also calculated. These results are used ...
Constraints on RG flow for four dimensional quantum field theories
Jack, I.; Osborn, H.
2014-06-01
The response of four dimensional quantum field theories to a Weyl rescaling of the metric in the presence of local couplings and which involve a, the coefficient of the Euler density in the energy momentum tensor trace on curved space, is reconsidered. Previous consistency conditions for the anomalous terms, which implicitly define a metric G on the space of couplings and give rise to gradient flow like equations for a, are derived taking into account the role of lower dimension operators. The results for infinitesimal Weyl rescaling are integrated to finite rescalings e2σ to a form which involves running couplings gσ and which interpolates between IR and UV fixed points. The results are also restricted to flat space where they give rise to broken conformal Ward identities. Expressions for the three loop Yukawa β-functions for a general scalar/fermion theory are obtained and the three loop contribution to the metric G for this theory is also calculated. These results are used to check the gradient flow equations to higher order than previously. It is shown that these are only valid when β→B, a modified β-function, and that the equations provide strong constraints on the detailed form of the three loop Yukawa β-function. N=1 supersymmetric Wess-Zumino theories are also considered as a special case. It is shown that the metric for the complex couplings in such theories may be restricted to a hermitian form.
Weidinger, Lukas; Bauer, Florian; von Delft, Jan
2017-01-01
We introduce an equilibrium formulation of the functional renormalization group (fRG) for inhomogeneous systems capable of dealing with spatially finite-ranged interactions. In the general third-order truncated form of fRG, the dependence of the two-particle vertex is described by O (N4) independent variables, where N is the dimension of the single-particle system. In a previous paper [Bauer et al., Phys. Rev. B 89, 045128 (2014), 10.1103/PhysRevB.89.045128], the so-called coupled-ladder approximation (CLA) was introduced and shown to admit a consistent treatment for models with a purely onsite interaction, reducing the vertex to O (N2) independent variables. In this work, we introduce an extended version of this scheme, called the extended coupled ladder approximation (eCLA), which includes a spatially extended feedback between the individual channels, measured by a feedback length L , using O (N2L2) independent variables for the vertex. We apply the eCLA in a static approximation and at zero temperature to three types of one-dimensional model systems, focusing on obtaining the linear response conductance. First, we study a model of a quantum point contact (QPC) with a parabolic barrier top and on-site interactions. In our setup, where the characteristic length lx of the QPC ranges between approximately 4-10 sites, eCLA achieves convergence once L becomes comparable to lx. It also turns out that the additional feedback stabilizes the fRG flow. This enables us, second, to study the geometric crossover between a QPC and a quantum dot, again for a one-dimensional model with on-site interactions. Third, the enlarged feedback also enables the treatment of a finite-ranged interaction extending over up to L sites. Using a simple estimate for the form of such a finite-ranged interaction in a QPC with a parabolic barrier top, we study its effects on the conductance and the density. We find that for low densities and sufficiently large interaction ranges the conductance
Energy Technology Data Exchange (ETDEWEB)
Giunta, G.; Belouettar, S. [Centre de Recherche Public Henri Tudor, 29, av. John F. Kennedy, L-1855, Luxembourg-Kirchberg, Luxembourg (Belgium)
2015-03-10
In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigations show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.
Experimental and three-dimensional finite element investigation of fatigue
Bomidi, John A. R.
Materials often fail at cyclic loads that are lower than their ultimate strength or even their yield strength due to progressive internal material degradation; commonly known as fatigue. Moreover, there is a wide scatter in observed fatigue lives of mechanical components operating under identical loading conditions. The randomness of fatigue failure is considered to be linked to basic microstructural effects such as random microstructure topology and the initiation/growth of cracks along inter/transgranular planes. Several modeling approaches have been previously presented ranging from 2D discrete element to 3D Finite Element methods with explicit representation of microstructure topology and continuum damage mechanics to capture dispersion in rolling contact fatigue life and fatigue spalling. There is, however, a need to compare the modeling approach with experimental fatigue test conditions in order to verify and as required enhance the modeling approach to capture observed fatigue failure. This dissertation presents experimental test results and three-dimensional modeling approach that capture fatigue failure. The three-dimensional modeling approach is enhanced according to the experimental observations to consider inter/trans granular failure, different modes of fatigue initiation and propagation and finally for considering effect of plasticity in fatigue of rolling contacts. The following phenomena have been investigated: (1) Fatigue of microbeams: (a )Results of fatigue life and failure from 3D modeling of intergranular fatigue in microbeams are compared with experimental observations reported in literature (2) Tensile fatigue of thin sheets: (a) A test rig with a new grip and alignment system is developed to address the challenges associated with thin sheet testing and conduct fatigue experiments. (b) The 3D fatigue model is enhanced to capture the dominant transgranular fatigue observed in the experiments. The observed and modeled fatigue life and failure
Comment on "Dual path integral representation for finite temperature quantum field theory"
Kazinski, P O
2008-01-01
I show that the novel dual path integral representation for finite temperature quantum field theory proposed in [Phys. Rev. D 77, 105030 (2008), arXiv:0803.1667 ] is a well-known representation of quantum mechanics in terms of symbols of operators.
Institute of Scientific and Technical Information of China (English)
Meng Xiang-Guo; Wang Ji-Suo; Liu Tang-Kun
2008-01-01
In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states(EONLPCSs),which can be realized via operating the superposed evolution operators D±(τ)on the state |q,0),is constructed,then their orthonormalized property,completeness relations and some nonclassical properties are discussed.It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations.Moreover,the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q,η and ξ.
Finite-temperature field theory and quantum noise in an electrical network
Energy Technology Data Exchange (ETDEWEB)
Garavaglia, T.
1988-10-15
Finite-temperature (0less than or equal toT
de Vega, Sandra; Cox, Joel D.; de Abajo, F. Javier García
2016-08-01
We study the potential of highly doped finite carbon nanotubes to serve as plasmonic elements that mediate the interaction between quantum emitters. Similar to graphene, nanotubes support intense plasmons that can be modulated by varying their level of electrical doping. These excitations exhibit large interaction with light and electron beams, as revealed upon examination of the corresponding light extinction cross-section and electron energy-loss spectra. We show that quantum emitters experience record-high Purcell factors, while they undergo strong mutual interaction mediated by their coupling to the tube plasmons. Our results show the potential of doped finite nanotubes as tunable plasmonic materials for quantum optics applications.
Finiteness of the vacuum energy density in quantum electrodynamics
Manoukian, Edward B.
1983-03-01
Recent interest in the finiteness problem of the vacuum energy density (VED) in finite QED has motivated us to reexamine this problem in the light of an analysis we have carried out earlier. By a loopwise summation procedure, supplemented by a renormalization-group analysis, we study the finiteness of the VED with α, the renormalized fine-structure constant, fixed in the process as the (infinite order) zero of the eigenvalue condition F[1](x)|x=α=0∞, and with the electron mass totally dynamical of origin. We propose a possible finite solution for the VED in QED which may require only one additional eigenvalue condition for α.
On the finite-dimensional PUA representations of the Shubnikov space groups
Broek, van den P.M.
1977-01-01
The finite-dimensional PUA epresentations of the Shubnikov space groups are discussed using the method of generalised induction given by Shaw and Lever. In particular we derive expressions for the calculation of the little groups.
Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
Lukácová-Medvid'ová, Maria; Saibertova, Jitka
2004-01-01
In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bich...
Quasi-one-dimensional density of states in a single quantum ring
Kim, Heedae; Lee, Woojin; Park, Seongho; Kyhm, Kwangseuk; Je, Koochul; Taylor, Robert A.; Nogues, Gilles; Dang, Le Si; Song, Jin Dong
2017-01-01
Generally confinement size is considered to determine the dimensionality of nanostructures. While the exciton Bohr radius is used as a criterion to define either weak or strong confinement in optical experiments, the binding energy of confined excitons is difficult to measure experimentally. One alternative is to use the temperature dependence of the radiative recombination time, which has been employed previously in quantum wells and quantum wires. A one-dimensional loop structure is often assumed to model quantum rings, but this approximation ceases to be valid when the rim width becomes comparable to the ring radius. We have evaluated the density of states in a single quantum ring by measuring the temperature dependence of the radiative recombination of excitons, where the photoluminescence decay time as a function of temperature was calibrated by using the low temperature integrated intensity and linewidth. We conclude that the quasi-continuous finely-spaced levels arising from the rotation energy give rise to a quasi-one-dimensional density of states, as long as the confined exciton is allowed to rotate around the opening of the anisotropic ring structure, which has a finite rim width.
Multisymplectic Structure-Preserving in Simple Finite Element Method in High Dimensional Case
Institute of Scientific and Technical Information of China (English)
BAI Yong-Qiang; LIU Zhen; PEI Ming; ZHENG Zhu-Jun
2003-01-01
In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure.
Renner, R.; Cirac, J. I.
2009-03-01
We show that the quantum de Finetti theorem holds for states on infinite-dimensional systems, provided they satisfy certain experimentally verifiable conditions. This result can be applied to prove the security of quantum key distribution based on weak coherent states or other continuous variable states against general attacks.
An exactly solvable three-dimensional nonlinear quantum oscillator
Energy Technology Data Exchange (ETDEWEB)
Schulze-Halberg, A. [Department of Mathematics and Actuarial Science, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States); Morris, J. R. [Department of Physics, Indiana University Northwest, 3400 Broadway, Gary, Indiana 46408 (United States)
2013-11-15
Exact analytical, closed-form solutions, expressed in terms of special functions, are presented for the case of a three-dimensional nonlinear quantum oscillator with a position dependent mass. This system is the generalization of the corresponding one-dimensional system, which has been the focus of recent attention. In contrast to other approaches, we are able to obtain solutions in terms of special functions, without a reliance upon a Rodrigues-type of formula. The wave functions of the quantum oscillator have the familiar spherical harmonic solutions for the angular part. For the s-states of the system, the radial equation accepts solutions that have been recently found for the one-dimensional nonlinear quantum oscillator, given in terms of associated Legendre functions, along with a constant shift in the energy eigenvalues. Radial solutions are obtained for all angular momentum states, along with the complete energy spectrum of the bound states.
Magnetic exchange disorder in low-dimensional quantum magnets
Energy Technology Data Exchange (ETDEWEB)
Blackmore, W.J.A. [U. Warwick, Physics; Goddard, P.A. [U. Warwick, Physics; Xiao, F. [U. Bern, Chemistry; Landee, C.P. [Clark University, Chemistry; Turnbull, M. M. [Clark University, Chemistry; Lancaster, T [U. Durham, Physics; Singleton, John [Los Alamos National Laboratory
2017-02-13
Low-dimensional quantum magnetism is currently of great interest due to the fact that reduced dimensionality can support strong quantum fluctuations, which may lead to unusual phenomena and quantum-critical behavior. The effect of random exchange strengths in two-dimensional (2D) antiferromagnets is still not fully understood despite much effort. This project aims to rectify this by investigating the high-field properties of the 2D coordination polymer (QuinH)_{2}Cu(Cl_{x}Br_{1-x})_{4}.2H_{2}O. The exchange pathway is through Cu-Halide-Cu bonds, and by randomizing the proportion of chlorine and bromine atoms in the unit cell, disorder can be introduced into the system.
The Quantum Well of One-Dimensional Photonic Crystals
Directory of Open Access Journals (Sweden)
Xiao-Jing Liu
2015-01-01
Full Text Available We have studied the transmissivity of one-dimensional photonic crystals quantum well (QW with quantum theory approach. By calculation, we find that there are photon bound states in the QW structure (BA6(BBABBn(AB6, and the numbers of the bound states are equal to n+1. We have found that there are some new features in the QW, which can be used to design optic amplifier, attenuator, and optic filter of multiple channel.
Quantum confinement effects in low-dimensional systems
Indian Academy of Sciences (India)
D Topwal
2015-06-01
The confinement effects of electrons in ultrathin films and nanowires grown on metallic and semiconducting substrates investigated using band mapping of their electronic structures using angle-resolved photoemission spectroscopy is discussed here. It has been shown that finite electron reflectivity at the interface is sufficient to sustain the formation of quantum well states and weak quantum well resonance states even in closely matched metals. The expected parabolic dispersion of sp-derived quantum well states for free-standing layers undergoes deviations from parabolic behaviour and modifications due to the underlying substrate bands, suggesting the effects of strong hybridization between the quantum well states and the substrate bands. Electron confinement effects in low dimensions as observed from the dispersionless features in the band structures are also discussed.
Ransom, Jonathan B.
2002-01-01
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
On Relations between One-Dimensional Quantum and Two-Dimensional Classical Spin Systems
Directory of Open Access Journals (Sweden)
J. Hutchinson
2015-01-01
Full Text Available We exploit mappings between quantum and classical systems in order to obtain a class of two-dimensional classical systems characterised by long-range interactions and with critical properties equivalent to those of the class of one-dimensional quantum systems treated by the authors in a previous publication. In particular, we use three approaches: the Trotter-Suzuki mapping, the method of coherent states, and a calculation based on commuting the quantum Hamiltonian with the transfer matrix of a classical system. This enables us to establish universality of certain critical phenomena by extension from the results in the companion paper for the classical systems identified.
Spin dynamics in a two-dimensional quantum gas
DEFF Research Database (Denmark)
Pedersen, Poul Lindholm; Gajdacz, Miroslav; Deuretzbacher, Frank
2014-01-01
We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions with superimp......We have investigated spin dynamics in a two-dimensional quantum gas. Through spin-changing collisions, two clouds with opposite spin orientations are spontaneously created in a Bose-Einstein condensate. After ballistic expansion, both clouds acquire ring-shaped density distributions...
Quantum Statistical Entropy of Five-Dimensional Black Hole
Institute of Scientific and Technical Information of China (English)
ZHAO Ren; WU Yue-Qin; ZHANG Sheng-Li
2006-01-01
The generalized uncertainty relation is introduced to calculate quantum statistic entropy of a black hole.By using the new equation of state density motivated by the generalized uncertainty relation, we discuss entropies of Bose field and Fermi field on the background of the five-dimensional spacetime. In our calculation, we need not introduce cutoff. There is not the divergent logarithmic term as in the original brick-wall method. And it is obtained that the quantum statistic entropy corresponding to black hole horizon is proportional to the area of the horizon. Further it is shown that the entropy of black hole is the entropy of quantum state on the surface of horizon. The black hole's entropy is the intrinsic property of the black hole. The entropy is a quantum effect. It makes people further understand the quantum statistic entropy.
On Global One-Dimensionality proposal in Quantum General Relativity
Glinka, L A
2008-01-01
Quantum General Relativity, better known as Quantum Gravity with additional epithets, currently is faraway from phenomenology. This mental crisis leads at most to empty hypotheses, but not to realistic physics. However, there exists the way, investigated by Dirac, which is constructive for experimental data predictions in astrophysics, high energy physics, and condensed matter physics. It is Field Theory. This article presents certain proposal for new discussion. General Relativity in 3+1 metric field gauge and its canonical quantization is developed. Reduction of the quantum geometrodynamics to Global One-Dimensional bosonic field theory, its quantization, and some conclusions are presented.
Asymmetric de Finetti Theorem for Infinite-dimensional Quantum Systems
Niu, Murphy Yuezhen
2016-01-01
The de Finetti representation theorem for continuous variable quantum system is first developed to approximate an N-partite continuous variable quantum state with a convex combination of independent and identical subsystems, which requires the original state to obey permutation symmetry conditioned on successful experimental verification on k of N subsystems. We generalize the de Finetti theorem to include asymmetric bounds on the variance of canonical observables and biased basis selection during the verification step. Our result thereby enables application of infinite-dimensional de Finetti theorem to situations where two conjugate measurements obey different statistics, such as the security analysis of quantum key distribution protocols based on squeezed state against coherent attack.
Quantum cosmology in an anisotropic n-dimensional universe
Alves-Júnior, F A P; Barreto, A B; Romero, C
2016-01-01
We investigate quantum cosmological models in an n-dimensional anisotropic universe in the presence of a massless scalar field. Our basic inspiration comes from Chodos and Detweiler's classical model which predicts an interesting behaviour of the extra dimension, shrinking down as time goes by. We work in the framework of a recent geometrical scalar-tensor theory of gravity. Classically, we obtain two distinct type of solutions. One of them has an initial singularity while the other represents a static universe considered as a whole. By using the canonical approach to quantum cosmology, we investigate how quantum effects could have had an influence in the past history of these universes.
Quantum skyrmions in two-dimensional chiral magnets
Takashima, Rina; Ishizuka, Hiroaki; Balents, Leon
2016-10-01
We study the quantum mechanics of magnetic skyrmions in the vicinity of the skyrmion-crystal to ferromagnet phase boundary in two-dimensional magnets. We show that the skyrmion excitation has an energy dispersion that splits into multiple bands due to the combination of magnus force and the underlying lattice. Condensation of the skyrmions can give rise to an intermediate phase between the skyrmion crystal and ferromagnet: a quantum liquid, in which skyrmions are not spatially localized. We show that the critical behavior depends on the spin size S and the topological number of the skyrmion. Experimental signatures of quantum skyrmions in inelastic neutron-scattering measurements are also discussed.
ON LOCKING-FREE FINITE ELEMENT SCHEMES FOR THREE-DIMENSIONAL ELASTICITY
Institute of Scientific and Technical Information of China (English)
He Qi; Lie-heng Wang; Wei-ying Zheng
2005-01-01
In the present paper, the authors discuss the locking phenomenon of the finite element method for three-dimensional elasticity as the Lame constant λ→∞. Three kinds of finite elements are proposed and analyzed to approximate the three-dimensional elasticity with pure displacement boundary condition. Optimal order error estimates which are uniform with respect to λ∈ (0, +∞) are obtained for three schemes. Furthermore, numerical results are presented to show that, our schemes are locking-free and and the trilinear conforming finite element scheme is locking.
Noninteracting fermions at finite temperature in a d -dimensional trap: Universal correlations
Dean, David S.; Le Doussal, Pierre; Majumdar, Satya N.; Schehr, Grégory
2016-12-01
We study a system of N noninteracting spinless fermions trapped in a confining potential, in arbitrary dimensions d and arbitrary temperature T . The presence of the confining trap breaks the translational invariance and introduces an edge where the average density of fermions vanishes. Far from the edge, near the center of the trap (the so-called "bulk regime"), where the fermions do not feel the curvature of the trap, physical properties of the fermions have traditionally been understood using the local density (or Thomas-Fermi) approximation. However, these approximations drastically fail near the edge where the density vanishes and thermal and quantum fluctuations are thus enhanced. The main goal of this paper is to show that, even near the edge, novel universal properties emerge, independently of the details of the shape of the confining potential. We present a unified framework to investigate both the bulk and the edge properties of the fermions. We show that for large N , these fermions in a confining trap, in arbitrary dimensions and at finite temperature, form a determinantal point process. As a result, any n -point correlation function, including the average density profile, can be expressed as an n ×n determinant whose entry is called the kernel, a central object for such processes. Near the edge, we derive the large-N scaling form of the kernels, parametrized by d and T . In d =1 and T =0 , this reduces to the so-called Airy kernel, that appears in the Gaussian unitary ensemble (GUE) of random matrix theory. In d =1 and T >0 we show a remarkable connection between our kernel and the one appearing in the (1 +1 )-dimensional Kardar-Parisi-Zhang equation at finite time. Consequently, our result provides a finite-T generalization of the Tracy-Widom distribution, that describes the fluctuations of the position of the rightmost fermion at T =0 , or those of the largest single-fermion momentum. In d >1 and T ≥0 , while the connection to GUE no longer holds
Three dimensional loop quantum gravity: physical scalar product and spin foam models
Noui, K; Noui, Karim; Perez, Alejandro
2004-01-01
In this paper, we address the problem of the dynamics in three dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space--corresponding to the quantization of the infinite dimensional kinematical configuration space of the theory--to the physical Hilbert space. In particular, we provide the definition of the physical scalar product which can be represented in terms of a sum over (finite) spin-foam amplitudes. Therefore, we establish a clear-cut connection between the canonical quantization of three dimensional gravity and spin-foam models. We emphasize two main properties of the result: first that no cut-off in the kinematical degrees of freedom of the theory is introduced (in contrast to standard `lattice' methods), and second that no ill-defined sum over spins (`bubble' divergences) are present in the spin foam representation.
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models
Noui, Karim; Perez, Alejandro
2005-05-01
In this paper, we address the problem of the dynamics in three-dimensional loop quantum gravity with zero cosmological constant. We construct a rigorous definition of Rovelli's generalized projection operator from the kinematical Hilbert space—corresponding to the quantization of the infinite-dimensional kinematical configuration space of the theory—to the physical Hilbert space. In particular, we provide the definition of the physical scalar product which can be represented in terms of a sum over (finite) spin-foam amplitudes. Therefore, we establish a clear-cut connection between the canonical quantization of three-dimensional gravity and spin-foam models. We emphasize two main properties of the result: first that no cut-off in the kinematical degrees of freedom of the theory is introduced (in contrast to standard 'lattice' methods), and second that no ill-defined sum over spins ('bubble' divergences) are present in the spin-foam representation.
Quantum single-particle properties in a one-dimensional curved space
Pedersen, J. K.; Fedorov, D. V.; Jensen, A. S.; Zinner, N. T.
2016-10-01
We consider one particle confined to a deformed one-dimensional wire. The quantum mechanical equivalent of the classical problem is not uniquely defined. We describe several possible Hamiltonians and corresponding solutions for a finite wire with fixed endpoints and non-vanishing curvature. We compute and compare the disparate eigenvalues and eigenfunctions obtained from different quantization prescriptions. The JWKB approximation without potential leads precisely to the square well spectrum and the coordinate dependent stretched or compressed box related eigenfunctions. The geometric potential arising from an adiabatic expansion in terms of curvature may be correct but it can only be valid for small curvature.
Two-dimensional finite-element temperature variance analysis
Heuser, J. S.
1972-01-01
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Liu, Chang; Zhu, Xian-chun; Zhang, Xing; Tai, Yin-xia; Yan, Sen
2011-02-01
To build the physical model of four suturae which are related to the growth of maxilla in the three-dimensional finite-element model of maxillofacial bones. A 16 years old volunteer with individual normal occlusion, good periodontium health condition and without diseases of temporomandibular joint was chosen to be the material of modeling. The three-dimensional finite-element model of the volunteer's maxillofacial bones was built using the CT scan and the finite-element modeling method. Finally we built the physical model of four suturae which were related to the growth of maxilla in the model of maxillofacial bones. The model of maxillofacial bones with 86,575 nodes and 485,915 elements was generated. This model contained four suturae including sutura frontomaxillaris, sutura zygomaticomaxillaris, sutura temporozygomatica and sutura pterygopalatine. A three-dimensional finite-element model of maxillofacial bones with good biological similarity was developed.
Semi-relativistic hydrodynamics of three-dimensional and low-dimensional quantum plasma
Andreev, Pavel; Kuz'menkov, Leonid
2014-01-01
Contributions of the current-current and Darwin interactions and weak-relativistic addition to kinetic energy in the quantum hydrodynamic equations are considered. Features of hydrodynamic equations for two-dimensional layer of plasma (two-dimensional electron gas for instance) are described. It is shown that the force fields caused by the Darwin interaction and weak-relativistic addition to kinetic energy are partially reduced. Dispersion of three- and two-dimensional semi-relativistic Langmuir waves is calculated.
Energy Technology Data Exchange (ETDEWEB)
Stránský, Pavel [Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague (Czech Republic); Macek, Michal [Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague (Czech Republic); Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, CT 06520-8120 (United States); Leviatan, Amiram [Racah Institute of Physics, The Hebrew University, 91904 Jerusalem (Israel); Cejnar, Pavel, E-mail: pavel.cejnar@mff.cuni.cz [Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovičkách 2, 18000 Prague (Czech Republic)
2015-05-15
This article extends our previous analysis Stránský et al. (2014) of Excited-State Quantum Phase Transitions (ESQPTs) in systems of dimension two. We focus on the oscillatory component of the quantum state density in connection with ESQPT structures accompanying a first-order ground-state transition. It is shown that a separable (integrable) system can develop rather strong finite-size precursors of ESQPT expressed as singularities in the oscillatory component of the state density. The singularities originate in effectively 1-dimensional dynamics and in some cases appear in multiple replicas with increasing excitation energy. Using a specific model example, we demonstrate that these precursors are rather resistant to proliferation of chaotic dynamics. - Highlights: • Oscillatory components of state density and spectral flow studied near ESQPTs. • Enhanced finite-size precursors of ESQPT caused by fully/partly separable dynamics. • These precursors appear due to criticality of a subsystem with lower dimension. • Separability-induced finite-size effects disappear in case of fully chaotic dynamics.
Nishimura, Kohji; Nishimori, Hidetoshi; Ochoa, Andrew J.; Katzgraber, Helmut G.
2016-09-01
We study the problem to infer the ground state of a spin-glass Hamiltonian using data from another Hamiltonian with interactions disturbed by noise from the original Hamiltonian, motivated by the ground-state inference in quantum annealing on a noisy device. It is shown that the average Hamming distance between the inferred spin configuration and the true ground state is minimized when the temperature of the noisy system is kept at a finite value, and not at zero temperature. We present a spin-glass generalization of a well-established result that the ground state of a purely ferromagnetic Hamiltonian is best inferred at a finite temperature in the sense of smallest Hamming distance when the original ferromagnetic interactions are disturbed by noise. We use the numerical transfer-matrix method to establish the existence of an optimal finite temperature in one- and two-dimensional systems. Our numerical results are supported by mean-field calculations, which give an explicit expression of the optimal temperature to infer the spin-glass ground state as a function of variances of the distributions of the original interactions and the noise. The mean-field prediction is in qualitative agreement with numerical data. Implications on postprocessing of quantum annealing on a noisy device are discussed.
Finite-temperature correlations in the Lieb-Liniger one-dimensional Bose gas
Panfil, M.; Caux, J.-S.
2014-01-01
We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional, strongly correlated system: the integrable one-dimensional Bose gas with a repulsive δ-function interaction (the Lieb-Liniger model). Focusing on the dynamical density-density f
Leibniz algebras associated with some finite-dimensional representation of Diamond Lie algebra
Camacho, Luisa M.; Ladra, Manuel; Karimjanov, Iqboljon A.; Omirov, Bakhrom A.
2016-03-01
In this paper we classify Leibniz algebras whose associated Lie algebra is four-dimensional Diamond Lie algebra 𝕯 and the ideal generated by squares of elements is represented by one of the finite-dimensional indecomposable D-modules Un 1, Un 2 or Wn 1 or Wn 2.
Quantum Fluids of Self-Assembled Chains of Polar Molecules at Finite Temperature
Institute of Scientific and Technical Information of China (English)
ZHU Kun-Yan; TAN Lei; GAO Xiang; WANG Daw-Wei
2008-01-01
The finite temperature properties of self-assembled dipole chains of polar molecules in strongly confined pancake traps are investigated.The single-chain vibrations at finite temperature,which become important for long chains in a strongly interacting regime,are found to lower the transition temperature and to shift the chain distribution by less than 10%.We also propose experimental parameters to observe such quantum phase transition.
Dimensional flow in discrete quantum geometries
Calcagni, Gianluca; Thürigen, Johannes
2014-01-01
In various theories of quantum gravity, one observes a change in the spectral dimension from the topological spatial dimension $d$ at large length scales to some smaller value at small, Planckian scales. While the origin of such a flow is well understood in continuum approaches, in theories built on discrete structures a firm control of the underlying mechanism is still missing. We shed some light on the issue by presenting a particular class of quantum geometries with a flow in the spectral dimension, given by superpositions of states defined on regular complexes. For particular superposition coefficients parametrized by a real number $0<\\alpha
Finite-block-length analysis in classical and quantum information theory.
Hayashi, Masahito
2017-01-01
Coding technology is used in several information processing tasks. In particular, when noise during transmission disturbs communications, coding technology is employed to protect the information. However, there are two types of coding technology: coding in classical information theory and coding in quantum information theory. Although the physical media used to transmit information ultimately obey quantum mechanics, we need to choose the type of coding depending on the kind of information device, classical or quantum, that is being used. In both branches of information theory, there are many elegant theoretical results under the ideal assumption that an infinitely large system is available. In a realistic situation, we need to account for finite size effects. The present paper reviews finite size effects in classical and quantum information theory with respect to various topics, including applied aspects.
Quantum electron-vibrational dynamics at finite temperature: Thermo field dynamics approach
Borrelli, Raffaele; Gelin, Maxim F.
2016-12-01
Quantum electron-vibrational dynamics in molecular systems at finite temperature is described using an approach based on the thermo field dynamics theory. This formulation treats temperature effects in the Hilbert space without introducing the Liouville space. A comparison with the theoretically equivalent density matrix formulation shows the key numerical advantages of the present approach. The solution of thermo field dynamics equations with a novel technique for the propagation of tensor trains (matrix product states) is discussed. Numerical applications to model spin-boson systems show that the present approach is a promising tool for the description of quantum dynamics of complex molecular systems at finite temperature.
Non perturbative methods in two dimensional quantum field theory
Abdalla, Elcio; Rothe, Klaus D
1991-01-01
This book is a survey of methods used in the study of two-dimensional models in quantum field theory as well as applications of these theories in physics. It covers the subject since the first model, studied in the fifties, up to modern developments in string theories, and includes exact solutions, non-perturbative methods of study, and nonlinear sigma models.
Local distinguishability of quantum states in infinite dimensional systems
Ogata, Y
2005-01-01
We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and classical communications, even for infinite dimensional systems. An estimate of the local discrimination probability is also given for some family of more than two pure states.
Higher dimensional supersymmetric quantum mechanics and Dirac equation
Indian Academy of Sciences (India)
L P Singh; B Ram
2002-04-01
We exhibit the supersymmetric quantum mechanical structure of the full 3+1 dimensional Dirac equation considering `mass' as a function of coordinates. Its usefulness in solving potential problems is discussed with speciﬁc examples. We also discuss the `physical' signiﬁcance of the supersymmetric states in this formalism.
Irreducible quantum group modules with finite dimensional weight spaces
DEFF Research Database (Denmark)
Pedersen, Dennis Hasselstrøm
We classify all irreducible weight modules for a quantized enveloping algebra U q (g) at most q ∈ C ∗ when the simple Lie algebra g is not of type G 2 . More precisely, our classificiation is carried out when q is either an odd root of unity or transcendental over Q. By a weight module we mean...
Bauman, Sky
2008-01-01
In a previous companion paper [arXiv:0712.3532], we proposed two new regulators for quantum field theories in spacetimes with compactified extra dimensions. Unlike most other regulators which have been used in the extra-dimension literature, these regulators are specifically designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. In this paper, we use these regulators in order to develop a method for extracting ultraviolet-finite results from one-loop calculations. This method also allows us to derive Wilsonian effective field theories for Kaluza-Klein modes at different energy scales. Our method operates by ensuring that divergent corrections to parameters describing the physics of the excited Kaluza-Klein modes are absorbed into the corresponding parameters for zero modes, thereby eliminating the need to introduce independent counterterms for parameters characterizing differe...
Inglis, Stephen; Melko, Roger G
2013-01-01
We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC) simulations for the purpose of calculating the Rényi entanglement entropies and associated mutual information. The algorithm converges an estimate for an analog to the density of states for stochastic series expansion QMC, allowing a direct calculation of Rényi entropies without explicit thermodynamic integration. We benchmark results for the mutual information on two-dimensional (2D) isotropic and anisotropic Heisenberg models, a 2D transverse field Ising model, and a three-dimensional Heisenberg model, confirming a critical scaling of the mutual information in cases with a finite-temperature transition. We discuss the benefits and limitations of broad sampling techniques compared to standard importance sampling methods.
Large \\theta_13 from finite quantum corrections in quasi-degenerate neutrino mass spectrum
Araki, Takeshi
2011-01-01
We study finite quantum corrections for several well known neutrino mixing matrices and find that it is hard to account for the large value of \\theta_13 recently reported by T2K and MINOS. To nicely reproduce all experimentally favored neutrino mixing angles and masses, we propose a new neutrino mixing pattern. We also demonstrate a simple realization by slightly extending the standard model to illustrate the quantum corrections.
Three-Dimensional Wiring for Extensible Quantum Computing: The Quantum Socket
Béjanin, J. H.; McConkey, T. G.; Rinehart, J. R.; Earnest, C. T.; McRae, C. R. H.; Shiri, D.; Bateman, J. D.; Rohanizadegan, Y.; Penava, B.; Breul, P.; Royak, S.; Zapatka, M.; Fowler, A. G.; Mariantoni, M.
2016-10-01
Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error-correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and the measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: the quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum socket is based on spring-mounted microwires—the three-dimensional wires—that push directly on a microfabricated chip, making electrical contact. A small wire cross section (approximately 1 mm), nearly nonmagnetic components, and functionality at low temperatures make the quantum socket ideal for operating solid-state qubits. The wires have a coaxial geometry and operate over a frequency range from dc to 8 GHz, with a contact resistance of approximately 150 m Ω , an impedance mismatch of approximately 10 Ω , and minimal cross talk. As a proof of principle, we fabricate and use a quantum socket to measure high-quality superconducting resonators at a temperature of approximately 10 mK. Quantum error-correction codes such as the surface code will largely benefit from the quantum socket, which will make it possible to address qubits located on a two-dimensional lattice. The present implementation of the socket could be readily extended to accommodate a
Three dimensional mathematical model of tooth for finite element analysis
Directory of Open Access Journals (Sweden)
Puškar Tatjana
2010-01-01
Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
[Three dimensional mathematical model of tooth for finite element analysis].
Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka
2010-01-01
The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids
Holzmann, Markus; Morales, Miguel A; Tubmann, Norm M; Ceperley, David M; Pierleoni, Carlo
2016-01-01
Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation functions. We introduce new effective procedures, such as using the potential and wavefunction split-up into long and short range functions to simplify the method and we discuss how to treat backflow wavefunctions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems.
High-dimensional quantum key distribution with the entangled single-photon-added coherent state
Wang, Yang; Bao, Wan-Su; Bao, Hai-Ze; Zhou, Chun; Jiang, Mu-Sheng; Li, Hong-Wei
2017-04-01
High-dimensional quantum key distribution (HD-QKD) can generate more secure bits for one detection event so that it can achieve long distance key distribution with a high secret key capacity. In this Letter, we present a decoy state HD-QKD scheme with the entangled single-photon-added coherent state (ESPACS) source. We present two tight formulas to estimate the single-photon fraction of postselected events and Eve's Holevo information and derive lower bounds on the secret key capacity and the secret key rate of our protocol. We also present finite-key analysis for our protocol by using the Chernoff bound. Our numerical results show that our protocol using one decoy state can perform better than that of previous HD-QKD protocol with the spontaneous parametric down conversion (SPDC) using two decoy states. Moreover, when considering finite resources, the advantage is more obvious.
Numerical study for the c-dependence of fractal dimension in two-dimensional quantum gravity
Kawamoto, N; Kawamoto, Noboru; Yotsuji, Kenji
2002-01-01
We numerically investigate the fractal structure of two-dimensional quantum gravity coupled to matter central charge c for $-2 \\leq c \\leq 1$. We reformulate Q-state Potts model into the model which can be identified as a weighted percolation cluster model and can make continuous change of Q, which relates c, on the dynamically triangulated lattice. The c-dependence of the critical coupling is measured from the percolation probability and susceptibility. The c-dependence of the string susceptibility of the quantum surface is evaluated and has very good agreement with the theoretical predictions. The c-dependence of the fractal dimension based on the finite size scaling hypothesis is measured and has excellent agreement with one of the theoretical predictions previously proposed except for the region near $c\\approx 1$.
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.
Stability analysis of finite difference schemes for quantum mechanical equations of motion
Chattaraj, P. K.; Deb, B. M.; Koneru, S. Rao
1987-10-01
For a pdf involving both space and time variables, stability criteria are presently shown to change drastically when the equation contains i, as in the quantum-mechanical equations of motion. It is further noted that the stability of finite difference schemes for quantum-mechanical equations of motion depends on both spatial and temporal zoning. It is possible to compare a free particle Green's function to the solution of a simple diffusion equation, and the quantum-mechanical motion of a free particle to Fresnel diffraction in optics.
Polarized heat current generated by quantum pumping in two-dimensional topological insulators
Ronetti, F.; Carrega, M.; Ferraro, D.; Rech, J.; Jonckheere, T.; Martin, T.; Sassetti, M.
2017-03-01
We consider the transport properties of a two-dimensional topological insulator in a double quantum point contact geometry in the presence of a time-dependent external field. In the proposed setup an external gate is placed above a single constriction and it couples only with electrons belonging to the top edge. This asymmetric configuration and the presence of an ac signal allow for a quantum pumping mechanism, which, in turn, can generate finite heat and charge currents in an unbiased device configuration. A microscopic model for coupling with the external time-dependent gate potential is developed and the induced finite heat and charge currents are investigated. We demonstrate that in the noninteracting case, heat flow is associated with a single spin component, due to the helical nature of the edge states, and therefore a finite and polarized heat current is obtained in this configuration. The presence of e -e interchannel interactions strongly affects the current signal, lowering the degree of polarization of the system. Finally, we also show that separate heat and charge flows can be achieved, varying the amplitude of the external gate.
Quantum discriminant analysis for dimensionality reduction and classification
Cong, Iris; Duan, Luming
2016-07-01
We present quantum algorithms to efficiently perform discriminant analysis for dimensionality reduction and classification over an exponentially large input data set. Compared with the best-known classical algorithms, the quantum algorithms show an exponential speedup in both the number of training vectors M and the feature space dimension N. We generalize the previous quantum algorithm for solving systems of linear equations (2009 Phys. Rev. Lett. 103 150502) to efficiently implement a Hermitian chain product of k trace-normalized N ×N Hermitian positive-semidefinite matrices with time complexity of O({log}(N)). Using this result, we perform linear as well as nonlinear Fisher discriminant analysis for dimensionality reduction over M vectors, each in an N-dimensional feature space, in time O(p {polylog}({MN})/{ε }3), where ɛ denotes the tolerance error, and p is the number of principal projection directions desired. We also present a quantum discriminant analysis algorithm for data classification with time complexity O({log}({MN})/{ε }3).
On a First-Order Quantum Phase Transition in a Finite System
Leviatan, A
2006-01-01
We examine the dynamics at the critical-point of a general first-order quantum phase transition in a finite system. Suitable Hamiltonians are constructed whose spectra exhibit coexistence of states corresponding to two degenerate minima in the energy surface separated by an arbitrary barrier. Explicit expressions are derived for wave functions and obesrvables at the critical-point.
Quantum Fluctuation in Mesoscopic Coupled LC Electric Circuits at FiniteTemperature
Institute of Scientific and Technical Information of China (English)
LIANG Xian-Ting; FAN Hong-Yi
2001-01-01
We consider the quantization of two coupled LC circuits with mutual inductance at a finite temperature T. It is shown that the quantum mechanical zero-point fluctuations of currents in the two circuits both increase with upgoing T. Thermal field dynamics and Weyl-Wigner theorern are used in our calculation of ensemble average of the observables.
Symmetry and Degeneracy in Quantum Mechanics. Self-Duality in Finite Spin Systems
Osacar, C.; Pacheco, A. F.
2009-01-01
The symmetry of self-duality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…
Symmetry and Degeneracy in Quantum Mechanics. Self-Duality in Finite Spin Systems
Osacar, C.; Pacheco, A. F.
2009-01-01
The symmetry of self-duality (Savit 1980 "Rev. Mod. Phys. 52" 453) of some models of statistical mechanics and quantum field theory is discussed for finite spin blocks of the Ising chain in a transverse magnetic field. The existence of this symmetry in a specific type of these blocks, and not in others, is manifest by the degeneracy of their…
Quantum Monte Carlo calculations of two neutrons in finite volume
Klos, P; Tews, I; Gandolfi, S; Gezerlis, A; Hammer, H -W; Hoferichter, M; Schwenk, A
2016-01-01
Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial for determining observables from the calculated energies. Using the L\\"uscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.
Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2004-01-01
The subject of the paper is the derivation of finite volume evolution Galerkin schemes for three-dimensional wave equation system. The aim is to construct methods which take into account all of the infinitely many directions of propagation of bicharacteristics. The idea is to evolve the initial function using the characteristic cone and then to project onto a finite element space. Numerical experiments are presented to demonstrate the accuracy and the multidimensional behaviour of the solutio...
Three-dimensional finite element analysis of critical pre-twist strain angle for torsional axis
Institute of Scientific and Technical Information of China (English)
ZHOU Guo-feng; LI Xiao-yan; SHI Yao-wu; XU Bin-shi
2005-01-01
A three-dimensional elasto-plastic finite element analysis of pre-twist process for a torsional axis made of 45GrNiMoVA steel, was carried out using a commercial finite element analysis code, MSC MARC 2001. The results show that the critical pre-twist strain angle is 0. 027 rad and the maximum elastic shear stress after pre-twist is 1 694 MPa for the torsional axis.
Invariants of 3-Manifolds derived from finite dimensional hopf algebras
Kauffman, L H; Louis H Kauffman; David E Radford
1994-01-01
Abstract: This paper studies invariants of 3-manifolds derived from certain fin ite dimensional Hopf algebras. The invariants are based on right integrals for these algebras. It is shown that the resulting class of invariants is distinct from the class of Witten-Reshetikhin-Turaev invariants.
Ising Model Coupled to Three-Dimensional Quantum Gravity
Baillie, C F
1992-01-01
We have performed Monte Carlo simulations of the Ising model coupled to three-dimensional quantum gravity based on a summation over dynamical triangulations. These were done both in the microcanonical ensemble, with the number of points in the triangulation and the number of Ising spins fixed, and in the grand canoncal ensemble. We have investigated the two possible cases of the spins living on the vertices of the triangulation (``diect'' case) and the spins living in the middle of the tetrahedra (``dual'' case). We observed phase transitions which are probably second order, and found that the dual implementation more effectively couples the spins to the quantum gravity.
Topological Quantum Optics in Two-Dimensional Atomic Arrays
Perczel, J.; Borregaard, J.; Chang, D. E.; Pichler, H.; Yelin, S. F.; Zoller, P.; Lukin, M. D.
2017-07-01
We demonstrate that two-dimensional atomic emitter arrays with subwavelength spacing constitute topologically protected quantum optical systems where the photon propagation is robust against large imperfections while losses associated with free space emission are strongly suppressed. Breaking time-reversal symmetry with a magnetic field results in gapped photonic bands with nontrivial Chern numbers and topologically protected, long-lived edge states. Due to the inherent nonlinearity of constituent emitters, such systems provide a platform for exploring quantum optical analogs of interacting topological systems.
Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Guth, Larry; Lubotzky, Alexander
2014-08-01
Using 4-dimensional arithmetic hyperbolic manifolds, we construct some new homological quantum error correcting codes. They are low density parity check codes with linear rate and distance nɛ. Their rate is evaluated via Euler characteristic arguments and their distance using {Z}_2-systolic geometry. This construction answers a question of Zémor ["On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction," in Proceedings of Second International Workshop on Coding and Cryptology (IWCC), Lecture Notes in Computer Science Vol. 5557 (2009), pp. 259-273], who asked whether homological codes with such parameters could exist at all.
Finite Casimir Energies in Renormalizable Quantum Field Theory
Milton, K A
2004-01-01
Quantum vacuum energy has been known to have observable consequences since 1948 when Casimir calculated the force of attraction between parallel uncharged plates, a phenomenon confirmed experimentally with ever increasing precision. Casimir himself suggested that a similar attractive self-stress existed for a conducting spherical shell, but Boyer obtained a repulsive stress. Other geometries and higher dimensions have been considered over the years. Local effects, and divergences associated with surfaces and edges have been investigated by several authors. Quite recently, Graham et al. have re-examined such calculations, using conventional techniques of perturbative quantum field theory to remove divergences, and have suggested that previous self-stress results may be suspect. Here we show that most of the examples considered in their work are misleading; in particular, it is well-known that in two dimensions a circular boundary has a divergence in the Casimir energy for massless fields, while for general dim...
Tight finite-key analysis for quantum cryptography.
Tomamichel, Marco; Lim, Charles Ci Wen; Gisin, Nicolas; Renner, Renato
2012-01-17
Despite enormous theoretical and experimental progress in quantum cryptography, the security of most current implementations of quantum key distribution is still not rigorously established. One significant problem is that the security of the final key strongly depends on the number, M, of signals exchanged between the legitimate parties. Yet, existing security proofs are often only valid asymptotically, for unrealistically large values of M. Another challenge is that most security proofs are very sensitive to small differences between the physical devices used by the protocol and the theoretical model used to describe them. Here we show that these gaps between theory and experiment can be simultaneously overcome by using a recently developed proof technique based on the uncertainty relation for smooth entropies.
Quantum state discrimination bounds for finite sample size
Audenaert, Koenraad M R; Verstraete, Frank
2012-01-01
In the problem of quantum state discrimination, one has to determine by measurements the state of a quantum system, based on the a priori side information that the true state is one of two given and completely known states, rho or sigma. In general, it is not possible to decide the identity of the true state with certainty, and the optimal measurement strategy depends on whether the two possible errors (mistaking rho for sigma, or the other way around) are treated as of equal importance or not. Recent results on the quantum Chernoff and Hoeffding bounds show that, if several copies of the system are available then the optimal error probabilities decay exponentially in the number of copies, and the decay rate is given by a certain statistical distance between rho and sigma (the Chernoff distance and the Hoeffding distances, respectively). While these results provide a complete solution for the asymptotic problem, they are not completely satisfying from a practical point of view. Indeed, in realistic scenarios ...
Finite-dimensional attractors for the Kirchhoff models with critical exponents
Zhijian, Yang
2012-03-01
The paper studies the existence of the finite-dimensional global attractor and exponential attractor for the dynamical system associated with the Kirchhoff models utt - ∇ . {|∇u|m - 1∇u} - Δut + Δ2u + h(ut) + g(u) = f(x). It proves that for the subcritical and critical cases: 1
A finite-dimensional reduction method for slightly supercritical elliptic problems
Directory of Open Access Journals (Sweden)
Riccardo Molle
2004-01-01
Full Text Available We describe a finite-dimensional reduction method to find solutions for a class of slightly supercritical elliptic problems. A suitable truncation argument allows us to work in the usual Sobolev space even in the presence of supercritical nonlinearities: we modify the supercritical term in such a way to have subcritical approximating problems; for these problems, the finite-dimensional reduction can be obtained applying the methods already developed in the subcritical case; finally, we show that, if the truncation is realized at a sufficiently large level, then the solutions of the approximating problems, given by these methods, also solve the supercritical problems when the parameter is small enough.
A finite area scheme for shallow granular flows on three-dimensional surfaces
Rauter, Matthias
2017-04-01
Shallow granular flow models have become a popular tool for the estimation of natural hazards, such as landslides, debris flows and avalanches. The shallowness of the flow allows to reduce the three-dimensional governing equations to a quasi two-dimensional system. Three-dimensional flow fields are replaced by their depth-integrated two-dimensional counterparts, which yields a robust and fast method [1]. A solution for a simple shallow granular flow model, based on the so-called finite area method [3] is presented. The finite area method is an adaption of the finite volume method [4] to two-dimensional curved surfaces in three-dimensional space. This method handles the three dimensional basal topography in a simple way, making the model suitable for arbitrary (but mildly curved) topography, such as natural terrain. Furthermore, the implementation into the open source software OpenFOAM [4] is shown. OpenFOAM is a popular computational fluid dynamics application, designed so that the top-level code mimics the mathematical governing equations. This makes the code easy to read and extendable to more sophisticated models. Finally, some hints on how to get started with the code and how to extend the basic model will be given. I gratefully acknowledge the financial support by the OEAW project "beyond dense flow avalanches". Savage, S. B. & Hutter, K. 1989 The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics 199, 177-215. Ferziger, J. & Peric, M. 2002 Computational methods for fluid dynamics, 3rd edn. Springer. Tukovic, Z. & Jasak, H. 2012 A moving mesh finite volume interface tracking method for surface tension dominated interfacial fluid flow. Computers & fluids 55, 70-84. Weller, H. G., Tabor, G., Jasak, H. & Fureby, C. 1998 A tensorial approach to computational continuum mechanics using object-oriented techniques. Computers in physics 12(6), 620-631.
Energy Technology Data Exchange (ETDEWEB)
Weber, Carsten
2008-07-01
This work is focused on the optical dynamics of mesoscopic semiconductor heterostructures, using as prototypes zero-dimensional quantum dots and quantum cascade lasers which consist of quasitwo- dimensional quantum wells. Within a density matrix theory, a microscopic many-particle theory is applied to study scattering effects in these structures: the coupling to external as well as local fields, electron-phonon coupling, coupling to impurities, and Coulomb coupling. For both systems, the investigated effects are compared to experimentally observed results obtained during the past years. In quantum dots, the three-dimensional spatial confinement leads to the necessity to consider a quantum kinetic description of the dynamics, resulting in non-Markovian electron-phonon effects. This can be seen in the spectral phonon sidebands due to interaction with acoustic phonons as well as a damping of nonlinear Rabi oscillations which shows a nonmonotonous intensity and pulse duration dependence. An analysis of the inclusion of the self-interaction of the quantum dot shows that no dynamical local field terms appear for the simple two-level model. Considering local fields which have their origin in many quantum dots, consequences for a two-level quantum dot such as a zero-phonon line broadening and an increasing signal in photon echo experiments are found. For the use of quantum dots in an optical spin control scheme, it is found that the dephasing due to the electron-phonon interaction can be dominant in certain regimes. Furthermore, soliton and breather solutions are studied analytically in nonlinear quantum dot ensembles. Generalizing to quasi-two-dimensional structures, the intersubband dynamics of quantum cascade laser structures is investigated. A dynamical theory is considered in which the temporal evolution of the subband populations and the current density as well as the influence of scattering effects is studied. In the nonlinear regime, the scattering dependence and
A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton
Arrighi, Pablo
2010-01-01
We describe a simple n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the intrinsically universal QCA. Several steps of the intrinsically universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA.
Nonlinearly-enhanced energy transport in many dimensional quantum chaos
Brambila, D. S.
2013-08-05
By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter.
Multiple Potts Models Coupled to Two-Dimensional Quantum Gravity
Baillie, C F
1992-01-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of {\\it multiple} $q=2,3,4$ state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the $c>1$ region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for $c>1$. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for $c>1$.
Multiple Potts models coupled to two-dimensional quantum gravity
Baillie, C. F.; Johnston, D. A.
1992-07-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of multiple q=2, 3, 4 state Potts models on dynamical phi-cubed graphs of spherical topology in order to investigate the c>1 region of two-dimensional quantum gravity. Contrary to naive expectation we find no obvious signs of pathological behaviour for c>1. We discuss the results in the light of suggestions that have been made for a modified DDK ansatz for c>1.
Physical quantities and dimensional analysis: from mechanics to quantum gravity
Trancanelli, Diego
2015-01-01
Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional analysis, I will embark in a journey through various branches of physics, from basic mechanics to quantum gravity. I will also discuss a little bit about the fundamental constants of Nature, the so-called "cube of Physics", and the natural system of units.
Matveev, A. D.
2016-11-01
To calculate the three-dimensional elastic body of heterogeneous structure under static loading, a method of multigrid finite element is provided, when implemented on the basis of algorithms of finite element method (FEM), using homogeneous and composite threedimensional multigrid finite elements (MFE). Peculiarities and differences of MFE from the currently available finite elements (FE) are to develop composite MFE (without increasing their dimensions), arbitrarily small basic partition of composite solids consisting of single-grid homogeneous FE of the first order can be used, i.e. in fact, to use micro approach in finite element form. These small partitions allow one to take into account in MFE, i.e. in the basic discrete models of composite solids, complex heterogeneous and microscopically inhomogeneous structure, shape, the complex nature of the loading and fixation and describe arbitrarily closely the stress and stain state by the equations of three-dimensional elastic theory without any additional simplifying hypotheses. When building the m grid FE, m of nested grids is used. The fine grid is generated by a basic partition of MFE, the other m —1 large grids are applied to reduce MFE dimensionality, when m is increased, MFE dimensionality becomes smaller. The procedures of developing MFE of rectangular parallelepiped, irregular shape, plate and beam types are given. MFE generate the small dimensional discrete models and numerical solutions with a high accuracy. An example of calculating the laminated plate, using three-dimensional 3-grid FE and the reference discrete model is given, with that having 2.2 milliards of FEM nodal unknowns.
Finite amplitude waves in two-dimensional lined ducts
Nayfeh, A. H.; Tsai, M.-S.
1974-01-01
A second-order uniform expansion is obtained for nonlinear wave propagation in a two-dimensional duct lined with a point-reacting acoustic material consisting of a porous sheet followed by honeycomb cavities and backed by the impervious wall of the duct. The waves in the duct are coupled with those in the porous sheet and the cavities. An analytical expression is obtained for the absorption coefficient in terms of the sound frequency, the physical properties of the porous sheet, and the geometrical parameters of the flow configuration. The results show that the nonlinearity flattens and broadens the absorption vs. frequency curve, irrespective of the geometrical dimensions or the porous material acoustic properties, in agreement with experimental observations.
Dipolar quantum electrodynamics of the two-dimensional electron gas
Todorov, Yanko
2015-03-01
Similarly to a previous work on the homogeneous electron gas [Y. Todorov, Phys. Rev. B 89, 075115 (2014), 10.1103/PhysRevB.89.075115], we apply the Power-Zienau-Wooley (PZW) formulation of the quantum electrodynamics to the case of an electron gas quantum confined by one-dimensional potential. We provide a microscopic description of all collective plasmon modes of the gas, oscillating both along and perpendicular to the direction of quantum confinement. Furthermore, we study the interaction of the collective modes with a photonic structure, planar metallic waveguide, by using the full expansion of the electromagnetic field into normal modes. We show how the boundary conditions for the electromagnetic field influence both the transverse light-matter coupling and the longitudinal particle-particle interactions. The PZW descriptions appear thus as a convenient tool to study semiconductor quantum optics in geometries where quantum-confined particles interact with strongly confined electromagnetic fields in microresonators, such as the ones used to achieve the ultrastrong light-matter coupling regime.
Lorimer, W. L.; Lieu, D. K.; Hull, J. R.; Mulcahy, T. M.; Rossing, T. D.
A permanent magnet quadrupole spinning over an aluminum disk was constructed, and drag torque was measured for various speeds and gap sizes. The experiment was modeled using a three-dimensional finite element program. Experimental and analytical results were compared, and the effect of magnet polarity was determined.
Large parallel volumes of finite and compact sets in d-dimensional Euclidean space
DEFF Research Database (Denmark)
Kampf, Jürgen; Kiderlen, Markus
The r-parallel volume V (Cr) of a compact subset C in d-dimensional Euclidean space is the volume of the set Cr of all points of Euclidean distance at most r > 0 from C. According to Steiner’s formula, V (Cr) is a polynomial in r when C is convex. For finite sets C satisfying a certain geometric ...
Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System
Jing Yu; Jingwei Han
2014-01-01
Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation and $r$ -matrix are also given in this paper.
Two-Component Super AKNS Equations and Their Finite-Dimensional Integrable Super Hamiltonian System
Directory of Open Access Journals (Sweden)
Jing Yu
2014-01-01
Full Text Available Starting from a matrix Lie superalgebra, two-component super AKNS system is constructed. By making use of monononlinearization technique of Lax pairs, we find that the obtained two-component super AKNS system is a finite-dimensional integrable super Hamiltonian system. And its Lax representation and r-matrix are also given in this paper.
Generalized results on the role of new-time transformations in finite-dimensional Poisson systems
Energy Technology Data Exchange (ETDEWEB)
Hernandez-Bermejo, Benito, E-mail: benito.hernandez@urjc.e [Departamento de Fisica, Escuela Superior de Ciencias Experimentales y Tecnologia, Universidad Rey Juan Carlos, Calle Tulipan S/N, 28933 Mostoles, Madrid (Spain)
2010-01-25
The problem of characterizing all new-time transformations preserving the Poisson structure of a finite-dimensional Poisson system is completely solved in a constructive way. As a corollary, this leads to a broad generalization of previously known results. Examples are given.
The finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model
Balog, Janos(Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, MTA Lendület Holographic QFT Group, 1525, Budapest 114, P.O.B. 49, Hungary); Hegedus, Arpad
2009-01-01
Nonlinear integral equations are proposed for the description of the full finite size spectrum of the 2-dimensional O(3) nonlinear sigma-model in a periodic box. Numerical results for the energy eigenvalues are compared to the rotator spectrum and perturbation theory for small volumes and with the recently proposed generalized Luscher formulas at large volumes.
Coherent States for generalized oscillator with finite-dimensional Hilbert space
Borzov, Vadim V.; Damaskinsky, Eugene V.
2006-01-01
The construction of oscillator-like systems connected with the given set of orthogonal polynomials and coherent states for such systems developed by authors is extended to the case of the systems with finite-dimensional state space. As example we consider the generalized oscillator connected with Krawtchouk polynomials.
A new look at the harmonic oscillator problem in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Bagchi, B. [Calcutta Univ. (India). Dept. of Applied Mathematics; Roy, P.K. [Department of Physics, Haldia Government College, Haldia 721 657, West Bengal (India)
1995-05-08
In this Letter some basic properties of a truncated oscillator are studied. By using finite-dimensional representation matrices of the truncated oscillator we construct new parasupersymmetric schemes and remark on their relevance to the transition operators of the non-interacting N-level system endowed with bosonic modes. ((orig.)).
A three-dimensional finite element model of the polymerization process in dental restorations.
Barink, M.; Mark, P.C. van der; Fennis, W.M.M.; Kuys, R.H.; Kreulen, C.M.; Verdonschot, N.J.J.
2003-01-01
Restoration of dental restorations with resin composite is hampered by shrinkage of the material during the polymerization process. In this study, we simulated the polymerization process in a detailed three-dimensional finite element model of a human upper premolar with a cusp-replacing restoration.
Three-dimensional finite element simulation of intermingled-fiber hybrid composite behavior
Mital, Subodh K.; Chamis, Christos C.
1992-01-01
Three-dimensional finite element methods and the intraply hybrid micromechanics equations are used to predict composite properties for a unidirectional graphite-epoxy primary composite with S-glass fibers used as hybridizing fibers. The micromechanics equations are embedded in a computer code ICAN (Integrated Composites Analyzer). The three-dimensional finite element model consists of three-by-three unit cell array, with a total fiber volume ratio of 0.54. There is a good agreement between the composite properties and microstresses obtained from both methods. The results indicate that the finite element methods and micromechanics equations can be used to obtain the properties of intermingled hybrid composites needed for analysis/design of hybrid composite structures.
Three dimensional finite temperature SU(3) gauge theory near the phase transition
Bialas, Piotr; Morel, Andre; Petersson, Bengt
2012-01-01
We have measured the correlation function of Polyakov loops on the lattice in three dimensional SU(3) gauge theory near its finite temperature phase transition. Using a new and powerful application of finite size scaling, we furthermore extend the measurements of the critical couplings to considerably larger values of the lattice sizes, both in the temperature and space directions, than was investigated earlier in this theory. With the help of these measurements we perform a detailed finite size scaling analysis, showing that for the critical exponents of the two dimensional three state Potts model the mass and the susceptibility fall on unique scaling curves. This strongly supports the expectation that the gauge theory is in the same universality class. The Nambu-Goto string model on the other hand predicts that the exponent \
Laser driven impurity states in two-dimensional quantum dots and quantum rings
Laroze, D.; Barseghyan, M.; Radu, A.; Kirakosyan, A. A.
2016-11-01
The hydrogenic donor impurity states in two-dimensional GaAs/Ga0.7Al0.3As quantum dot and quantum ring have been investigated under the action of intense laser field. A laser dressed effect on both electron confining and electron-impurity Coulomb interaction potentials has been considered. The single electron energy spectrum and wave functions have been found using the effective mass approximation and exact diagonalization technique. The accidental degeneracy of the impurity states have been observed for different positions of the impurity and versus values of the laser field parameter. The obtained theoretical results indicate a novel opportunity to tune the performance of quantum dots and quantum rings and to control their specific properties by means of laser field.
Warehime, Mick; Alexander, Millard H
2014-07-14
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic one-dimensional models. Application is made here to a symmetric reaction (H+H2), a heavy-light-light reaction (F+H2), and a heavy-light-heavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atom-diatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.
Energy Technology Data Exchange (ETDEWEB)
Warehime, Mick [Chemical Physics Program, University of Maryland, College Park, Maryland 20742-2021 (United States); Alexander, Millard H., E-mail: mha@umd.edu [Department of Chemistry and Biochemistry and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742-2021 (United States)
2014-07-14
We restate the application of the finite element method to collinear triatomic reactive scattering dynamics with a novel treatment of the scattering boundary conditions. The method provides directly the reactive scattering wave function and, subsequently, the probability current density field. Visualizing these quantities provides additional insight into the quantum dynamics of simple chemical reactions beyond simplistic one-dimensional models. Application is made here to a symmetric reaction (H+H{sub 2}), a heavy-light-light reaction (F+H{sub 2}), and a heavy-light-heavy reaction (F+HCl). To accompany this article, we have written a MATLAB code which is fast, simple enough to be accessible to a wide audience, as well as generally applicable to any problem that can be mapped onto a collinear atom-diatom reaction. The code and user's manual are available for download from http://www2.chem.umd.edu/groups/alexander/FEM.
Finite action, holographic conformal anomaly and quantum brane-worlds in d5 gauged supergravity
Nojiri, S; Odintsov, S D; Ogushi, S
2002-01-01
We report our recent results concerning d5 gauged supergravity (dilatonic gravity) considered on AdS background. The finite action on such background as well as d4 holographic conformal anomaly (via AdS/CFT correspondence) are found. In such formalism the bulk potential is kept to be arbitrary, dilaton dependent function. Holographic RG in such theory is briefly discussed. d5 AdS brane-world Universe induced by quantum effects of brane CFT is constructed. Such brane is spherical, hyperbolic or flat one. Hence, the possibility of quantum creation of inflationary brane-world Universe is shown.
On the origin of quantum criticality found at finite doping in 2D Hubbard model
Yang, Shuxiang; Fotso, Herbert; Moreno, Juana; Jarrell, Mark
2011-03-01
To better understand the excitations responsible for quantum criticality (QC) found at finite doping in the 2D Hubbard model, we analyze the vertices for different scattering channels obtained from the Dynamical Cluster Continuous-Time Quantum Monte Carlo simulation. By decomposing these vertices using the parquet equations we find that both superconductivity and the charge instabilities responsible for the QC come from the crossed spin channel contribution, and thus are driven by the spin-fluctuations. On contrast, the spin instability comes from the fully irreducible spin vertex contribution. We acknowledge the support from NSF OISE-0730290 and DOE SciDAC DE-FC02-06ER25792.
Energy Technology Data Exchange (ETDEWEB)
Jain, Shweta, E-mail: jshweta09@gmail.com; Sharma, Prerana [Department of Physics, Ujjain Engineering College, Ujjain, M.P.456010 (India); Chhajlani, R. K. [School of Studies in Physics, Vikram University Ujjain, M. P. - 456010 (India)
2015-07-31
The Jeans instability of self-gravitating quantum plasma is examined considering the effects of viscosity, finite Larmor radius (FLR) corrections and rotation. The analysis is done by normal mode analysis theory with the help of relevant linearized perturbation equations of the problem. The general dispersion relation is obtained using the quantum magneto hydrodynamic model. The modified condition of Jeans instability is obtained and the numerical calculations have been performed to show the effects of various parameters on the growth rate of Jeans instability.
Venkataraman, Divya
2016-01-01
Solutions to finite-dimensional (all spatial Fourier modes set to zero beyond a finite wavenumber $K_G$), inviscid equations of hydrodynamics at long times are known to be at variance with those obtained for the original infinite dimensional partial differential equations or their viscous counterparts. Surprisingly, the solution to such Galerkin-truncated equations develop sharp localised structures, called {\\it tygers} [Ray, et al., Phys. Rev. E {\\bf 84}, 016301 (2011)], which eventually lead to completely thermalised states associated with an equipartition energy spectrum. We now obtain precise estimates, theoretically and via direct numerical simulations, the time $\\tau_c$ at which thermalisation is triggered and show that $\\tau_c \\sim K_G^\\xi$, with $\\xi = -4/9$. Our results have several implications including for the analyticity strip method to numerically obtain evidence for or against blow-ups of the three-dimensional incompressible Euler equations.
Hamiltonian finite-temperature quantum field theory from its vacuum on partially compactified space
Reinhardt, Hugo
2016-01-01
The partition function of a relativistic invariant quantum field theory is expressed by its vacuum energy calculated on a spatial manifold with one dimension compactified to a 1-sphere $S^1 (\\beta)$, whose circumference $\\beta$ represents the inverse temperature. Explicit expressions for the usual energy density and pressure in terms of the energy density on the partially compactified spatial manifold $\\mathbb{R}^2 \\times S^1 (\\beta)$ are derived. To make the resulting expressions mathematically well-defined a Poisson resummation of the Matsubara sums as well as an analytic continuation in the chemical potential are required. The new approach to finite-temperature quantum field theories is advantageous in a Hamilton formulation since it does not require the usual thermal averages with the density operator. Instead, the whole finite-temperature behaviour is encoded in the vacuum wave functional on the spatial manifold $\\mathbb{R}^2 \\times S^1 (\\beta)$. We illustrate this approach by calculating the pressure of...
Kota, V K B
2015-01-01
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say $m$ particles in $N$ single particle states and interacting via $k$-body interactions, we have EGUE($k$) and the embedding algebra is $U(N)$. A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (same initial and final systems), nuclear beta and double beta decay (different initial and final systems), particle addition to/removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities, we have derived formulas for lower order bivariate moments of the strength densities generated by a variety of transition operators. For a spinless fermion system, using EGUE($k$) representation for Hamiltonian and an independent EGUE($...
Quantum creep in a highly crystalline two-dimensional superconductor
Saito, Yu; Kasahara, Yuichi; Ye, Jianting; Iwasa, Yoshihiro; Nojima, Tsutomu
Conventional studies on quantum phase transitions, especially on superconductor-insulator or superconductor-metal-insulator transitions have been performed in deposited metallic thin films such as Bismuth or MoGe. Although the techniques of thin films deposition have been considerably improved, unintentional disorder such as impurities and deficiencies, generating the pinning centers, seems to still exist in such systems. The mechanical exfoliated highly crystalline two-dimensional material can be a good candidate to realize a less-disordered 2D superconductor with extremely weak pinning, combined with transfer method or ionic-liquid gating. We report on the quantum metal, namely, magnetic-field-induced metallic state observed in an ion-gated two-dimensional superconductor based on an ultra-highly crystalline layered band insulator, ZrNCl. We found that the superconducting state is extremely fragile against external magnetic fields; that is, zero resistance state immediately disappears, once an external magnetic field switches on. This is because the present system is relatively clean and the pinning potential is extremely weak, which cause quantum tunneling and flux flow of vortices, resulting in metallic ground state.
C*-Structure of Quantum Double for Finite Hopf C*-Algebra
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Let H be a finite Hopf C*-algebra and H' be its dual Hopf algebra. Drinfeld's quantum double D(H) of H is a Hopf *-algebra. There is a faithful positive linear functional θ on D(H). Through the associated Gelfand-Naimark-Segal (GNS) representation, D(H) has a faithful *-representation so that it becomes a Hopf C*-algebra. The canonical embedding map of H into D(H) is isometric.
Finite-size scaling study of the three-dimensional classical Heisenberg model
Holm, C; Holm, Christian; Janke, Wolfhard
1993-01-01
We use the single-cluster Monte Carlo update algorithm to simulate the three-dimensional classical Heisenberg model in the critical region on simple cubic lattices of size $L^3$ with $L=12, 16, 20, 24, 32, 40$, and $48$. By means of finite-size scaling analyses we compute high-precision estimates of the critical temperature and the critical exponents, using extensively histogram reweighting and optimization techniques. Measurements of the autocorrelation time show the expected reduction of critical slowing down at the phase transition. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors in finite-size scaling analyses.
Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations
Institute of Scientific and Technical Information of China (English)
Tongke
2010-01-01
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
Energy Technology Data Exchange (ETDEWEB)
Srivastava, Vineet K., E-mail: vineetsriiitm@gmail.com [ISRO Telemetry, Tracking and Command Network (ISTRAC), Bangalore-560058 (India); Awasthi, Mukesh K. [Department of Mathematics, University of Petroleum and Energy Studies, Dehradun-248007 (India); Singh, Sarita [Department of Mathematics, WIT- Uttarakhand Technical University, Dehradun-248007 (India)
2013-12-15
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
Directory of Open Access Journals (Sweden)
Vineet K. Srivastava
2013-12-01
Full Text Available This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM, for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
Phase transitions in a one-dimensional multibarrier potential of finite range
Bar, D
2002-01-01
We have previously studied properties of a one-dimensional potential with $N$ equally spaced identical barries in a (fixed) finite interval for both finite and infinite $N$. It was observed that scattering and spectral properties depend sensitively on the ratio $c$ of spacing to width of the barriers (even in the limit $N \\to \\infty$). We compute here the specific heat of an ensemble of such systems and show that there is critical dependence on this parameter, as well as on the temperature, strongly suggestive of phase transitions.
Finite-size analysis of continuous-variable quantum key distribution
Leverrier, Anthony; Grangier, Philippe
2010-01-01
The goal of this paper is to extend the framework of finite size analysis recently developed for quantum key distribution to continuous-variable protocols. We do not solve this problem completely here, and we mainly consider the finite size effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than the ones obtained in the asymptotic regime. However, we show that recent continuous-variable protocols are able to provide fully secure secret keys in the finite size scenario, over distances larger than 50 km.
Wang, Chao; Huang, Peng; Huang, Duan; Lin, Dakai; Zeng, Guihua
2016-02-01
Practical security of the continuous-variable quantum key distribution (CVQKD) system with finite sampling bandwidth of analog-to-digital converter (ADC) at the receiver's side is investigated. We find that the finite sampling bandwidth effects may decrease the lower bound of secret key rate without awareness of the legitimate communicators. This leaves security loopholes for Eve to attack the system. In addition, this effect may restrains the linear relationship of secret key bit rate with repetition rate of the system; subsequently, there is a saturation value for the secret key bit rate with the repetition rate. To resist such kind of effects, we propose a dual sampling detection approach in which two ADCs are employed so that the finite sampling bandwidth effects are removed.
High-dimensional quantum cryptography with twisted light
Mirhosseini, Mohammad; O'Sullivan, Malcolm N; Rodenburg, Brandon; Malik, Mehul; Gauthier, Daniel J; Boyd, Robert W
2014-01-01
Quantum key distribution (QKD) systems have conventionally relied on the polarization of light for encoding. This limits the amount of information that can be sent per photon and puts a tight bound on the error such a system can tolerate. Here we show an experimental realization of a multilevel QKD system that uses the orbital angular momentum (OAM) of photons. Through the use of a 7-dimensional alphabet encoded in OAM, we achieve a channel capacity of 2.1 bits per sifted photon which is more than double the maximum allowed capacity of polarization-based QKD systems. Our experiment uses a digital micro-mirror device for the rapid generation of OAM modes at 4 kHz, and a mode sorter capable of sorting single photons based on OAM with a separation efficiency of 93%. Further, our scheme provides an increased tolerance to errors, leading to a quantum communication channel that is more robust against eavesdropping.
Entanglement and majorization in (1+1)-dimensional quantum systems
Orus, R
2005-01-01
Motivated by the idea of entanglement loss along Renormalization Group flows, analytical majorization relations are proven for the ground state of (1+1)-dimensional conformal field theories. For any of these theories, majorization is proven to hold in the spectrum of the reduced density matrices in a bipartite system when changing the size L of one of the subsystems. Continuous majorization along uniparametric flows is also proven as long as part of the conformal structure is preserved under the deformation and some monotonicity conditions hold as well. As particular examples of our derivations, we study the cases of the XX, Heisenberg and XY quantum spin chains. Our results provide in a rigorous way explicit proves for all the majorization conjectures raised by Latorre, Lutken, Rico, Vidal and Kitaev in previous papers on quantum spin chains.
An introduction to integrable techniques in one-dimensional quantum systems
Franchini, Fabio
2016-01-01
This monograph introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style ...
An introduction to integrable techniques for one-dimensional quantum systems
Franchini, Fabio
2017-01-01
This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and t...
Finite Dimensional Compensators for Infinite Dimensional Systems with Unbounded Control Action.
1984-05-01
from infinite dimensional linear systems theory that A + GC . V(A) + X generates an exponentially stable semigroup on X (see (5) or [161). It is also...Matheatica Aplicada e Computacional, 2 (1983). 15] R.F. CURTAIN/A.J. PRITCHARD Infinite Dimensional Linear Systems Theory LNCIS 8, Springer-Verlag
Zhukovsky, V. Ch.; Krevchik, V. D.; Semenov, M. B.; Krevchik, P. V.; Zaytsev, R. V.; Egorov, I. A.
2016-11-01
The field and temperature dependence of the probability of two-dimensional dissipative tunneling is studied in the framework of one-instanton approximation for a model double-well oscillator potential in an external electric field at finite temperature with account for the influence of two local phonon modes for quantum dots in a system of a combined atomic force and a scanning tunneling microscope. It is demonstrated that in the mode of synchronous parallel transfer of tunneling particles from the cantilever tip to the quantum dot the two local phonon modes result in the occurrence of two stable peaks in the curve of the 2D dissipative tunneling probability as a function of the field. Qualitative comparison of the theoretical curve in the limit of weak dissociation and the experimental current-voltage characteristic for quantum dots that grow from colloidal gold under a cantilever tip at the initial stage of quantum-dot formation when the quantum dot size does not exceed 10 nm is performed. It is established that one of the two stable peaks that correspond to interaction of tunneling particles with two local phonon modes in the temperature dependence of the 2D dissipative tunneling probability can be split in two, which corresponds to the tunneling channel interference mechanism. It is found that the theoretically predicted and experimentally observed mode of quantum beats occurs near the bifurcation point.
The XY model coupled to two-dimensional quantum gravity
Baillie, C. F.; Johnston, D. A.
1992-09-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we discovered in our earlier work on various Potts models with the same value of the central charge, c, carries over to the XY model, which has c=1.
Affine group representation formalism for four dimensional, Lorentzian, quantum gravity
Ching-Yi, Chou; Soo, Chopin
2012-01-01
The Hamiltonian constraint of 4-dimensional General Relativity is recast explicitly in terms of the Chern--Simons functional and the local volume operator. In conjunction with the algebraic quantization program, application of the affine quantization concept due to Klauder facilitates the construction of solutions to all of the the quantum constraints in the Ashtekar variables and their associated Hilbert space. A physical Hilbert space is constructed for Lorentzian signature gravity with nonzero cosmological constant in the form of unitary, irreducible representations of the affine group.
Fourier's law for quasi-one-dimensional chaotic quantum systems
Seligman, Thomas H.; Weidenmüller, Hans A.
2011-05-01
We derive Fourier's law for a completely coherent quasi-one-dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.
Magnetic quantum dot in two-dimensional topological insulators
Li, Guo; Zhu, Jia-Lin; Yang, Ning
2017-03-01
Magnetic quantum dots in two-dimensional band and topological insulators are studied by solving the modified Dirac model under nonuniform magnetic fields. The Landau levels split into discrete states with certain angular momentum. The states splitting from the zero Landau levels lie in the energy gap for topological insulators but are out of the gap for band insulators. It is found that the ground states oscillate between the spin-up and spin-down states when the magnetic field or the dot size changes. The oscillation manifests itself as changes of sign and strength of charge currents near the dot's edge.
The XY Model Coupled to Two-Dimensional Quantum Gravity
Baillie, C F; 10.1016/0370-2693(92)91037-A
2009-01-01
We perform Monte Carlo simulations using the Wolff cluster algorithm of the XY model on both fixed and dynamical phi-cubed graphs (i.e. without and with coupling to two-dimensional quantum gravity). We compare the numerical results with the theoretical expectation that the phase transition remains of KT type when the XY model is coupled to gravity. We also examine whether the universality we discovered in our earlier work on various Potts models with the same value of the central charge, $c$, carries over to the XY model, which has $c=1$.
Higuchi, Atsushi; Martin, Giles D. R.
2006-01-01
We extend our previous work [A. Higuchi and G. D. R. Martin, Found. Phys. 35, 1149 (2005)FNDPA40015-901810.1007/s10701-005-6405-0], which compared the predictions of quantum electrodynamics concerning radiation reaction with those of the Abraham-Lorentz-Dirac theory for a charged particle in linear motion. Specifically, we calculate the predictions for the change in position of a charged-scalar particle, moving in three-dimensional space, due to the effect of radiation reaction in the one-photon-emission process in quantum electrodynamics. The scalar particle is assumed to be accelerated for a finite period of time by a three-dimensional electromagnetic potential dependent only on one of the spacetime coordinates. We perform this calculation in the ℏ→0 limit and show that the change in position agrees with that obtained in classical electrodynamics with the Lorentz-Dirac force treated as a perturbation. We also show for a time-dependent but space-independent electromagnetic potential that the forward-scattering amplitude at order e2 does not contribute to the position change in the ℏ→0 limit after the mass renormalization is taken into account.
Classical and quantum equations of motion of an n-dimensional BTZ black hole
Energy Technology Data Exchange (ETDEWEB)
Greenwood, Eric, E-mail: egreenwood@usi.edu
2016-05-10
We investigate the gravitational collapse of a non-rotating n-dimensional BTZ black hole in AdS space in the context of both classical and quantum mechanics. This is done by first deriving the conserved mass of a “spherically” symmetric domain wall, which is taken as the classical Hamiltonian of the black hole. Upon deriving the conserved mass, we also point out that, for a “spherically” symmetric shell, there is an easy and straight-forward way of determining the conserved mass, which is related to the proper time derivative of the interior and exterior times. This method for determining the conserved mass is generic to any situation (i.e. any equation of state), since it only depends on the energy per unit area, σ, of the shell. Classically, we show that the time taken for gravitational collapse follows that of the typical formation of a black hole via gravitational collapse; that is, an asymptotic observer will see that the collapse takes an infinite amount of time to occur, while an infalling observer will see the collapse to both the horizon and the classical singularity occur in a finite amount of time. Quantum mechanically, we take primary interest in the behavior of the collapse near the horizon and near the classical singularity from the point of view of both asymptotic and infalling observers. In the absence of radiation and fluctuations of the metric, quantum effects near the horizon do not change the classical conclusions for an asymptotic observer. The most interesting quantum mechanical effect comes in when investigating near the classical singularity. Here, we find, that the quantum effects in this region are able to remove the classical singularity at the origin, since the wave function is non-singular, and it also displays non-local effects, which depend on the energy density of the domain wall.
Pan, Xue; Chen, Li-Zhu; Wu, Yuan-Fang
2016-09-01
The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). This has been calculated to the sixth order in experiments. Corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class as QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that at non-zero external magnetic field, when the critical point is approached from the crossover side, the sixth order cumulant has a negative valley. The width of the negative valley narrows with decreasing external field. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising model, we calculated the sixth order cumulant of different sizes of systems. We discuss the finite-size effects on the temperature at which the cumulant changes sign. Supported by Fund Project of Sichuan Provincial Department of Education (16ZB0339), Fund Project of Chengdu Technological University for Doctor (2016RC004), Major State Basic Research Development Program of China (2014CB845402) and National Natural Science Foundation of China (11405088, 11221504)
Intrinsically universal n-dimensional quantum cellular automata
Arrighi, Pablo
2009-01-01
We describe an n-dimensional quantum cellular automaton (QCA) capable of simulating all others, in that the initial configuration and the forward evolution of any n-dimensional QCA can be encoded within the initial configuration of the universal QCA. Several steps of the universal QCA then correspond to one step of the simulated QCA. The simulation preserves the topology in the sense that each cell of the simulated QCA is encoded as a group of adjacent cells in the universal QCA. The encoding is linear and hence does not carry any of the cost of the computation. Part of our proof consists of showing that any QCA can be presented in the more canonical, operational form of a Partitioned QCA, thereby showing an equivalence between many definitions of QCA that are present in the literature.
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
Liu, Xiao-Ping; Zhou, Yuan; Wang, Yi-Fei; Gong, Chang-De
2016-06-01
We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers.
Quantum Phase Transition in the Two-Dimensional Random Transverse-Field Ising Model
Pich, C.; Young, A. P.
1998-03-01
We study the quantum phase transition in the random transverse-field Ising model by Monte Carlo simulations. In one-dimension it has been established that this system has the following striking behavior: (i) the dynamical exponent is infinite, and (ii) the exponents for the divergence of the average and typical correlation lengths are different. An important issue is whether this behavior is special to one-dimension or whether similar behavior persists in higher dimensions. Here we attempt to answer this question by studies of the two-dimensional model. Our simulations use the Wolff cluster algorithm and the results are analyzed by anisotropic finite size scaling, paying particular attention to the Binder ratio of moments of the order parameter distribution and the distribution of the spin-spin correlation functions for various distances.
Multifarious topological quantum phase transitions in two-dimensional topological superconductors
Liu, Xiao-Ping; Zhou, Yuan; Wang, Yi-Fei; Gong, Chang-De
2016-01-01
We study the two-dimensional topological superconductors of spinless fermions in a checkerboard-lattice Chern-insulator model. With the short-range p-wave superconducting pairing, multifarious topological quantum phase transitions have been found and several phases with high Chern numbers have been observed. We have established a rich phase diagram for these topological superconducting states. A finite-size checkerboard-lattice cylinder with a harmonic trap potential has been further investigated. Based upon the self-consistent numerical calculations of the Bogoliubov-de Gennes equations, various phase transitions have also been identified at different regions of the system. Multiple pairs of Majorana fermions are found to be well-separated and localized at the phase boundaries between the phases characterized by different Chern numbers. PMID:27329219
Emergent topology and dynamical quantum phase transitions in two-dimensional closed quantum systems
Bhattacharya, Utso; Dutta, Amit
2017-07-01
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of the notion of DTOP introduced in Budich and Heyl [Phys. Rev. B 93, 085416 (2016), 10.1103/PhysRevB.93.085416] for one-dimensional situations. This DTOP is obtained from the "gauge-invariant" Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time-evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.
Finite element method for one-dimensional rill erosion simulation on a curved slope
Directory of Open Access Journals (Sweden)
Lijuan Yan
2015-03-01
Full Text Available Rill erosion models are important to hillslope soil erosion prediction and to land use planning. The development of rill erosion models and their use has become increasingly of great concern. The purpose of this research was to develop mathematic models with computer simulation procedures to simulate and predict rill erosion. The finite element method is known as an efficient tool in many other applications than in rill soil erosion. In this study, the hydrodynamic and sediment continuity model equations for a rill erosion system were solved by the Galerkin finite element method and Visual C++ procedures. The simulated results are compared with the data for spatially and temporally measured processes for rill erosion under different conditions. The results indicate that the one-dimensional linear finite element method produced excellent predictions of rill erosion processes. Therefore, this study supplies a tool for further development of a dynamic soil erosion prediction model.
Dimensionality and Finite Number Effect on BCS Transition of Atomic Fermi Gas
Institute of Scientific and Technical Information of China (English)
CUI Hai-Tao; WANG Lin-Cheng; YI Xue-Xi
2005-01-01
The effect of finite number and dimensionality has been discussed in this paper. The finite number effect has a negative correction to final temperature for 2D or 3D atomic Fermi gases. The changing of final temperature obtained by scanning from BEC region to BCS region are 10% or so with N ≤ 103 and can be negligible when N ＞ 103.However, in 1D atomic Fermi gas, the effect gives a positive correction which greatly changes the final temperature in Fermi gas. This behavior is completely opposed to the 2D and 3D cases and a proper explanation is still to be found.Dimensionality also has a positive correction, in which the more tightly trapping, the higher final temperature one gets with the same particle number. A discussion is also presented.
Finite-size effects in quasi-one-dimensional conductors with a charge-density wave
Energy Technology Data Exchange (ETDEWEB)
Zaitsev-Zotov, Sergei V [Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Moscow (Russian Federation)
2004-06-30
Recent studies of finite-size effects in charge-density wave conductors are reviewed. Various manifestations of finite-size effects, including the transverse-size dependence of the nonlinear-conduction threshold field, the Peierls transition temperature, high-frequency conduction, and the relaxation rates of metastable states, are discussed. Resistivity jumps in thin samples, the smeared threshold field for nonlinear conduction, and threshold conduction above the Peierls transition temperature are considered, as are mesoscopic oscillations of the threshold field, one-dimensional conduction in thin crystals, absolute negative conductivity of quasi-one-dimensional conductors, the length dependence of the phase-slip voltage, and the Aharonov-Bohm oscillations in sliding CDWs. Problems yet to be solved are discussed. (reviews of topical problems)
Directory of Open Access Journals (Sweden)
Carlos Salinas
2011-05-01
Full Text Available The work was aimed at simulating two-dimensional wood drying stress using the control-volume finite element method (CVFEM. Stress/strain was modeled by moisture content gradients regarding shrinkage and mechanical sorption in a cross-section of wood. CVFEM was implemented with triangular finite elements and lineal interpolation of the independent variable which were programmed in Fortran 90 language. The model was validated by contrasting results with similar ones available in the specialised literature. The present model’s results came from isothermal (20ºC drying of quaking aspen (Populus tremuloides: two-dimensional distribution of stress/strain and water content, 40, 80, 130, 190 and 260 hour drying time and evolution of normal stress (2.5 <σ͓ ͓ < 1.2, MPa, from the interior to the exterior of wood.
Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite
Li, Xuetao; Binienda, Wieslaw K.; Goldberg, Robert K.
2010-01-01
A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.
Three-dimensional finite element modeling of a magnet array spinning above a conductor
Lorimer, W. L.; Lieu, D. K.; Hull, J. R.; Mulcahy, T. M.; Rossing, T. D.
Drag forces due to eddy currents induced by the relative motion of a conductor and a magnetic field occur in many practical devices: motors, brakes, magnetic bearings, and magnetically levitated vehicles. Recently, finite element codes have included solvers for three dimensional eddy current geometries and have the potential to be very useful in the design and analysis of these devices. In this paper, numerical results from three dimensional modeling of a magnet array spinning above a conductor are compared to experimental results in order to assess the capabilities of these codes.
Natale, Andrea
2016-01-01
We analyse the multiscale properties of energy-conserving upwind-stabilised finite element discretisations of the two-dimensional incompressible Euler equations. We focus our attention on two particular methods: the Lie derivative discretisation introduced in Natale and Cotter (2016a) and the SUPG discretisation of the vorticity advection equation. Such discretisations provide control on enstrophy by modelling different types of scale interactions. We quantify the performance of the schemes in reproducing the non-local energy backscatter that characterises two-dimensional turbulent flows.
Elastic fields of stationary and moving dislocations in three dimensional finite samples
1997-01-01
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in three dimensional, not necessarily isotropic, finite samples. A line integral representation is found for the stress field, thus satisfying the expectation that stresses should depend on the location of the dislocation loop, but not on the location of surfaces bounded by such loops that are devoid of physical significance. In the stationary case the line integral...
Frequency bands of negative refraction in finite one-dimensional photonic crystals
Institute of Scientific and Technical Information of China (English)
Chen Yuan-Yuan; Huang Zhao-Ming; Shi Jie-Long; Li Chun-Fang; Wang Qi
2007-01-01
We have discussed theoretically the negative refraction in finite one-dimensional (1D) photonic crystals (PCs)composed of alternative layers with high index contrast. The frequency bands of negative refraction are obtained with the help of the photonic band structure, the group velocity and the power transmittance, which are all obtained in analytical expression. There shows negative transverse position shift at the endface when negative refraction occurs,which is analysed in detail.
CONVERGENCE OF AN EXPLICIT UPWIND FINITE ELEMENT METHOD TO MULTI-DIMENSIONAL CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Jin-chao Xu; Lung-an Ying
2001-01-01
An explicit upwind finite element method is given for the numerical computation to multi-dimensional scalar conservation laws. It is proved that this scheme is consistent to the equation and monotone, and the approximate solution satisfies discrete entropy inequality.To guarantee the limit of approximate solutions to be a measure valued solution, we prove an energy estimate. Then the Lp strong convergence of this scheme is proved.
Banks, H. T.; Smith, Ralph C.; Wang, Yun
1994-01-01
Based on a distributed parameter model for vibrations, an approximate finite dimensional dynamic compensator is designed to suppress vibrations (multiple modes with a broad band of frequencies) of a circular plate with Kelvin-Voigt damping and clamped boundary conditions. The control is realized via piezoceramic patches bonded to the plate and is calculated from information available from several pointwise observed state variables. Examples from computational studies as well as use in laboratory experiments are presented to demonstrate the effectiveness of this design.
Dynamics of a harmonic oscillator in a finite-dimensional Hilbert space
Energy Technology Data Exchange (ETDEWEB)
Kuang Leman (CCAST (World Lab.), Beijing, BJ (China) Dept. of Physics and Inst. of Physics, Hunan Normal Univ. (China)); Wang Fabo (Dept. of Physics, Hunan Normal Univ. (China)); Zhou Yanguo (Dept. of Physics, Hunan Normal Univ. (China))
1993-11-29
Some dynamical properties of a finite-dimensional Hilbert space harmonic oscillator (FDHSHO) are studied. The time evolution of the position and momentum operators and the second-order quadrature squeezing are investigated in detail. It is shown that the coherent states of the FDHSHO are not the minimum uncertainty states of the position and momentum operators of the FDHSHO. It is found that the second-order squeezing of the quadrature operators vanishes and reappears periodically in the time evolution. (orig.)
Linear Commuting Maps on Parab olic Subalgebras of Finite-dimensional Simple Lie Algebras
Institute of Scientific and Technical Information of China (English)
CHEN Zheng-xin; WANG Bing
2014-01-01
A map ϕ on a Lie algebra g is called to be commuting if [ϕ(x), x] = 0 for all x∈g. Let L be a finite-dimensional simple Lie algebra over an algebraically closed field F of characteristic 0, P a parabolic subalgebra of L. In this paper, we prove that a linear mapϕon P is commuting if and only ifϕis a scalar multiplication map on P .
Third order finite volume evolution Galerkin (FVEG) methods for two-dimensional wave equation system
Lukácová-Medvid'ová, Maria; Warnecke, Gerald; Zahaykah, Yousef
2003-01-01
The subject of the paper is the derivation and analysis of third order finite volume evolution Galerkin schemes for the two-dimensional wave equation system. To achieve this the first order approximate evolution operator is considered. A recovery stage is carried out at each level to generate a piecewise polynomial approximation from the piecewise constants, to feed into the calculation of the fluxes. We estimate the truncation error and give numerical examples to demonstrate the higher order...
Analysis of 3-dimensional finite element after reconstruction of impaired ankle deltoid ligament
Ji, Yunhan; Tang, Xianzhong; Li, Yifan; Xu, Wei; Qiu, Wenjun
2016-01-01
We compared four repair techniques for impaired ankle ligament deltoideum, namely Wiltberger, Deland, Kitaoka and Hintermann using a 3-dimensional finite element. We built an ankle ligament deltoideum model, including six pieces of bone structures, gristles and main ligaments around the ankle. After testing the model, we built an impaired ligament deltoideum model plus four reconstruction models. Subsequently, different levels of force on ankles with different flexion were imposed and ankle b...
Finite-dimensional constrained fuzzy control for a class of nonlinear distributed process systems.
Wu, Huai-Ning; Li, Han-Xiong
2007-10-01
This correspondence studies the problem of finite-dimensional constrained fuzzy control for a class of systems described by nonlinear parabolic partial differential equations (PDEs). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, a systematic modeling procedure is given to construct exactly a Takagi-Sugeno (T-S) fuzzy model for the finite-dimensional ODE system under state constraints. Then, based on the T-S fuzzy model, a sufficient condition for the existence of a stabilizing fuzzy controller is derived, which guarantees that the state constraints are satisfied and provides an upper bound on the quadratic performance function for the finite-dimensional slow system. The resulting fuzzy controllers can also guarantee the exponential stability of the closed-loop PDE system. Moreover, a local optimization algorithm based on the linear matrix inequalities is proposed to compute the feedback gain matrices of a suboptimal fuzzy controller in the sense of minimizing the quadratic performance bound. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.
Criticality in Two-Dimensional Quantum Systems: Tensor Network Approach
Ran, Shi-Ju; Li, Wei; Lewenstein, Maciej; Su, Gang
2016-01-01
Determination and characterization of criticality in two-dimensional (2D) quantum many-body systems belong to the most important challenges and problems of quantum physics. In this paper we propose an efficient scheme to solve this problem by utilizing the infinite projected entangled pair state (iPEPS), and tensor network (TN) representations. We show that the criticality of a 2D state is faithfully reproduced by the ground state (dubbed as boundary state) of a one-dimensional effective Hamiltonian constructed from its iPEPS representation. We demonstrate that for a critical state the correlation length and the entanglement spectrum of the boundary state are essentially different from those of a gapped iPEPS. This provides a solid indicator that allows to identify the criticality of the 2D state. Our scheme is verified on the resonating valence bond (RVB) states on kagom\\'e and square lattices, where the boundary state of the honeycomb RVB is found to be described by a $c=1$ conformal field theory. We apply ...
Classical and quantum phases of low-dimensional dipolar systems
Energy Technology Data Exchange (ETDEWEB)
Cartarius, Florian
2016-09-22
In this thesis we present a detailed study of the phase diagram of ultracold bosonic atoms confined along a tight atomic wave guide, along which they experience an optical lattice potential. In this quasi-one dimensional model we analyse the interplay between interactions and quantum fluctuations in (i) determining the non-equilibrium steady state after a quench and (ii) giving rise to novel equilibrium phases, when the interactions combine the s-wave contact interaction and the anisotropic long range dipole-dipole interactions. In detail, in the first part of the thesis we study the depinning of a gas of impenetrable bosons following the sudden switch of of the optical lattice. By means of a Bose-Fermi mapping we infer the exact quantum dynamical evolution and show that in the thermodynamic limit the system is in a non-equilibrium steady state without quasi-long range order. In the second part of the thesis, we study the effect of quantum fluctuations on the linear-zigzag instability in the ground state of ultracold dipolar bosons, as a function of the strength of the transverse confinement. We first analyse the linear-zigzag instability in the classical regime, and then use our results to develop a multi-mode Bose-Hubbard model for the system. We then develop several numerical methods, to determine the ground state.
Quantum control of finite-time disentanglement in qubit-qubit and qubit-qutrit systems
Energy Technology Data Exchange (ETDEWEB)
Ali, Mazhar
2009-07-13
This thesis is a theoretical study of entanglement dynamics and its control of qubit-qubit and qubit-qutrit systems. In particular, we focus on the decay of entanglement of quantum states interacting with dissipative environments. Qubit-qubit entanglement may vanish suddenly while interacting with statistically independent vacuum reservoirs. Such finite- time disentanglement is called sudden death of entanglement (ESD). We investigate entanglement sudden death of qubit-qubit and qubit-qutrit systems interacting with statistically independent reservoirs at zero- and finite-temperature. It is shown that for zero-temperature reservoirs, some entangled states exhibit sudden death while others lose their entanglement only after infinite time. Thus, there are two possible routes of entanglement decay, namely sudden death and asymptotic decay. We demonstrate that starting with an initial condition which leads to finite-time disentanglement, we can alter the future course of entanglement by local unitary actions. In other words, it is possible to put the quantum states on other track of decay once they are on a particular route of decay. We show that one can accelerate or delay sudden death. However, there is a critical time such that if local actions are taken before that critical time then sudden death can be delayed to infinity. Any local unitary action taken after that critical time can only accelerate or delay sudden death. In finite-temperature reservoirs, we demonstrate that a whole class of entangled states exhibit sudden death. This conclusion is valid if at least one of the reservoirs is at finite-temperature. However, we show that we can still hasten or delay sudden death by local unitary transformations up to some finite time. We also study sudden death for qubit-qutrit systems. Similar to qubit-qubit systems, some states exhibit sudden death while others do not. However, the process of disentanglement can be effected due to existence of quantum interference
The Three-Dimensional Finite-Volume Non-Hydrostatic Icosahedral Model (NIM)
Lee, J. L.; MacDonald, A. E.
2014-12-01
A multi-scales Non-hydrostatic Icosahedral Model (NIM) has been developed at Earth System Research Laboratory (ESRL) to meet NOAA's future prediction mission ranging from mesoscale short-range, high-impact weather forecasts to longer-term intra-seasonal climate prediction. NIM formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM is designed to utilize the state-of-art computing architecture such as Graphic Processing Units (GPU) processors to run globally at kilometer scale resolution to explicitly resolve convective storms and complex terrains. The novel features of NIM numerical design include: 1.1. A local coordinate system upon which finite-volume integrations are undertaken. The use of a local Cartesian coordinate greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. 1.2. A general indirect addressing scheme developed for modeling on irregular grid. It arranges the icosahedral grid with a one-dimensional vector loop structure, table specified memory order, and an indirect addressing scheme that yields very compact code despite the complexities of this grid. 1.3. Use of three-dimensional finite-volume integration over control volumes constructed on the height coordinates. Three-dimensional finite-volume integration accurately represents the Newton Third Law over terrain and improves pressure gradient force over complex terrain. 1.4. Use of the Runge-Kutta 4th order conservative and positive-definite transport scheme 1.5. NIM dynamical solver has been implemented on CPU as well as GPU. As one of the potential candidates for NWS next generation models, NIM dynamical core has been successfully verified with various benchmark test cases including those proposed by DCMIP
Quantum Computing - A new Implementation of Simon Algorithm for 3-Dimensional Registers
Directory of Open Access Journals (Sweden)
Adina Bărîlă
2015-03-01
Full Text Available Quantum computing is a new field of science aiming to use quantum phenomena in order to perform operations on data. The Simon algorithm is one of the quantum algorithms which solves a certain problem exponentially faster than any classical algorithm solving the same problem. Simulating of quantum algorithms is very important since quantum hardware is not available outside of the research labs. QCL (Quantum Computation Language is the most advanced implemented quantum computer simulator and was conceived by Bernhard Ömer. The paper presents an implementation in QCL of the Simon algorithm in the case of 3-dimensional registers.
Matrix product state calculations for one-dimensional quantum chains and quantum impurity models
Energy Technology Data Exchange (ETDEWEB)
Muender, Wolfgang
2011-09-28
This thesis contributes to the field of strongly correlated electron systems with studies in two distinct fields thereof: the specific nature of correlations between electrons in one dimension and quantum quenches in quantum impurity problems. In general, strongly correlated systems are characterized in that their physical behaviour needs to be described in terms of a many-body description, i.e. interactions correlate all particles in a complex way. The challenge is that the Hilbert space in a many-body theory is exponentially large in the number of particles. Thus, when no analytic solution is available - which is typically the case - it is necessary to find a way to somehow circumvent the problem of such huge Hilbert spaces. Therefore, the connection between the two studies comes from our numerical treatment: they are tackled by the density matrix renormalization group (DMRG) and the numerical renormalization group (NRG), respectively, both based on matrix product states. The first project presented in this thesis addresses the problem of numerically finding the dominant correlations in quantum lattice models in an unbiased way, i.e. without using prior knowledge of the model at hand. A useful concept for this task is the correlation density matrix (CDM) which contains all correlations between two clusters of lattice sites. We show how to extract from the CDM, a survey of the relative strengths of the system's correlations in different symmetry sectors as well as detailed information on the operators carrying long-range correlations and the spatial dependence of their correlation functions. We demonstrate this by a DMRG study of a one-dimensional spinless extended Hubbard model, while emphasizing that the proposed analysis of the CDM is not restricted to one dimension. The second project presented in this thesis is motivated by two phenomena under ongoing experimental and theoretical investigation in the context of quantum impurity models: optical absorption
Form the density-of-states method to finite density quantum field theory
Langfeld, Kurt
2016-01-01
During the last 40 years, Monte Carlo calculations based upon Importance Sampling have matured into the most widely employed method for determinig first principle results in QCD. Nevertheless, Importance Sampling leads to spectacular failures in situations in which certain rare configurations play a non-secondary role as it is the case for Yang-Mills theories near a first order phase transition or quantum field theories at finite matter density when studied with the re-weighting method. The density-of-states method in its LLR formulation has the potential to solve such overlap or sign problems by means of an exponential error suppression. We here introduce the LLR approach and its generalisation to complex action systems. Applications include U(1), SU(2) and SU(3) gauge theories as well as the Z3 spin model at finite densities and heavy-dense QCD.
Energy Technology Data Exchange (ETDEWEB)
Boche, H., E-mail: boche@tum.de, E-mail: janis.noetzel@tum.de; Nötzel, J., E-mail: boche@tum.de, E-mail: janis.noetzel@tum.de [Lehrstuhl für Theoretische Informationstechnik, Technische Universität München, 80290 München (Germany)
2014-12-15
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.
Boche, H.; Nötzel, J.
2014-12-01
This work is motivated by a quite general question: Under which circumstances are the capacities of information transmission systems continuous? The research is explicitly carried out on finite arbitrarily varying quantum channels (AVQCs). We give an explicit example that answers the recent question whether the transmission of messages over AVQCs can benefit from assistance by distribution of randomness between the legitimate sender and receiver in the affirmative. The specific class of channels introduced in that example is then extended to show that the unassisted capacity does have discontinuity points, while it is known that the randomness-assisted capacity is always continuous in the channel. We characterize the discontinuity points and prove that the unassisted capacity is always continuous around its positivity points. After having established shared randomness as an important resource, we quantify the interplay between the distribution of finite amounts of randomness between the legitimate sender and receiver, the (nonzero) probability of a decoding error with respect to the average error criterion and the number of messages that can be sent over a finite number of channel uses. We relate our results to the entanglement transmission capacities of finite AVQCs, where the role of shared randomness is not yet well understood, and give a new sufficient criterion for the entanglement transmission capacity with randomness assistance to vanish.
Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz
1996-01-01
Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.
Rigol, Marcos
2011-03-01
Little more than fifty years ago, Fermi, Pasta, and Ulam set up a numerical experiment to prove the ergodic hypothesis for a one-dimensional lattice of harmonic oscillators when nonlinear couplings were added. Much to their surprise, the system exhibited long-time periodic dynamics with no signals of ergodic behavior. Those results motivated intense research, which ultimately gave rise to the modern chaos theory and to a better understanding of the basic principles of classical statistical mechanics. More recently, experiments with ultracold gases in one-dimensional geometries have challenged our understanding of the quantum domain. After bringing a nearly isolated system out of equilibrium, no signals of relaxation to the expected thermal equilibrium distribution were observed. Some of those results can be understood in the framework of integrable quantum systems, but then it remains the question of why thermalization did not occur even when the system was supposed to be far from integrability. In the latter regime, thermalization is expected to occur and can be understood on the basis of the eigenstate thermalization hypothesis. In this talk, we utilize quantum quenches to study how thermalization breaks down in finite one-dimensional lattices as one approaches an integrable point. We establish a direct connection between the presence or absence of thermalization and the validity or failure of the eigenstate thermalization hypothesis, respectively. This work was supported by the US Office of Naval Research.
Po, Hoi Chun; Zhou, Qi
2015-08-13
Bosons have a natural instinct to condense at zero temperature. It is a long-standing challenge to create a high-dimensional quantum liquid that does not exhibit long-range order at the ground state, as either extreme experimental parameters or sophisticated designs of microscopic Hamiltonians are required for suppressing the condensation. Here we show that synthetic gauge fields for ultracold atoms, using either the Raman scheme or shaken lattices, provide physicists a simple and practical scheme to produce a two-dimensional algebraic quantum liquid at the ground state. This quantum liquid arises at a critical Lifshitz point, where a two-dimensional quartic dispersion emerges in the momentum space, and many fundamental properties of two-dimensional bosons are changed in its proximity. Such an ideal simulator of the quantum Lifshitz model allows experimentalists to directly visualize and explore the deconfinement transition of topological excitations, an intriguing phenomenon that is difficult to access in other systems.
Quantum scattering theory of a single-photon Fock state in three-dimensional spaces.
Liu, Jingfeng; Zhou, Ming; Yu, Zongfu
2016-09-15
A quantum scattering theory is developed for Fock states scattered by two-level systems in three-dimensional free space. It is built upon the one-dimensional scattering theory developed in waveguide quantum electrodynamics. The theory fully quantizes the incident light as Fock states and uses a non-perturbative method to calculate the scattering matrix.
Arkhipov, S M; Odesskii, A V; Feigin, B; Vassiliev, V
1998-01-01
This volume presents the first collection of articles consisting entirely of work by faculty and students of the Higher Mathematics College of the Independent University of Moscow (IUM). This unique institution was established to train elite students to become research scientists. Covered in the book are two main topics: quantum groups and low-dimensional topology. The articles were written by participants of the Feigin and Vassiliev seminars, two of the most active seminars at the IUM.
Three-dimensional supersonic flow around double compression ramp with finite span
Lee, H. S.; Lee, J. H.; Park, G.; Park, S. H.; Byun, Y. H.
2017-01-01
Three-dimensional flows of Mach number 3 around a double-compression ramp with finite span have been investigated numerically. Shadowgraph visualisation images obtained in a supersonic wind tunnel are used for comparison. A three-dimensional Reynolds-averaged Navier-Stokes solver was used to obtain steady numerical solutions. Two-dimensional numerical results are also compared. Four different cases were studied: two different second ramp angles of 30° and 45° in configurations with and without sidewalls, respectively. Results showed that there is a leakage of mass and momentum fluxes heading outwards in the spanwise direction for three-dimensional cases without sidewalls. The leakage changed the flow characteristics of the shock-induced boundary layer and resulted in the discrepancy between the experimental data and two-dimensional numerical results. It is found that suppressing the flow leakage by attaching the sidewalls enhances the two-dimensionality of the experimental data for the double-compression ramp flow.
Holographic geometry of cMERA for quantum quenches and finite temperature
Mollabashi, Ali; Naozaki, Masahiro; Ryu, Shinsei; Takayanagi, Tadashi
2014-03-01
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal in arXiv:1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in arXiv:1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.
Holographic geometry of cMERA for quantum quenches and finite temperature
Energy Technology Data Exchange (ETDEWEB)
Mollabashi, Ali [School of physics, Institute for Research in Fundamental Sciences (IPM),Tehran (Iran, Islamic Republic of); Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Naozaki, Masahiro [Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Ryu, Shinsei [Department of Physics, University of Illinois at Urbana-Champaign,1110 West Green St, Urbana IL 61801 (United States); Takayanagi, Tadashi [Yukawa Institute for Theoretical Physics, Kyoto University,Kyoto 606-8502 (Japan); Kavli Institute for the Physics and Mathematics of the Universe, University of Tokyo,Kashiwa, Chiba 277-8582 (Japan)
2014-03-21
We study the time evolution of cMERA (continuous MERA) under quantum quenches in free field theories. We calculate the corresponding holographic metric using the proposal in http://arxiv.org/abs/1208.3469 and confirm that it qualitatively agrees with its gravity dual given by a half of the AdS black hole spacetime, argued by Hartman and Maldacena in http://arxiv.org/abs/1303.1080. By doubling the cMERA for the quantum quench, we give an explicit construction of finite temperature cMERA. We also study cMERA in the presence of chemical potential and show that there is an enhancement of metric in the infrared region corresponding to the Fermi energy.
Occurrence of discontinuities in the performance of finite-time quantum Otto cycles
Zheng, Yuanjian; Hänggi, Peter; Poletti, Dario
2016-07-01
We study a quantum Otto cycle in which the strokes are performed in finite time. The cycle involves energy measurements at the end of each stroke to allow for the respective determination of work. We then optimize for the work and efficiency of the cycle by varying the time spent in the different strokes and find that the optimal value of the ratio of time spent on each stroke goes through sudden changes as the parameters of this cycle vary continuously. The position of these discontinuities depends on the optimized quantity under consideration such as the net work output or the efficiency.
Calculating modes of quantum wire systems using a finite difference technique
Directory of Open Access Journals (Sweden)
T Mardani
2013-03-01
Full Text Available In this paper, the Schrodinger equation for a quantum wire is solved using a finite difference approach. A new aspect in this work is plotting wave function on cross section of rectangular cross-sectional wire in two dimensions, periodically. It is found that the correct eigen energies occur when wave functions have a complete symmetry. If the value of eigen energy has a small increase or decrease in neighborhood of the correct energy the symmetry will be destroyed and aperturbation value at the first of wave function will be observed. In addition, the demand on computer memory varies linearly with the size of the system under investigation.
Three-dimensional finite element analysis of the human temporomandibular joint disc.
Beek, M; Koolstra, J H; van Ruijven, L J; van Eijden, T M
2000-03-01
A three-dimensional finite element model of the articular disc of the human temporomandibular joint has been developed. The geometry of the articular cartilage and articular disc surfaces in the joint was measured using a magnetic tracking device. First, polynomial functions were fitted through the coordinates of these scattered measurements. Next, the polynomial description was transformed into a triangulated description to allow application of an automatic mesher. Finally, a finite element mesh of the articular disc was created by filling the geometry with tetrahedral elements. The articulating surfaces of the mandible and skull were modeled by quadrilateral patches. The finite element mesh and the patches were combined to create a three-dimensional model in which unrestricted sliding of the disc between the articulating surfaces was allowed. Simulation of statical joint loading at the closed jaw position predicted that the stress and strain distributions were located primarily in the intermediate zone of the articular disc with the highest values in the lateral part. Furthermore, it was predicted that considerable deformations occurred for relatively small joint loads and that relatively large variations in the direction of joint loading had little influence on the distribution of the deformations.
Alessandri, Angelo; Gaggero, Mauro; Zoppoli, Riccardo
2012-06-01
Optimal control for systems described by partial differential equations is investigated by proposing a methodology to design feedback controllers in approximate form. The approximation stems from constraining the control law to take on a fixed structure, where a finite number of free parameters can be suitably chosen. The original infinite-dimensional optimization problem is then reduced to a mathematical programming one of finite dimension that consists in optimizing the parameters. The solution of such a problem is performed by using sequential quadratic programming. Linear combinations of fixed and parameterized basis functions are used as the structure for the control law, thus giving rise to two different finite-dimensional approximation schemes. The proposed paradigm is general since it allows one to treat problems with distributed and boundary controls within the same approximation framework. It can be applied to systems described by either linear or nonlinear elliptic, parabolic, and hyperbolic equations in arbitrary multidimensional domains. Simulation results obtained in two case studies show the potentials of the proposed approach as compared with dynamic programming.
Quantum information entropy for one-dimensional system undergoing quantum phase transition
Xu-Dong, Song; Shi-Hai, Dong; Yu, Zhang
2016-05-01
Calculations of the quantum information entropy have been extended to a non-analytically solvable situation. Specifically, we have investigated the information entropy for a one-dimensional system with a schematic “Landau” potential in a numerical way. Particularly, it is found that the phase transitional behavior of the system can be well expressed by the evolution of quantum information entropy. The calculated results also indicate that the position entropy Sx and the momentum entropy Sp at the critical point of phase transition may vary with the mass parameter M but their sum remains as a constant independent of M for a given excited state. In addition, the entropy uncertainty relation is proven to be robust during the whole process of the phase transition. Project supported by the National Natural Science Foundation of China (Grant No. 11375005) and partially by 20150964-SIP-IPN, Mexico.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F.
2017-03-01
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS6×S2 warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L ≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p ,q ) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Holographic Duals for Five-Dimensional Superconformal Quantum Field Theories.
D'Hoker, Eric; Gutperle, Michael; Uhlemann, Christoph F
2017-03-10
We construct global solutions to type IIB supergravity with 16 residual supersymmetries whose space-time is AdS_{6}×S^{2} warped over a Riemann surface. Families of solutions are labeled by an arbitrary number L≥3 of asymptotic regions, in each of which the supergravity fields match those of a (p,q) five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as nontrivial UV fixed points of perturbatively nonrenormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Holographic duals for five-dimensional superconformal quantum field theories
D'Hoker, Eric; Uhlemann, Christoph F
2016-01-01
We construct global solutions to Type IIB supergravity with 16 residual supersymmetries whose space-time is $AdS_6 \\times S^2$ warped over a Riemann surface. Families of solutions are labeled by an arbitrary number $L\\geq 3$ of asymptotic regions, in each of which the supergravity fields match those of a $(p,q)$ five-brane, and may therefore be viewed as near-horizon limits of fully localized intersections of five-branes in Type IIB string theory. These solutions provide compelling candidates for holographic duals to a large class of five-dimensional superconformal quantum field theories which arise as non-trivial UV fixed points of perturbatively non-renormalizable Yang-Mills theories, thereby making them more directly accessible to quantitative analysis.
Spin from defects in two-dimensional quantum field theory
Novak, Sebastian
2015-01-01
We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in terms of a triangulation equipped with extra data. The amplitude for the spin surfaces is defined to be the amplitude for the underlying oriented surface together with a defect network dual to the triangulation. Independence of the triangulation and of the other choices follows if the line defect and junctions are obtained from a Delta-separable Frobenius algebra with involutive Nakayama automorphism in the monoidal category of topological defects. For rational conformal field theory we can give a more explicit description of the defect category, and we work out two examples related to free fermions in detail: the Ising model and the so(n) WZW model at level 1.
Soliton nanoantennas in two-dimensional arrays of quantum dots
Gligorić, G; Hadžievski, Lj; Slepyan, G Ya; Malomed, B A
2015-01-01
We consider two-dimensional (2D) arrays of self-organized semiconductor quantum dots (QDs) strongly interacting with electromagnetic field in the regime of Rabi oscillations. The QD array built of two-level states is modelled by two coupled systems of discrete nonlinear Schr\\"{o}dinger equations. Localized modes in the form of single-peaked fundamental and vortical stationary Rabi solitons and self-trapped breathers have been found. The results for the stability, mobility and radiative properties of the Rabi modes suggest a concept of a self-assembled 2D \\textit{% soliton-based nano-antenna}, which should be stable against imperfections In particular, we discuss the implementation of such a nano-antenna in the form of surface plasmon solitons in graphene, and illustrate possibilities to control their operation by means of optical tools.
Ultrabroadband two-quantum two-dimensional electronic spectroscopy
Gellen, Tobias A.; Bizimana, Laurie A.; Carbery, William P.; Breen, Ilana; Turner, Daniel B.
2016-08-01
A recent theoretical study proposed that two-quantum (2Q) two-dimensional (2D) electronic spectroscopy should be a background-free probe of post-Hartree-Fock electronic correlations. Testing this theoretical prediction requires an instrument capable of not only detecting multiple transitions among molecular excited states but also distinguishing molecular 2Q signals from nonresonant response. Herein we describe a 2Q 2D spectrometer with a spectral range of 300 nm that is passively phase stable and uses only beamsplitters and mirrors. We developed and implemented a dual-chopping balanced-detection method to resolve the weak molecular 2Q signals. Experiments performed on cresyl violet perchlorate and rhodamine 6G revealed distinct 2Q signals convolved with nonresonant response. Density functional theory computations helped reveal the molecular origin of these signals. The experimental and computational results demonstrate that 2Q electronic spectra can provide a singular probe of highly excited electronic states.
Crossed Andreev effects in two-dimensional quantum Hall systems
Hou, Zhe; Xing, Yanxia; Guo, Ai-Min; Sun, Qing-Feng
2016-08-01
We study the crossed Andreev effects in two-dimensional conductor/superconductor hybrid systems under a perpendicular magnetic field. Both a graphene/superconductor hybrid system and an electron gas/superconductor one are considered. It is shown that an exclusive crossed Andreev reflection, with other Andreev reflections being completely suppressed, is obtained in a high magnetic field because of the chiral edge states in the quantum Hall regime. Importantly, the exclusive crossed Andreev reflection not only holds for a wide range of system parameters, e.g., the size of system, the width of central superconductor, and the quality of coupling between the graphene and the superconductor, but also is very robust against disorder. When the applied bias is within the superconductor gap, a robust Cooper-pair splitting process with high-efficiency can be realized in this system.
Quantum magnetotransport in a modulated two-dimensional electron gas
Park, Tae-ik; Gumbs, Godfrey
1997-09-01
Quantum mechanical calculations of the magnetotransport coefficients of a modulated two-dimensional electron gas in a perpendicular magnetic field are presented using the Kubo method. The model modulation potential used is such that the effect of the steepness of the potential and its strength on the band part of the longitudinal resistivity ρxxand the Hall resistivity ρxycould be studied. In the extreme limit of a very steep potential, a two-dimensional square array of antidots is simulated. Impurity scattering is included in the self-consistent t-matrix approximation. The results show that for a strong lateral superlattice potential, ρxyis quenched in the low magnetic field regime and as the magnetic field increases there is a large negative Hall resistivity. The intensity of this negative peak is suppressed as the strength of the modulation potential is decreased. It is also shown that the height of the negative peak depends on the steepness of the potential. The longitudinal resistivity also has some interesting features. There are Aharonov-Bohm oscillations and a double peak structure which depends on both the strength of the modulation potential as well as its slope. The numerical results show that the position and intensity of the lower peak is not very sensitive to a change in the strength of the lattice potential or its steepness. However, the upper peak is greatly reduced when the lattice potential is diminished in strength. The double peak feature in ρxxand the negative peak and quenching of the Hall effect at low magnetic fields have been observed experimentally for antidots in both the quasiclassical and quantum regimes.
Quantum holographic encoding in a two-dimensional electron gas
Energy Technology Data Exchange (ETDEWEB)
Moon, Christopher
2010-05-26
The advent of bottom-up atomic manipulation heralded a new horizon for attainable information density, as it allowed a bit of information to be represented by a single atom. The discrete spacing between atoms in condensed matter has thus set a rigid limit on the maximum possible information density. While modern technologies are still far from this scale, all theoretical downscaling of devices terminates at this spatial limit. Here, however, we break this barrier with electronic quantum encoding scaled to subatomic densities. We use atomic manipulation to first construct open nanostructures - 'molecular holograms' - which in turn concentrate information into a medium free of lattice constraints: the quantum states of a two-dimensional degenerate Fermi gas of electrons. The information embedded in the holograms is transcoded at even smaller length scales into an atomically uniform area of a copper surface, where it is densely projected into both two spatial degrees of freedom and a third holographic dimension mapped to energy. In analogy to optical volume holography, this requires precise amplitude and phase engineering of electron wavefunctions to assemble pages of information volumetrically. This data is read out by mapping the energy-resolved electron density of states with a scanning tunnelling microscope. As the projection and readout are both extremely near-field, and because we use native quantum states rather than an external beam, we are not limited by lensing or collimation and can create electronically projected objects with features as small as {approx}0.3 nm. These techniques reach unprecedented densities exceeding 20 bits/nm{sup 2} and place tens of bits into a single fermionic state.
Ding, Yunhong; Bacco, Davide; Dalgaard, Kjeld; Cai, Xinlun; Zhou, Xiaoqi; Rottwitt, Karsten; Oxenløwe, Leif Katsuo
2017-06-01
Quantum key distribution provides an efficient means to exchange information in an unconditionally secure way. Historically, quantum key distribution protocols have been based on binary signal formats, such as two polarization states, and the transmitted information efficiency of the quantum key is intrinsically limited to 1 bit/photon. Here we propose and experimentally demonstrate, for the first time, a high-dimensional quantum key distribution protocol based on space division multiplexing in multicore fiber using silicon photonic integrated lightwave circuits. We successfully realized three mutually unbiased bases in a four-dimensional Hilbert space, and achieved low and stable quantum bit error rate well below both the coherent attack and individual attack limits. Compared to previous demonstrations, the use of a multicore fiber in our protocol provides a much more efficient way to create high-dimensional quantum states, and enables breaking the information efficiency limit of traditional quantum key distribution protocols. In addition, the silicon photonic circuits used in our work integrate variable optical attenuators, highly efficient multicore fiber couplers, and Mach-Zehnder interferometers, enabling manipulating high-dimensional quantum states in a compact and stable manner. Our demonstration paves the way to utilize state-of-the-art multicore fibers for noise tolerance high-dimensional quantum key distribution, and boost silicon photonics for high information efficiency quantum communications.
Finite Element Analysis of Electromagnetic Waves in Two-Dimensional Transformed Bianisotropic Media
Liu, Yan; Guenneau, Sebastien
2015-01-01
We analyse wave propagation in two-dimensional bianisotropic media with the Finite Element Method (FEM). We start from the Maxwell-Tellegen's equations in bianisotropic media, and derive some system of coupled Partial Difference Equations (PDEs) for longitudinal electric and magnetic field components. Perfectly Matched Layers (PMLs) are discussed to model such unbounded media. We implement these PDEs and PMLs in a finite element software. We apply transformation optics in order to design some bianisotropic media with interesting functionalities, such as cloaks, concentrators and rotators. We propose a design of metamaterial with concentric layers made of homogeneous media with isotropic permittivity, permeability and magneto-electric parameters that mimic the required effective anisotropic tensors of a bianisotropic cloak in the long wavelength limit (homogenization approach). Our numerical results show that well-known metamaterials can be transposed to bianisotropic media.
Institute of Scientific and Technical Information of China (English)
张德悦; 马富明
2004-01-01
In this paper, we consider the electromagnetic scattering from periodic chiral structures. The structure is periodic in one direction and invariant in another direction. The electromagnetic fields in the chiral medium are governed by the Maxwell equations together with the Drude-Born-Fedorov equations. We simplify the problem to a two-dimensional scattering problem and we show that for all but possibly a discrete set of wave numbers, there is a unique quasi-periodic weak solution to the diffraction problem. The diffraction problem can be solved by finite element method. We also establish uniform error estimates for the finite element method and the error estimates when the truncation of the nonlocal transparent boundary operators takes place.
Monte Carlo study of Lefschetz thimble structure in one-dimensional Thirring model at finite density
Fujii, Hirotsugu; Kikukawa, Yoshio
2015-01-01
We consider the one-dimensional massive Thirring model formulated on the lattice with staggered fermions and an auxiliary compact vector (link) field, which is exactly solvable and shows a phase transition with increasing the chemical potential of fermion number: the crossover at a finite temperature and the first order transition at zero temperature. We complexify its path-integration on Lefschetz thimbles and examine its phase transition by hybrid Monte Carlo simulations on the single dominant thimble. We observe a discrepancy between the numerical and exact results in the crossover region for small inverse coupling $\\beta$ and/or large lattice size $L$, while they are in good agreement at the lower and higher density regions. We also observe that the discrepancy persists in the continuum limit keeping the temperature finite and it becomes more significant toward the low-temperature limit. This numerical result is consistent with our analytical study of the model's thimble structure. And these results imply...
Finite element simulation of three-dimensional temperature field in underwater welding
Institute of Scientific and Technical Information of China (English)
Liu Xiwen; Wang Guorong; Shi Yonghua; Zhong Jiguang
2007-01-01
Mathematical models of three-dimensional temperature fields in underwater welding with moving heat sources are built. Double ellipsoid Gauss model is proposed as heat sources models. Several factors which affect the temperature fields of underwater welding are analyzed. Water has little influence on thermal efficiency. Water convection coefficient varies with the temperature difference between the water and the workpiece, and water convection makes molten pool freeze quickly. With the increase of water depth, the dimensions of heat sources model should be reduced as arc shrinks. Finite element technology is used to solve mathematical models. ANSYS software is used as finite element tool, and ANSYS Parametric Design Language is used to develop subprograms for loading the moving heat sources and the various convection coefficients. Experiment results show that computational results by using double ellipsoid Gauss heat sources model accord well with the experimental results.
INTERVAL FINITE VOLUME METHOD FOR UNCERTAINTY SIMULATION OF TWO-DIMENSIONAL RIVER WATER QUALITY
Institute of Scientific and Technical Information of China (English)
HE Li; ZENG Guang-ming; HUANG Guo-he; LU Hong-wei
2004-01-01
Under the interval uncertainties, by incorporating the discretization form of finite volume method and interval algebra theory, an Interval Finite Volume Method (IFVM) was developed to solve water quality simulation issues for two-dimensional river when lacking effective data of flow velocity and flow quantity. The IFVM was practically applied to a segment of the Xiangjiang River because the Project of Hunan Inland Waterway Multipurpose must be started working after the environmental impact assessment for it. The simulation results suggest that there exist rather apparent pollution zones of BOD5 downstream the Dongqiaogang discharger and that of COD downstream Xiaoxiangjie discharger, but the pollution sources have no impact on the safety of the three water plants located in this river segment. Although the developed IFVM is to be perfected, it is still a powerful tool under interval uncertainties for water environmental impact assessment, risk analysis, and water quality planning, etc. besides water quality simulation studied in this paper.
Zhou, Tianci; Faulkner, Thomas; Fradkin, Eduardo
2016-01-01
We investigate the entanglement entropy (EE) of circular entangling cuts in the 2+1-dimensional quantum Lifshitz model, whose ground state wave function is a spatially conformal invariant state of the Rokhsar-Kivelson type, whose weight is the Gibbs weight of 2D Euclidean free boson. We show that the finite subleading corrections of EE to the area-law term as well as the mutual information are conformal invariants and calculate them for cylinder, disk-like and spherical manifolds with various spatial cuts. The subtlety due to the boson compactification in the replica trick is carefully addressed. We find that in the geometry of a punctured plane with many small holes, the constant piece of EE is proportional to the number of holes, indicating the ability of entanglement to detect topological information of the configuration. Finally, we compare the mutual information of two small distant disks with Cardy's relativistic CFT scaling proposal. We find that in the quantum Lifshitz model, the mutual information al...
Exact two-body solutions and quantum defect theory of two-dimensional dipolar quantum gas
Jie, Jianwen; Qi, Ran
2016-10-01
In this paper, we provide the two-body exact solutions of the two-dimensional (2D) Schrödinger equation with isotropic +/- 1/{r}3 interactions. An analytic quantum defect theory is constructed based on these solutions and it is applied to investigate the scattering properties as well as two-body bound states of an ultracold polar molecules confined in a quasi-2D geometry. Interestingly, we find that for the attractive case, the scattering resonance happens simultaneously in all partial waves, which has not been observed in other systems. The effect of this feature on the scattering phase shift across such resonances is also illustrated.
Institute of Scientific and Technical Information of China (English)
Chen Li-Bing; Lu Hong; Jin Rui-Bo
2007-01-01
We present a systematic simple method to implement a generalized quantum control-NOT (CNOT) gate on two d-dimensional distributed systems. First, we show how the nonlocal generalized quantum CNOT gate can be implemented with unity fidelity and unity probability by using a maximally entangled pair of qudits as a quantum channel. We also put forward a scheme for probabilistically implementing the nonlocal operation with unity fidelity by employing a partially entangled qudit pair as a quantum channel. Analysis of the scheme indicates that the use of partially entangled quantum channel for implementing the nonlocal generalized quantum CNOT gate leads to the CNOT gate can be used in the entanglement swapping between particles belonging to distant users in a communication network and distributed quantum computer.
Hua, Ming; Tao, Ming-Jie; Deng, Fu-Guo
2016-02-24
We propose a quantum processor for the scalable quantum computation on microwave photons in distant one-dimensional superconducting resonators. It is composed of a common resonator R acting as a quantum bus and some distant resonators rj coupled to the bus in different positions assisted by superconducting quantum interferometer devices (SQUID), different from previous processors. R is coupled to one transmon qutrit, and the coupling strengths between rj and R can be fully tuned by the external flux through the SQUID. To show the processor can be used to achieve universal quantum computation effectively, we present a scheme to complete the high-fidelity quantum state transfer between two distant microwave-photon resonators and another one for the high-fidelity controlled-phase gate on them. By using the technique for catching and releasing the microwave photons from resonators, our processor may play an important role in quantum communication as well.
Equilibrium charge distribution on a finite straight one-dimensional wire
Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Alkhambashi, Majid; Farouk, Ahmed
2017-09-01
The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges.
Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
Joung, E; Noui, K
2008-01-01
We study a three dimensional non-commutative space emerging in the context of three dimensional Euclidean quantum gravity. Our starting point is the assumption that the isometry group is deformed to the Drinfeld double D(SU(2)). We generalize to the deformed case the construction of the flat Euclidean space as the quotient of its isometry group ISU(2) by SU(2). We show that the algebra of functions becomes the non-commutative algebra of SU(2) distributions endowed with the convolution product. This construction gives the action of ISU(2) on the algebra and allows the determination of plane waves and coordinate functions. In particular, we show that: (i) plane waves have bounded momenta; (ii) to a given momentum are associated several SU(2) elements leading to an effective description of an element in the algebra in terms of several physical scalar fields; (iii) their product leads to a deformed addition rule of momenta consistent with the bound on the spectrum. We generalize to the non-commutative setting the...
A 3-dimensional finite-difference method for calculating the dynamic coefficients of seals
Dietzen, F. J.; Nordmann, R.
1989-01-01
A method to calculate the dynamic coefficients of seals with arbitrary geometry is presented. The Navier-Stokes equations are used in conjunction with the k-e turbulence model to describe the turbulent flow. These equations are solved by a full 3-dimensional finite-difference procedure instead of the normally used perturbation analysis. The time dependence of the equations is introduced by working with a coordinate system rotating with the precession frequency of the shaft. The results of this theory are compared with coefficients calculated by a perturbation analysis and with experimental results.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
Bessel-Modal Method for Finite-Height Two-Dimensional Photonic Crystal
Institute of Scientific and Technical Information of China (English)
SHI Jun-Feng; HUANG Sheng-Ye; WANG Dong-Sheng
2005-01-01
@@ By applying the dyadic Green function, the dispersion relation of two-dimensional photonic crystal can be ex pressed as the cylindrical wave expansions of eigenmodes. With the aid of Green's theorem, the plane-wavecoefficients of eigenmodes are reconstructed and employed to formulate the scattering matrix of finite-height twodimensional photonic crystal. These operations make the convergence rate very rapid, and reduce the dimension of the scattering matrix. As a demonstration, we present the transmission and electromagnetic field distributions for an InGaAsIn photonic crystal, and investigate their convergence.
Energy Technology Data Exchange (ETDEWEB)
Castellani, Marco; Giuli, Massimiliano, E-mail: massimiliano.giuli@univaq.it [University of L’Aquila, Department of Information Engineering, Computer Science and Mathematics (Italy)
2016-02-15
We study pseudomonotone and quasimonotone quasivariational inequalities in a finite dimensional space. In particular we focus our attention on the closedness of some solution maps associated to a parametric quasivariational inequality. From this study we derive two results on the existence of solutions of the quasivariational inequality. On the one hand, assuming the pseudomonotonicity of the operator, we get the nonemptiness of the set of the classical solutions. On the other hand, we show that the quasimonoticity of the operator implies the nonemptiness of the set of nonzero solutions. An application to traffic network is also considered.
Directory of Open Access Journals (Sweden)
Santhosh George
2004-01-01
Full Text Available Simplified regularization using finite-dimensional approximations in the setting of Hilbert scales has been considered for obtaining stable approximate solutions to ill-posed operator equations. The derived error estimates using an a priori and a posteriori choice of parameters in relation to the noise level are shown to be of optimal order with respect to certain natural assumptions on the ill posedness of the equation. The results are shown to be applicable to a wide class of spline approximations in the setting of Sobolev scales.
Encounter distribution of two random walkers on a finite one-dimensional interval
Energy Technology Data Exchange (ETDEWEB)
Tejedor, Vincent; Schad, Michaela; Metzler, Ralf [Physics Department, Technical University of Munich, James Franck Strasse, 85747 Garching (Germany); Benichou, Olivier; Voituriez, Raphael, E-mail: metz@ph.tum.de [Laboratoire de Physique Theorique de la Matiere Condensee (UMR 7600), Universite Pierre et Marie Curie, 4 Place Jussieu, 75255 Paris Cedex (France)
2011-09-30
We analyse the first-passage properties of two random walkers confined to a finite one-dimensional domain. For the case of absorbing boundaries at the endpoints of the interval, we derive the probability that the two particles meet before either one of them becomes absorbed at one of the boundaries. For the case of reflecting boundaries, we obtain the mean first encounter time of the two particles. Our approach leads to closed-form expressions that are more easily tractable than a previously derived solution in terms of the Weierstrass' elliptic function. (paper)
A History of the Description of the Three-Dimensional Finite Rotation
Fraiture, Luc
2009-01-01
A history of the description of a three-dimensional finite rotation is given starting with Cardano in the middle of the sixteenth century and ending with Bryan in the beginning of the past century. Description means both a textual description and/or a mathematical representation. To appreciate the historical context of the milestones reached over the centuries, the background and personality of the main players in this history are given. At the end, a short critical discussion is added, reviewing the present names of rotation parameters in use related to the scientists which have been considered here.
Curvatures and discrete Gauss-Codazzi equation in (2+1)-dimensional loop quantum gravity
Ariwahjoedi, Seramika; Rovelli, Carlo; Zen, Freddy P
2015-01-01
We derive the Gauss-Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss-Codazzi equation for a discrete (2+1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2+1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.
Sikkenk, Tycho S.; Coester, Kris; Buhrandt, Stefan; Fritz, Lars; Schmidt, Kai P.
2017-02-01
The classical Ising model on the frustrated three-dimensional (3D) swedenborgite lattice has disordered spin liquid ground states for all ratios of inter- and intraplanar couplings. Quantum fluctuations due to a transverse field give rise to several exotic phenomena. In the limit of weakly coupled kagome layers we find a 3D version of disorder by disorder degeneracy lifting. For large out-of-plane couplings one-dimensional macrospins are formed, which realize a disordered macrospin liquid phase on an emerging two-dimensional triangular lattice. We speculate about a possibly exotic version of quantum criticality that connects the polarized phase to the macrospin liquid.
Quantum manifolds with classical limit
Hohmann, Manuel; Wohlfarth, Mattias N R
2008-01-01
We propose a mathematical model of quantum spacetime as an infinite-dimensional manifold locally homeomorphic to an appropriate Schwartz space. This extends and unifies both the standard function space construction of quantum mechanics and the manifold structure of spacetime. In this picture we demonstrate that classical spacetime emerges as a finite-dimensional manifold through the topological identification of all quantum points with identical position expectation value. We speculate on the possible relevance of this geometry to quantum field theory and gravity.
Energy Technology Data Exchange (ETDEWEB)
Dattoli, Giuseppe; Torre, Amalia [ENEA, Centro Ricerche Frascati, Rome (Italy). Dipt. Innovazione; Ottaviani, Pier Luigi [ENEA, Centro Ricerche Bologna (Italy); Vasquez, Luis [Madris, Univ. Complutense (Spain). Dept. de Matemateca Aplicado
1997-10-01
The finite-difference based integration method for evolution-line equations is discussed in detail and framed within the general context of the evolution operator picture. Exact analytical methods are described to solve evolution-like equations in a quite general physical context. The numerical technique based on the factorization formulae of exponential operator is then illustrated and applied to the evolution-operator in both classical and quantum framework. Finally, the general view to the finite differencing schemes is provided, displaying the wide range of applications from the classical Newton equation of motion to the quantum field theory.
Kawakami, Shun; Sasaki, Toshihiko; Koashi, Masato
2017-07-01
An essential step in quantum key distribution is the estimation of parameters related to the leaked amount of information, which is usually done by sampling of the communication data. When the data size is finite, the final key rate depends on how the estimation process handles statistical fluctuations. Many of the present security analyses are based on the method with simple random sampling, where hypergeometric distribution or its known bounds are used for the estimation. Here we propose a concise method based on Bernoulli sampling, which is related to binomial distribution. Our method is suitable for the Bennett-Brassard 1984 (BB84) protocol with weak coherent pulses [C. H. Bennett and G. Brassard, Proceedings of the IEEE Conference on Computers, Systems and Signal Processing (IEEE, New York, 1984), Vol. 175], reducing the number of estimated parameters to achieve a higher key generation rate compared to the method with simple random sampling. We also apply the method to prove the security of the differential-quadrature-phase-shift (DQPS) protocol in the finite-key regime. The result indicates that the advantage of the DQPS protocol over the phase-encoding BB84 protocol in terms of the key rate, which was previously confirmed in the asymptotic regime, persists in the finite-key regime.
Partition of unity finite element method for quantum mechanical materials calculations
Pask, John E
2016-01-01
The current state of the art for large-scale quantum-mechanical simulations is the planewave (PW) pseudopotential method, as implemented in codes such as VASP, ABINIT, and many others. However, since the PW method uses a global Fourier basis, with strictly uniform resolution at all points in space, it suffers from substantial inefficiencies in calculations involving atoms with localized states, such as first-row and transition-metal atoms, and requires significant nonlocal communications, which limit parallel efficiency. Real-space methods such as finite-differences and finite-elements have partially addressed both resolution and parallel-communications issues but have been plagued by one key disadvantage relative to PW: excessive number of degrees of freedom needed to achieve the required accuracies. We present a real-space partition of unity finite element (PUFE) method to solve the Kohn-Sham equations of density functional theory. In the PUFE method, we build the known atomic physics into the solution proc...
Sandvik, Anders W
2007-06-01
Using ground-state projector quantum Monte Carlo simulations in the valence-bond basis, it is demonstrated that nonfrustrating four-spin interactions can destroy the Néel order of the two-dimensional S=1/2 Heisenberg antiferromagnet and drive it into a valence-bond solid (VBS) phase. Results for spin and dimer correlations are consistent with a single continuous transition, and all data exhibit finite-size scaling with a single set of exponents, z=1, nu=0.78+/-0.03, and eta=0.26+/-0.03. The unusually large eta and an emergent U(1) symmetry, detected using VBS order parameter histograms, provide strong evidence for a deconfined quantum critical point.
Finite-time barriers to front propagation in two-dimensional fluid flows
Mahoney, John R
2015-01-01
Recent theoretical and experimental investigations have demonstrated the role of certain invariant manifolds, termed burning invariant manifolds (BIMs), as one-way dynamical barriers to reaction fronts propagating within a flowing fluid. These barriers form one-dimensional curves in a two-dimensional fluid flow. In prior studies, the fluid velocity field was required to be either time-independent or time-periodic. In the present study, we develop an approach to identify prominent one-way barriers based only on fluid velocity data over a finite time interval, which may have arbitrary time-dependence. We call such a barrier a burning Lagrangian coherent structure (bLCS) in analogy to Lagrangian coherent structures (LCSs) commonly used in passive advection. Our approach is based on the variational formulation of LCSs using curves of stationary "Lagrangian shear", introduced by Farazmand, Blazevski, and Haller [Physica D 278-279, 44 (2014)] in the context of passive advection. We numerically validate our techniqu...
Energy Technology Data Exchange (ETDEWEB)
Song, Youlin [Zhengzhou University, China; Zhao, Ke [ORNL; Jia, Yu [Zhengzhou University, China; Hu, Xing [Zhengzhou University, China; Zhang, Zhenyu [ORNL
2008-01-01
Finite size effects on the optical properties of one-dimensional 1D and two-dimensional 2D nanoshell dimer arrays are investigated using generalized Mie theory and coupled dipole approximation within the context of surface-enhanced Raman spectroscopy SERS. It is shown that the huge enhancement in the electromagnetic EM field at the center of a given dimer oscillates with the length of the 1D array. For an array of fixed length, the EM enhancement also oscillates along the array, but with a different period. Both types of oscillations can be attributed to the interference of the dynamic dipole fields from different dimers in the array. When generalized to 2D arrays, EM enhancement higher than that of the 1D arrays can be gained with a constant magnitude, a salient feature advantageous to experimental realization of single-molecule SERS. 2008 American Institute of Physics. DOI: 10.1063/1.3009293
Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
Charbonneau, Patrick; Kurchan, Jorge; Parisi, Giorgio; Urbani, Pierfrancesco; Zamponi, Francesco
2017-03-01
Despite decades of work, gaining a first-principles understanding of amorphous materials remains an extremely challenging problem. However, recent theoretical breakthroughs have led to the formulation of an exact solution of a microscopic glass-forming model in the mean-field limit of infinite spatial dimension. Numerical simulations have remarkably confirmed the dimensional robustness of some of the predictions. This review describes these latest advances. More specifically, we consider the dynamical and thermodynamic descriptions of hard spheres around the dynamical, Gardner, and jamming transitions. Comparing mean-field predictions with the finite-dimensional simulations, we identify robust aspects of the theory and uncover its more sensitive features. We conclude with a brief overview of ongoing research.
Latif, A. Afiff; Ibrahim, M. Rasidi; Rahim, E. A.; Cheng, K.
2017-04-01
The conventional milling has many difficulties in the processing of hard and brittle material. Hence, ultrasonic vibration assisted milling (UVAM) was proposed to overcome this problem. The objective of this research is to study the behavior of compliance mechanism (CM) as the critical part affect the performance of the UVAM. The design of the CM was investigated and focuses on 1-Dimensional. Experimental result was obtained from a portable laser digital vibrometer. While the 1-Dimensional value such as safety factor, deformation of hinges and stress analysis are obtained from finite elements simulation. Finally, the findings help to find the best design judging from the most travelled distance of the piezoelectric actuators. In addition, this paper would provide a clear picture the behavior of the CM embedded in the UVAM, which can provide good data and to improve the machining on reducing tool wear, and lower cutting force on the workpiece surface roughness.
Development and application of a three-dimensional finite element vapor intrusion model.
Pennell, Kelly G; Bozkurt, Ozgur; Suuberg, Eric M
2009-04-01
Details of a three-dimensional finite element model of soil vapor intrusion, including the overall modeling process and the stepwise approach, are provided. The model is a quantitative modeling tool that can help guide vapor intrusion characterization efforts. It solves the soil gas continuity equation coupled with the chemical transport equation, allowing for both advective and diffusive transport. Three-dimensional pressure, velocity, and chemical concentration fields are produced from the model. Results from simulations involving common site features, such as impervious surfaces, porous foundation sub-base material, and adjacent structures are summarized herein. The results suggest that site-specific features are important to consider when characterizing vapor intrusion risks. More importantly, the results suggest that soil gas or subslab gas samples taken without proper regard for particular site features may not be suitable for evaluating vapor intrusion risks; rather, careful attention needs to be given to the many factors that affect chemical transport into and around buildings.
Institute of Scientific and Technical Information of China (English)
LI De-Jun; MI Xian-Wu; DENG Ke; TANG Yi
2006-01-01
In the classical lattice theory, solitons and locaLized modes can exist in many one-dimensional nonlinear lattice chains, however, in the quantum lattice theory, whether quantum solitons and localized modes can exist or not in the one-dimensional lattice chains is an interesting problem. By using the number state method and the Hartree approximation combined with the method of multiple scales, we investigate quantum solitons and localized modes in a one-dimensional lattice chain with the nonlinear substrate potential. It is shown that quantum solitons do exist in this nonlinear lattice chain, and at the boundary of the phonon Brillouin zone, quantum solitons become quantum localized modes, phonons are pinned to the lattice of the vicinity at the central position j = j0.
Two-dimensional ion trap lattice on a microchip for quantum simulation
Sterling, R C; Weidt, S; Lake, K; Srinivasan, P; Webster, S C; Kraft, M; Hensinger, W K
2013-01-01
Using a controllable quantum system it is possible to simulate other highly complex quantum systems efficiently overcoming an in-principle limitation of classical computing. Trapped ions constitute such a highly controllable quantum system. So far, no dedicated architectures for the simulation of two-dimensional spin lattices using trapped ions in radio-frequency ion traps have been produced, limiting the possibility of carrying out such quantum simulations on a large scale. We report the operation of a two-dimensional ion trap lattice integrated in a microchip capable of implementing quantum simulations of two-dimensional spin lattices. Our device provides a scalable microfabricated architecture for trapping such ion lattices with coupling strengths between neighbouring ions sufficient to provide a powerful platform for the implementation of quantum simulations. In order to realize this device we developed a specialist fabrication process that allows for the application of very large voltages. We fabricated ...
Quantum search on the two-dimensional lattice using the staggered model with Hamiltonians
Portugal, R.; Fernandes, T. D.
2017-04-01
Quantum search on the two-dimensional lattice with one marked vertex and cyclic boundary conditions is an important problem in the context of quantum algorithms with an interesting unfolding. It avails to test the ability of quantum walk models to provide efficient algorithms from the theoretical side and means to implement quantum walks in laboratories from the practical side. In this paper, we rigorously prove that the recent-proposed staggered quantum walk model provides an efficient quantum search on the two-dimensional lattice, if the reflection operators associated with the graph tessellations are used as Hamiltonians, which is an important theoretical result for validating the staggered model with Hamiltonians. Numerical results show that on the two-dimensional lattice staggered models without Hamiltonians are not as efficient as the one described in this paper and are, in fact, as slow as classical random-walk-based algorithms.
Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich
2013-12-01
This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.
New quantum codes from dual-containing cyclic codes over finite rings
Tang, Yongsheng; Zhu, Shixin; Kai, Xiaoshan; Ding, Jian
2016-11-01
Let R=F_{2m}+uF_{2m}+\\cdots +ukF_{2m}, where F_{2m} is the finite field with 2m elements, m is a positive integer, and u is an indeterminate with u^{k+1}=0. In this paper, we propose the constructions of two new families of quantum codes obtained from dual-containing cyclic codes of odd length over R. A new Gray map over R is defined, and a sufficient and necessary condition for the existence of dual-containing cyclic codes over R is given. A new family of 2m-ary quantum codes is obtained via the Gray map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R. In particular, a new family of binary quantum codes is obtained via the Gray map, the trace map and the Calderbank-Shor-Steane construction from dual-containing cyclic codes over R.
Pan, Xue; Wu, Yuan-Fang
2016-01-01
The high-order cumulants of conserved charges are suggested to be sensitive observables to search for the critical point of Quantum Chromodynamics (QCD). The order has been calculated to the sixth one at experiments. The corresponding theoretical studies on the sixth order cumulant are necessary. Based on the universality of the critical behavior, we study the temperature dependence of the sixth order cumulant of the order parameter using the parametric representation of the three-dimensional Ising model, which is expected to be in the same universality class with QCD. The density plot of the sign of the sixth order cumulant is shown on the temperature and external magnetic field plane. We found that when the critical point is approached from the crossover side, the sixth order cumulant is negative. Qualitatively, the trend is similar to the result of Monte Carlo simulation on a finite-size system. Quantitatively, the temperature of the sign change is different. Through Monte Carlo simulation of the Ising mod...
Directory of Open Access Journals (Sweden)
Jiang-Jun Zhou
2017-01-01
Full Text Available In this study, we developed and validated a refined three-dimensional finite element model of middle femoral comminuted fracture to compare the biomechanical stability after two kinds of plate fixation: a newly designed assembly locking compression plate (NALCP and a locking compression plate (LCP. CT data of a male volunteer was converted to middle femoral comminuted fracture finite element analysis model. The fracture was fixated by NALCP and LCP. Stress distributions were observed. Under slow walking load and torsion load, the stress distribution tendency of the two plates was roughly uniform. The anterolateral femur was the tension stress area, and the bone block shifted toward the anterolateral femur. Maximum stress was found on the lateral border of the number 5 countersink of the plate. Under a slow walking load, the NALCP maximum stress was 2.160e+03 MPa and the LCP was 8.561e+02 MPa. Under torsion load, the NALCP maximum stress was 2.260e+03 MPa and the LCP was 6.813e+02 MPa. Based on those results of finite element analysis, the NALCP can provide adequate mechanical stability for comminuted fractures, which would help fixate the bone block and promote bone healing.
Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander
2011-01-01
A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.
[Establishment of 3-dimensional finite element model of human knee joint and its biomechanics].
Yuan, Ping; Wang, Wanchun
2010-01-01
To establish a 3-dimensional (3-D) finite element knee model in healthy Chinese males, to verify the validity of the model, and to analyze the biomechanics of this model under axial load, flexion moment, varus/valgus torque, and internal/external axial torque. A set of consecutive transectional computerized tomography images of normal male knee joints in upright weight-bearing position was selected. With image processing and inversion technology, the 3-D finite element model of the normal knee joint was established through the software ABAQOUS/STANDARD Version-6.5.Biomechanical analysis of this model was processed under axial load, flexion moment, varus/valgus torque, and internal/external axial torque. A 3-D finite element model of healthy Chinese males was successfully established. The ranges of motion of varus and valgus were both small and the difference between them has no statistical significance (P>0.05). The motion of internal and external rotation of the knee took place only in flexion situation.The range of motion of external rotation was larger than that of internal rotation in the same knee (Pknee resembles the actual knee segments. It can imitate the knee response to different loads. This model could be used for further study on knee biomechanics.
Three Dimensional Viscous Finite Element Formulation For Acoustic Fluid Structure Interaction
Cheng, Lei; White, Robert D.; Grosh, Karl
2010-01-01
A three dimensional viscous finite element model is presented in this paper for the analysis of the acoustic fluid structure interaction systems including, but not limited to, the cochlear-based transducers. The model consists of a three dimensional viscous acoustic fluid medium interacting with a two dimensional flat structure domain. The fluid field is governed by the linearized Navier-Stokes equation with the fluid displacements and the pressure chosen as independent variables. The mixed displacement/pressure based formulation is used in the fluid field in order to alleviate the locking in the nearly incompressible fluid. The structure is modeled as a Mindlin plate with or without residual stress. The Hinton-Huang’s 9-noded Lagrangian plate element is chosen in order to be compatible with 27/4 u/p fluid elements. The results from the full 3d FEM model are in good agreement with experimental results and other FEM results including Beltman’s thin film viscoacoustic element [2] and two and half dimensional inviscid elements [21]. Although it is computationally expensive, it provides a benchmark solution for other numerical models or approximations to compare to besides experiments and it is capable of modeling any irregular geometries and material properties while other numerical models may not be applicable. PMID:20174602
Reductions in finite-dimensional integrable systems and special points of classical r-matrices
Skrypnyk, T.
2016-12-01
For a given 𝔤 ⊗ 𝔤-valued non-skew-symmetric non-dynamical classical r-matrices r(u, v) with spectral parameters, we construct the general form of 𝔤-valued Lax matrices of finite-dimensional integrable systems satisfying linear r-matrix algebra. We show that the reduction in the corresponding finite-dimensional integrable systems is connected with "the special points" of the classical r-matrices in which they become degenerated. We also propose a systematic way of the construction of additional integrals of the Lax-integrable systems associated with the symmetries of the corresponding r-matrices. We consider examples of the Lax matrices and integrable systems that are obtained in the framework of the general scheme. Among them there are such physically important systems as generalized Gaudin systems in an external magnetic field, ultimate integrable generalization of Toda-type chains (including "modified" or "deformed" Toda chains), generalized integrable Jaynes-Cummings-Dicke models, integrable boson models generalizing Bose-Hubbard dimer models, etc.
Semi-automatic computer construction of three-dimensional shapes for the finite element method.
Aharon, S; Bercovier, M
1993-12-01
Precise estimation of spatio-temporal distribution of ions (or other constitutives) in three-dimensional geometrical configuration plays a major role in biology. Since a direct experimental information regarding the free intracellular Ca2+ spatio-temporal distribution is not available to date, mathematical models have been developed. Most of the existing models are based on the classical numerical method of finite-difference (FD). Using this method one is limited when dealing with complicated geometry, general boundary conditions and variable or non-linear material properties. These difficulties are easily solved when the finite-element-method (FEM) is employed. The first step in the implementation of the FEM procedure is the mesh generation which is the single most tedious, time consuming task and vulnerable to mistake. In order to overcome these limitations we developed a new interface called AUTOMESH. This tool is used as a preprocessor program which generates two- and three-dimensional meshes for some known and often-used shapes in neurobiology. AUTOMESH creates an appropriate mesh by using the mesh generator commercial tool of FIDAP.
Institute of Scientific and Technical Information of China (English)
LUO Zu-jiang; ZHANG Ying-ying; WU Yong-xia
2008-01-01
For deep foundation pit dewatering in the Yangtze River Delta, it is easy to make a dramatic decrease of the underground water level surrounding the dewatering area and cause land subsidence and geologic disasters. In this work, a three-dimensional finite element simulation method was applied in the forth subway of Dongjiadu tunnel repair foundation pit dewatering in Shanghai. In order to control the decrease of the underground water level around the foundation pit, the foundation pit dewatering method was used to design the optimization project of dewatering ,which was simulated under these conditions that the aquifers deposited layer by layer, the bottom of the aquifers went deep to 144.45 m, the retaining wall of foundation pit shield went deep to 65 m, the filters of the extraction wells were located between 44 m to 59 m, the water level in the deep foundation pit was decreased by 34 m, and the maximum decrease of water level outside the foundation pit was 3 m. It is shown that the optimization project and the practical case are consistent with each other. Accordingly, the three-dimensional finite element numerical simulation is the basic theory of optimization design of engineering structures of dewatering in deep foundation pit in such areas.
Three dimensional finite element analysis and optimal design of cast-iron bronze-inlaid gate
Tang, Liangbao; Fang, Yuefei
2005-12-01
The three-dimensional finite element model of the body of cast-iron bronze-inlaid gate is established to calculate its deformation and stress. By calculation, we obtain the law of deformation and stress under static water pressure. Then we optimize the structure of the body of cast-iron bronze-inlaid gate vie above calculation results. To validate the effect of proposed method, an engineering example of 1000mm×1500mm gate in a certain sewage process plant is introduced. The comparisons are made between the calculation results of the proposed method and those obtained by conventional design. The comparison results show that three dimensional finite element methods can obtain the actual stress and deformation of the gate body under static water pressure. In addition, we further optimize the structure and dimension of the cast-iron bronze-inlaid gate. The final optimization results show that the proposed method can reduce the weight of the gate by 20% compared those results by conventional design.
Xu, Cenke
Several examples of quantum spin systems and pseudo spin systems have been studied, and unconventional states of matters and phase transitions have been realized in all these systems under consideration. In the p +/- ip superconductor Josephson lattice and the p--band cold atomic system trapped in optical lattices, novel phases which behave similarly to 1+1 dimensional systems are realized, despite the fact that the real physical systems are in two or three dimensional spaces. For instance, by employing a spin-wave analysis together with a new duality transformation, we establish the existence and stability of a novel gapless "critical phase", which we refer to as a "bond algebraic liquid". This novel critical phase is analogous to the 1+1 dimensional algebraic boson liquid phase. The reason for the novel physics is that there is a quasilocal gauge symmetry in the effective low energy Hamiltonian. In a spin-1 system on the kagome lattice, and a hard-core boson system on the honeycomb lattice, the low energy physics is controlled by two components of compact U(1) gauge symmetries that emerge at low energy. Making use of the confinement nature of the 2+1 dimensional compact gauge theories and the powerful duality between gauge theories and height field theories, the crystalline phase diagrams are studied for both systems, and the transitions to other phases are also considered. These phase diagrams might be accessible in strongly correlated materials, or atomic systems in optical lattices. A novel quantum ground state of matter is realized in a bosonic model on three dimensional fcc lattice with emergent low energy excitations. The novel phase obtained is a stable gapless boson liquid phase, with algebraic boson density correlations. The stability of this phase is protected against the instanton effect and superfluidity by self-duality and large gauge symmetries on both sides of the duality. The gapless collective excitations of this phase closely resemble the
Chen, Y. F.; Tung, J. C.; Tuan, P. H.; Yu, Y. T.; Liang, H. C.; Huang, K. F.
2017-01-01
A general method is developed to characterize the family of classical periodic orbits from the quantum Green's function for the two-dimensional (2D) integrable systems. A decomposing formula related to the beta function is derived to link the quantum Green's function with the individual classical periodic orbits. The practicality of the developed formula is demonstrated by numerically analyzing the 2D commensurate harmonic oscillators and integrable quantum billiards. Numerical analyses reveal that the emergence of the classical features in quantum Green's functions principally comes from the superposition of the degenerate states for 2D harmonic oscillators. On the other hand, the damping factor in quantum Green's functions plays a critical role to display the classical features in mesoscopic regime for integrable quantum billiards, where the physical function of the damping factor is to lead to the coherent superposition of the nearly degenerate eigenstates.
Full-thickness tears of the supraspinatus tendon: A three-dimensional finite element analysis.
Quental, C; Folgado, J; Monteiro, J; Sarmento, M
2016-12-08
Knowledge regarding the likelihood of propagation of supraspinatus tears is important to allow an early identification of patients for whom a conservative treatment is more likely to fail, and consequently, to improve their clinical outcome. The aim of this study was to investigate the potential for propagation of posterior, central, and anterior full-thickness tears of different sizes using the finite element method. A three-dimensional finite element model of the supraspinatus tendon was generated from the Visible Human Project data. The mechanical behaviour of the tendon was fitted from experimental data using a transversely isotropic hyperelastic constitutive model. The full-thickness tears were simulated at the supraspinatus tendon insertion by decreasing the interface area. Tear sizes from 10% to 90%, in 10% increments, of the anteroposterior length of the supraspinatus footprint were considered in the posterior, central, and anterior regions of the tendon. For each tear, three finite element analyses were performed for a supraspinatus force of 100N, 200N, and 400N. Considering a correlation between tendon strain and the risk of tear propagation, the simulated tears were compared qualitatively and quantitatively by evaluating the volume of tendon for which a maximum strain criterion was not satisfied. The finite element analyses showed a significant impact of tear size and location not only on the magnitude, but also on the patterns of the maximum principal strains. The mechanical outcome of the anterior full-thickness tears was consistently, and significantly, more severe than that of the central or posterior full-thickness tears, which suggests that the anterior tears are at greater risk of propagating than the central or posterior tears.
Friedberg, R; Zhao Wei Qin
2000-01-01
We present a new method to derive low-lying N-dimensional quantum wave functions by quadrature along a single trajectory. The N-dimensional Schroedinger equation is cast into a series of readily integrable first order ordinary differential equations. Our approach resembles the familiar W.K.B. approximation in one dimension, but is designed to explore the classically forbidden region and has a much wider applicability than W.K.B.. The method also provides a perturbation series expansion and the Green's functions of the wave equation in N-dimension, all by quadratures along a single trajectory. A number of examples are given for illustration, including a simple algorithm to evaluate the Stark effect in closed form to any finite order of the electric field.
Dynamical properties of the sine-Gordon quantum spin magnet Cu-PM at zero and finite temperature
Tiegel, Alexander C.; Honecker, Andreas; Pruschke, Thomas; Ponomaryov, Alexey; Zvyagin, Sergei A.; Feyerherm, Ralf; Manmana, Salvatore R.
2016-03-01
The material copper pyrimidine dinitrate (Cu-PM) is a quasi-one-dimensional spin system described by the spin-1/2 X X Z Heisenberg antiferromagnet with Dzyaloshinskii-Moriya interactions. Based on numerical results obtained by the density-matrix renormalization group, exact diagonalization, and accompanying electron spin resonance (ESR) experiments we revisit the spin dynamics of this compound in an applied magnetic field. Our calculations for momentum and frequency-resolved dynamical quantities give direct access to the intensity of the elementary excitations at both zero and finite temperature. This allows us to study the system beyond the low-energy description by the quantum sine-Gordon model. We find a deviation from the Lorentz invariant dispersion for the single-soliton resonance. Furthermore, our calculations only confirm the presence of the strongest boundary bound state previously derived from a boundary sine-Gordon field theory, while composite boundary-bulk excitations have too low intensities to be observable. Upon increasing the temperature, we find a temperature-induced crossover of the soliton and the emergence of new features, such as interbreather transitions. The latter observation is confirmed by our ESR experiments on Cu-PM over a wide range of the applied field.
Peterson, Michael
2009-03-01
The fractional quantum Hall effect (FQHE) in the second orbital Landau level at even-denominator filling factor 5/2 remains mysterious and is currently motivating many scientists not only because of its connection to a possible implementation of a fault tolerant topological quantum computer (Das Sarma et al., PRL 94, 166802(2005)). In this work, we theoretically consider the effect of the quasi-two-dimensional nature of the experimental fractional quantum Hall systems on a number of FQHE states in the lowest three orbital Landau levels. Our primary result is that the finite width of the quasi-two-dimensional systems produce a physical environment sufficient to stabilize the Moore-Read Pfaffian state thought to describe the FQHE at filling factor 5/2. This conclusion is based on exact calculations performed in the spherical and torus geometries, studying wave function overlap and ground state degeneracy. Furthermore, our results open the possibility of creating optimal experimental systems where the 5/2 FQHE state would more likely be described by the Moore-Read Pfaffian. We also discuss the role of the three-body interaction Hamiltonian that produces the Moore-Read Pfaffian as an exact ground state and particle-hole symmetry in the FQHE at 5/2. We acknowledge support from Microsoft Project Q. Work done in collaboration with Sankar Das Sarma, Thierry Jolicoeur, and Kwon Park.
Li, Hai-Sheng; Zhu, Qingxin; Zhou, Ri-Gui; Song, Lan; Yang, Xing-jiang
2014-04-01
Multi-dimensional color image processing has two difficulties: One is that a large number of bits are needed to store multi-dimensional color images, such as, a three-dimensional color image of needs bits. The other one is that the efficiency or accuracy of image segmentation is not high enough for some images to be used in content-based image search. In order to solve the above problems, this paper proposes a new representation for multi-dimensional color image, called a -qubit normal arbitrary quantum superposition state (NAQSS), where qubits represent colors and coordinates of pixels (e.g., represent a three-dimensional color image of only using 30 qubits), and the remaining 1 qubit represents an image segmentation information to improve the accuracy of image segmentation. And then we design a general quantum circuit to create the NAQSS state in order to store a multi-dimensional color image in a quantum system and propose a quantum circuit simplification algorithm to reduce the number of the quantum gates of the general quantum circuit. Finally, different strategies to retrieve a whole image or the target sub-image of an image from a quantum system are studied, including Monte Carlo sampling and improved Grover's algorithm which can search out a coordinate of a target sub-image only running in where and are the numbers of pixels of an image and a target sub-image, respectively.
Quantum simulations of a particle in one-dimensional potentials using NMR
Energy Technology Data Exchange (ETDEWEB)
Shankar, Ravi; Hegde, Swathi S.; Mahesh, T.S.
2014-01-03
A quantum computer made up of a controllable set of quantum particles has the potential to efficiently simulate other quantum systems. In this work we studied quantum simulations of single particle Shrödinger equation for certain one-dimensional potentials. Using a five-qubit NMR system, we achieve space discretization with four qubits, and the other qubit is used for preparation of initial states as well as measurement of spatial probabilities. The experimental relative probabilities compare favourably with the theoretical expectations, thus effectively mimicking a small scale quantum simulator.
Antiresonance Effect in Electronic Tunnelling through a One-Dimensional Quantum Dot Chain
Institute of Scientific and Technical Information of China (English)
SUN Pu-Nan
2006-01-01
@@ Electronic tunnelling through a one-dimensional quantum dot chain is theoretically studied, when two leads couple to the individual component quantum dots of the chain arbitrarily. If there are some dangling quantum dots in the chain outside the leads, the electron tunnelling through the quantum dot chain is wholly forbidden while the energy of the incident electron is just equal to the molecular energy levels of the dangling quantum dots,which is known as the antiresonance effect. In addition, the influence of electron interaction on the antiresonance effect is discussed within the Hartree-Fock approximation.
Efficiency at maximum power output of quantum heat engines under finite-time operation
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, ηm, of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures Th and Tc, respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), ηm becomes identical to the Carnot efficiency ηC=1-Tc/Th. For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency ηm at maximum power output is bounded from above by ηC/(2-ηC) and from below by ηC/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency ηCA=1-Tc/Th is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Efficiency at maximum power output of quantum heat engines under finite-time operation.
Wang, Jianhui; He, Jizhou; Wu, Zhaoqi
2012-03-01
We study the efficiency at maximum power, η(m), of irreversible quantum Carnot engines (QCEs) that perform finite-time cycles between a hot and a cold reservoir at temperatures T(h) and T(c), respectively. For QCEs in the reversible limit (long cycle period, zero dissipation), η(m) becomes identical to the Carnot efficiency η(C)=1-T(c)/T(h). For QCE cycles in which nonadiabatic dissipation and the time spent on two adiabats are included, the efficiency η(m) at maximum power output is bounded from above by η(C)/(2-η(C)) and from below by η(C)/2. In the case of symmetric dissipation, the Curzon-Ahlborn efficiency η(CA)=1-√(T(c)/T(h)) is recovered under the condition that the time allocation between the adiabats and the contact time with the reservoir satisfy a certain relation.
Efficiency, Power and Period of a model quantum heat engine working in a finite time
Bekele, Mulugeta; Dima, Tolasa A.; Alemye, Mekuannent; Chegeno, Warga
We take a spin-half quantum particle undergoing Carnot type cyclic process in a finite time assisted by two heat reservoirs and an external magnetic field. We find that the power of the heat engine is maximum at a particular period of the cyclic process and efficiency at the maximum power is at least half of the Carnot efficiency. We further apply the Omega-criterion for a figure of merit representing a compromise between useful power and lost power determining the corresponding efficiency for the optimization criterion to be at least three fourth of the Carnot efficiency. The authers are thankful to the International Science programme, IPS, Uppsala, Sweden for their support to our research lab.
Quantum Otto cycle with inner friction: finite-time and disorder effects
Alecce, A.; Galve, F.; Lo Gullo, N.; Dell'Anna, L.; Plastina, F.; Zambrini, R.
2015-07-01
The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finite-time cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to the temperature difference between heat baths. Finally we propose an alternative experimental implementation of the cycle where the spin is encoded in the degree of polarization of photons.
Two-dimensional thermal analysis of a fuel rod by finite volume method
Energy Technology Data Exchange (ETDEWEB)
Costa, Rhayanne Y.N.; Silva, Mario A.B. da; Lira, Carlos A.B. de O., E-mail: ryncosta@gmail.com, E-mail: mabs500@gmail.com, E-mail: cabol@ufpe.br [Universidade Federal de Pernambuco (UFPE), Recife, PE (Brazil). Departamaento de Energia Nuclear
2015-07-01
In a nuclear reactor, the amount of power generation is limited by thermal and physic limitations rather than by nuclear parameters. The operation of a reactor core, considering the best heat removal system, must take into account the fact that the temperatures of fuel and cladding shall not exceed safety limits anywhere in the core. If such considerations are not considered, damages in the fuel element may release huge quantities of radioactive materials in the coolant or even core meltdown. Thermal analyses for fuel rods are often accomplished by considering one-dimensional heat diffusion equation. The aim of this study is to develop the first paper to verify the temperature distribution for a two-dimensional heat transfer problem in an advanced reactor. The methodology is based on the Finite Volume Method (FVM), which considers a balance for the property of interest. The validation for such methodology is made by comparing numerical and analytical solutions. For the two-dimensional analysis, the results indicate that the temperature profile agree with expected physical considerations, providing quantitative information for the development of advanced reactors. (author)
Computational method for the quantum Hamilton-Jacobi equation: one-dimensional scattering problems.
Chou, Chia-Chun; Wyatt, Robert E
2006-12-01
One-dimensional scattering problems are investigated in the framework of the quantum Hamilton-Jacobi formalism. First, the pole structure of the quantum momentum function for scattering wave functions is analyzed. The significant differences of the pole structure of this function between scattering wave functions and bound state wave functions are pointed out. An accurate computational method for the quantum Hamilton-Jacobi equation for general one-dimensional scattering problems is presented to obtain the scattering wave function and the reflection and transmission coefficients. The computational approach is demonstrated by analysis of scattering from a one-dimensional potential barrier. We not only present an alternative approach to the numerical solution of the wave function and the reflection and transmission coefficients but also provide a computational aspect within the quantum Hamilton-Jacobi formalism. The method proposed here should be useful for general one-dimensional scattering problems.
CSIR Research Space (South Africa)
Mafu, M
2013-09-01
Full Text Available We present an experimental study of higher-dimensional quantum key distribution protocols based on mutually unbiased bases, implemented by means of photons carrying orbital angular momentum. We perform (d + 1) mutually unbiased measurements in a...
Strečka, Jozef; Verkholyak, Taras
2016-10-01
Magnetic properties of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are examined using quantum Monte Carlo simulations for two different quantum spin numbers S=1 and 3/2. The calculated magnetization curves at finite temperatures are confronted with zero-temperature magnetization data obtained within the density matrix renormalization group method, which imply an existence of two quantum critical points determining a breakdown of the gapped Lieb-Mattis ferrimagnetic phase and Tomonaga-Luttinger spin-liquid phase, respectively. While a square root behavior of the magnetization accompanying each quantum critical point is gradually smoothed upon rising temperature, the susceptibility and isothermal entropy change data at low temperatures provide a stronger evidence of the zero-temperature quantum critical points through marked local maxima and minima, respectively.
Institute of Scientific and Technical Information of China (English)
Zheng Rui; Liu Bang-Gui
2012-01-01
In order to gain a deeper understanding of the quantum criticality in the explicitly staggered dimerized Heisenberg models,we study a generalized staggered dimer model named the J0 J1-J2 model,which corresponds to the staggered J J’ model on a square lattice and a honeycomb lattice when J1/J0 equals 1 and 0,respectively.Using the quantum Monte Carlo method,we investigate all the quantum critical points of these models with J1/J0 changing from 0 to 1as a function of coupling ratio α =J2/J0.We extract all the critical values of the coupling ratio αc for these models,and we also obtain the critical exponents v,β/v,and η using different finite-size scaling ans(a)tz,.All these exponents are not consistent with the three-dimensional Heisenberg universality class,indicating some unconventional quantum ciritcial points in these models.
Scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity
Nishimura, J; Tsuchiya, A; Jun Nishimura; Shinya Tamura; Asato Tsuchiya
1994-01-01
Using (2+$\\epsilon$)-dimensional quantum gravity recently formulated by Kawai, Kitazawa and Ninomiya, we calculate the scaling dimensions of manifestly generally covariant operators in two-dimensional quantum gravity coupled to $(p,q)$ minimal conformal matter. In the spectrum appear all the scaling dimensions of the scaling operators in the matrix model except the boundary operators, while there are also many others which have no corresponding scaling dimensions in the matrix model.
Quasi-two-dimensional Dirac fermions and quantum magnetoresistance in LaAgBi$_2$
Wang, Kefeng; Graf, D.; Petrovic, C.
2016-01-01
We report quasi-two-dimensional Dirac fermions and quantum magnetoresistance in LaAgBi$_2$. The band structure shows several narrow bands with nearly linear energy dispersion and Dirac-cone-like points at the Fermi level. The quantum oscillation experiments revealed one quasi-two-dimensional Fermi pocket and another complex pocket with small cyclotron resonant mass. The in-plane transverse magnetoresistance exhibits a crossover at a critical field $B^*$ from semiclassical weak-field $B^2$ dep...
Superiority of semiclassical over quantum mechanical calculations for a three-dimensional system
Energy Technology Data Exchange (ETDEWEB)
Main, Joerg; Wunner, Guenter; Atilgan, Erdinc; Taylor, Howard S.; Dando, Paul A
2002-12-02
In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a three-dimensional system, viz. the hyperbolic four-sphere scattering system, we demonstrate the superiority of semiclassical versus quantum calculations. Semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques.
Superiority of semiclassical over quantum mechanical calculations for a three-dimensional system
Main, Jörg; Wunner, Günter; Atılgan, Erdinç; Taylor, Howard S.; Dando, Paul A.
2002-12-01
In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a three-dimensional system, viz. the hyperbolic four-sphere scattering system, we demonstrate the superiority of semiclassical versus quantum calculations. Semiclassical resonances can easily be obtained even in energy regions which are unattainable with the currently available quantum techniques.
(3+1)-Dimensional Quantum Mechanics from Monte Carlo Hamiltonian: Harmonic Oscillator
Institute of Scientific and Technical Information of China (English)
LUO Xiang-Qian; XU Hao; YANG Jie-Chao; WANG Yu-Li; CHANG Di; LIN Yin; Helmut Kroger
2001-01-01
In Lagrangian formulation, it is extremely difficult to compute the excited spectrum and wavefunctions ora quantum theory via Monte Carlo methods. Recently, we developed a Monte Carlo Hamiltonian method for investigating this hard problem and tested the algorithm in quantum-mechanical systems in 1+1 and 2t1 dimensions. In this paper we apply it to the study of thelow-energy quantum physics of the (3+1)-dimensional harmonic oscillator.``
Security of high speed quantum key distribution with finite detector dead time
Burenkov, Viacheslav; Fortescue, Ben; Lo, Hoi-Kwong
2010-01-01
The security of a high speed quantum key distribution system with finite detector dead time \\tau is analyzed. When the transmission rate becomes higher than the maximum count rate of the individual detectors (1/\\tau ), security issues affect the algorithm for sifting bits. Analytical calculations and numerical simulations of the Bennett-Brassard BB84 protocol are performed. We study Rogers et al.'s protocol (introduced in "Detector dead-time effects and paralyzability in high-speed quantum key distribution," New J. Phys. 9 (2007) 319) in the presence of an active eavesdropper Eve who has the power to perform an intercept-resend attack. It is shown that Rogers et al.'s protocol is no longer secure. More specifically, Eve can induce a basis-dependent detection efficiency at the receiver's end. Modified key sifting schemes that are secure in the presence of dead time and an active eavesdropper are then introduced. We analyze and compare these secure sifting schemes for this active Eve scenario, and calculate and...
Calculating Two-Dimensional Spectra with the Mixed Quantum-Classical Ehrenfest Method
van der Vegte, C. P.; Dijkstra, A. G.; Knoester, J.; Jansen, T. L. C.
2013-01-01
We present a mixed quantum-classical simulation approach to calculate two-dimensional spectra of coupled two-level electronic model systems. We include the change in potential energy of the classical system due to transitions in the quantum system using the Ehrenfest method. We study how this
Ge, Yingbin
2016-01-01
Hands-on exercises are designed for undergraduate physical chemistry students to derive two-dimensional quantum chemistry from scratch for the H atom and H[subscript 2] molecule, both in the ground state and excited states. By reducing the mathematical complexity of the traditional quantum chemistry teaching, these exercises can be completed…
Topology Change and the Emergence of Geometry in Two Dimensional Causal Quantum Gravity
Westra, W.
2007-01-01
Despite many attempts, gravity has vigorously resisted a unification with the laws of quantum mechanics. Besides a plethora of technical issues, one is also faced with many interesting conceptual problems. The study of quantum gravity in lower dimensional models ameliorates the technical difficultie
Calculating Two-Dimensional Spectra with the Mixed Quantum-Classical Ehrenfest Method
van der Vegte, C. P.; Dijkstra, A. G.; Knoester, J.; Jansen, T. L. C.
2013-01-01
We present a mixed quantum-classical simulation approach to calculate two-dimensional spectra of coupled two-level electronic model systems. We include the change in potential energy of the classical system due to transitions in the quantum system using the Ehrenfest method. We study how this feedba
Institute of Scientific and Technical Information of China (English)
Li Hong; Kong Xiao-Jun
2004-01-01
A simple method for calculating the free-exciton binding energies in the fractional-dimensional-space model for single-quantum-well structure has been extended to quantum-well wires and quantum dots, in which the real anisotropic system is modelled through an effective isotropic environment with a fractional dimension. In this scheme, the fractionaldimensional parameter is chosen via an analytical procedure and involves no ansatz. We calculated the ground-state binding energies of excitons and donors in quantum-well wires with rectangular cross sections. Our results are found to be in good agreement with previous variational calculations and available experimental measurements. We also discussed the ground-state exciton binding energy changing with different shapes of quantum-well wires.
[Three-dimensional Finite Element Analysis to T-shaped Fracture of Pelvis in Sitting Position].
Fan, Yanping; Lei, Jianyin; Liu, Haibo; Li, Zhiqiang; Cai, Xianhua; Chen, Weiyi
2015-10-01
We developed a three-dimensional finite element model of the pelvis. According to Letournel methods, we established a pelvis model of T-shaped fracture with its three different fixation systems, i. e. double column reconstruction plates, anterior column plate combined with posterior column screws and anterior column plate combined with quadrilateral area screws. It was found that the pelvic model was effective and could be used to simulate the mechanical behavior of the pelvis. Three fixation systems had great therapeutic effect on the T-shaped fracture. All fixation systems could increase the stiffness of the model, decrease the stress concentration level and decrease the displacement difference along the fracture line. The quadrilateral area screws, which were drilled into cortical bone, could generate beneficial effect on the T-type fracture. Therefore, the third fixation system mentioned above (i. e. the anterior column plate combined with quadrilateral area screws) has the best biomechanical stability to the T-type fracture.
Directory of Open Access Journals (Sweden)
Kunal Pathak
2016-09-01
Full Text Available The calcium signaling plays a crucial role in expansion and contraction of cardiac myocytes. This calcium signaling is achieved by calcium diffusion, buffering mechanisms and influx in cardiac myocytes. The various calcium distribution patterns required for achieving calcium signaling in myocytes are still not well understood. In this paper an attempt has been made to develop a model of calcium distribution in myocytes incorporating diffusion of calcium, point source and excess buffer approximation. The model has been developed for a two dimensional unsteady state case. Appropriate boundary conditions and initial condition have been framed. The finite element method has been employed to obtain the solution. The numerical results have been used to study the effect of buffers and source amplitude on calcium distribution in myocytes.
Finite-Difference Time-Domain Simulation for Three-dimensional Polarized Light Imaging
Menzel, Miriam; De Raedt, Hans; Michielsen, Kristel
2016-01-01
Three-dimensional Polarized Light Imaging (3D-PLI) is a promising technique to reconstruct the nerve fiber architecture of human post-mortem brains from birefringence measurements of histological brain sections with micrometer resolution. To better understand how the reconstructed fiber orientations are related to the underlying fiber structure, numerical simulations are employed. Here, we present two complementary simulation approaches that reproduce the entire 3D-PLI analysis: First, we give a short review on a simulation approach that uses the Jones matrix calculus to model the birefringent myelin sheaths. Afterwards, we introduce a more sophisticated simulation tool: a 3D Maxwell solver based on a Finite-Difference Time-Domain algorithm that simulates the propagation of the electromagnetic light wave through the brain tissue. We demonstrate that the Maxwell solver is a valuable tool to better understand the interaction of polarized light with brain tissue and to enhance the accuracy of the fiber orientati...
Shu, Chi-Wang
1998-01-01
This project is about the development of high order, non-oscillatory type schemes for computational fluid dynamics. Algorithm analysis, implementation, and applications are performed. Collaborations with NASA scientists have been carried out to ensure that the research is relevant to NASA objectives. The combination of ENO finite difference method with spectral method in two space dimension is considered, jointly with Cai [3]. The resulting scheme behaves nicely for the two dimensional test problems with or without shocks. Jointly with Cai and Gottlieb, we have also considered one-sided filters for spectral approximations to discontinuous functions [2]. We proved theoretically the existence of filters to recover spectral accuracy up to the discontinuity. We also constructed such filters for practical calculations.
Song, Youlin; Zhao, Ke; Jia, Yu; Hu, Xing; Zhang, Zhenyu
2009-03-01
Finite size effects on the optical properties of one-dimensional (1D) and 2D nanoshell dimer arrays are investigated using generalized Mie theory and coupled dipole approximation within the context of surface-enhanced Raman spectroscopy (SERS). It is shown that the huge enhancement in the electromagnetic (EM) field at the center of a given dimer oscillates with the length of the 1D array. For an array of fixed length, the EM enhancement also oscillates along the array, but with a different period. Both types of oscillations can be attributed to the interference of the dynamic dipole fields from different dimers in the array. When generalized to 2D arrays, EM enhancement higher than that of the 1D arrays can be gained with a constant magnitude, a salient feature advantageous to experimental realization of single-molecule SERS. [K. Zhao et al, J. Chem. Phys. 125, 081102 (2005); Y. L. Song et al, accepted by J. Chem. Phys.
A FINITE DIFFERENCE METHOD FOR THE ONE-DIMENSIONAL VARIATIONAL BOUSSINESQ EQUATIONS
Directory of Open Access Journals (Sweden)
A. Suryanto
2012-06-01
Full Text Available The variational Boussinesq equations derived by Klopman et. al. (2005 con-verse mass, momentum and positive-definite energy. Moreover, they were shown to have significantly improved frequency dispersion characteristics, making it suitable for wave simulation from relatively deep to shallow water. In this paper we develop a numerica lcode for the variational Boussinesq equations. This code uses a fourth-order predictor-corrector method for time derivatives and fourth-order finite difference method for the first-order spatial derivatives. The numerical method is validated against experimen-tal data for one-dimensional nonlinear wave transformation problems. Furthermore, the method is used to illustrate the dispersive effects on tsunami-type of wave propagation.
A solution of two-dimensional magnetohydrodynamic flow using the finite volume method
Directory of Open Access Journals (Sweden)
Naceur Sonia
2014-01-01
Full Text Available This paper presents the two dimensional numerical modeling of the coupling electromagnetic-hydrodynamic phenomena in a conduction MHD pump using the Finite volume Method. Magnetohydrodynamic problems are, thus, interdisciplinary and coupled, since the effect of the velocity field appears in the magnetic transport equations, and the interaction between the electric current and the magnetic field appears in the momentum transport equations. The resolution of the Maxwell's and Navier Stokes equations is obtained by introducing the magnetic vector potential A, the vorticity z and the stream function y. The flux density, the electromagnetic force, and the velocity are graphically presented. Also, the simulation results agree with those obtained by Ansys Workbench Fluent software.
Three-dimensional finite element modelling of the uniaxial tension test
DEFF Research Database (Denmark)
Østergaard, Lennart; Stang, Henrik
2002-01-01
Experimental determination of the stress-crack opening relationship (σ-w) for concrete as defined in the fictitious crack model has proven to be difficult. This is due to the problems that may arise from application of the inverse analysis method necessary for the derivation of the relationship....... One of the most direct methods for determination of the σ-w relationship is the uniaxial tension test, where a notched specimen is pulled apart while the tensile load and the crack opening displacement is observed. This method is appealing since the interpretation is straightforward. The method...... is examined in this paper through three dimensional finite element analyses. It is concluded that the interpretation of the uniaxial tension test is indeed straightforward, if the testing machine stiffness is sufficiently high....
Institute of Scientific and Technical Information of China (English)
Tatsuyuki NEZU
2006-01-01
The three-dimensional stress distributions in the area surrounding indentation pattern for three different materials,Al2O3,Si3N4 and SiC were analyzed by finite element method(FEM). Those theoretical results were also compared with the experimental ones by Rockwell hardness test. The effect of loading stress on the plastic deformation in specimens,surface was investigated on the assumption of shear strain energy theory by Huber-Mises when the materials were indented. The distributions of nomal stress,shear stress,and Mises stress were analysed with variations of loading conditions. It is clear that the analytical results for the stress distributions,the crack length and its density of probability are in good agreement with the experimental results.
Three-dimensional finite-element simulation of a turbulent push-pull ventilation system.
Flynn, M R; Ahn, K; Miller, C T
1995-10-01
A finite-element formulation with penalty approach to enforce continuity is employed here to simulate the three-dimensional velocity field resulting from a simple push-pull ventilation configuration. An analytic expression for the length scale and a transport equation for turbulent kinetic energy are coupled with the momentum equations. A coaxial square hood and jet are arranged with cross-draught perpendicular to the common centreline. Numerical predictions of the velocity and turbulence kinetic energy fields are evaluated in the plane of symmetry with hot film anemometry, and smoke-wire flow visualizations. The agreement of the simulated jet trajectories with flow visualizations is reasonable, as are velocities. Predictions of turbulence kinetic energy are not as good, particularly near the hood face. Despite the limitations the numerical approach is useful in assessing the impact of cross-draughts on the push-pull arrangement.
Transmission and reflection properties of two-dimensional finite metal crystals
Roszkiewicz, Agata; Nasalski, Wojciech
2017-07-01
Optical characteristics of a finite two-dimensional silver stripe photonic crystal of a square lattice are numerically analysed with use of multilayer Rigorous Coupled Wave Analysis. Qualitative changes in optical response of the crystal originated from modifications of the thickness and filling factors of each layer and the polarization direction of the incident wave are shown. The crystal manifests its various characteristics in wideband or narrowband reflection and transmission, while absorption remains low. The behaviour of the crystal is determined by its structure geometry yielding excitation of localized plasmons and collective modes together with interactions between them. The optical response of the square lattice structure is also compared with the response of a triangular lattice crystal.
Dynamical effects of a one-dimensional multibarrier potential of finite range
Bar, D
2002-01-01
We discuss the properties of a large number N of one-dimensional (bounded) locally periodic potential barriers in a finite interval. We show that the transmission coefficient, the scattering cross section $\\sigma$, and the resonances of $\\sigma$ depend sensitively upon the ratio of the total spacing to the total barrier width. We also show that a time dependent wave packet passing through the system of potential barriers rapidly spreads and deforms, a criterion suggested by Zaslavsky for chaotic behaviour. Computing the spectrum by imposing (large) periodic boundary conditions we find a Wigner type distribution. We investigate also the S-matrix poles; many resonances occur for certain values of the relative spacing between the barriers in the potential.
Chernov, A. V.
2013-12-01
Approximating finite-dimensional mathematical programming problems are studied that arise from piecewise constant discretization of controls in the optimization of distributed systems of a fairly broad class. The smoothness of the approximating problems is established. Gradient formulas are derived that make use of the analytical solution of the original control system and its adjoint, thus providing an opportunity for algorithmic separation of numerical optimization and the task of solving a controlled initial-boundary value problem. The approximating problems are proved to converge to the original optimization problem with respect to the functional as the discretization is refined. The application of the approach to optimization problems is illustrated by solving the semilinear wave equation controlled by applying an integral criterion. The results of numerical experiments are analyzed.
Finite difference method and analysis for three-dimensional semiconductor device of heat conduction
Institute of Scientific and Technical Information of China (English)
袁益让
1996-01-01
The mathematical model of the three-dimensional semiconductor devices of heat conduction is described by a system of four quasilinear partial differential equations for initial boundary value problem. One equation in elliptic form is for the electric potential; two equations of convection-dominated diffusion type are for the electron and hole concentration; and one heat conduction equation is for temperature. Characteristic finite difference schemes for two kinds of boundary value problems are put forward. By using the thick and thin grids to form a complete set and treating the product threefold-quadratic interpolation, variable time step method with the boundary condition, calculus of variations and the theory of prior estimates and techniques, the optimal error estimates in L2 norm are derived in the approximate solutions.
Institute of Scientific and Technical Information of China (English)
苏佳灿; 张春才; 禹宝庆; 许硕贵; 王家林; 纪方; 张雪松; 吴建国; 王保华; 薛召军; 丁祖泉
2003-01-01
Objective: To study the memory biomechanical character of anatomic distal radius Nitinol memory connector (DRMC) in treating distal radius fracture. Methods: Establishing three dimensional model and finite element analysis, we calculated the stress in and around the fracture faces when distal radius fracture was fixated with DRMC. Results: Axial holding stress produced by holding part of DRMC on distal radius was 14.66 MPa. The maximum stress of holding part was 40-70 MPa, the minimum stress was 3-7 MPa,and the stress of compression part was 20-40 MPa. Conclusion: The distribution of stress produced by DRMC around the fracture line is reasonable, and axial holding stress can help stabilize fracture during earlier period. The existence of longitudal compression and memory effect can transfer fixated disused section into developed section and enhance fracture healing.
Aerodynamic effects of simulated ice shapes on two-dimensional airfoils and a swept finite tail
Alansatan, Sait
An experimental study was conducted to investigate the effect of simulated glaze ice shapes on the aerodynamic performance characteristics of two-dimensional airfoils and a swept finite tail. The two dimensional tests involved two NACA 0011 airfoils with chords of 24 and 12 inches. Glaze ice shapes computed with the LEWICE code that were representative of 22.5-min and 45-min ice accretions were simulated with spoilers, which were sized to approximate the horn heights of the LEWICE ice shapes. Lift, drag, pitching moment, and surface pressure coefficients were obtained for a range of test conditions. Test variables included Reynolds number, geometric scaling, control deflection and the key glaze ice features, which were horn height, horn angle, and horn location. For the three-dimensional tests, a 25%-scale business jet empennage (BJE) with a T-tail configuration was used to study the effect of ice shapes on the aerodynamic performance of a swept horizontal tail. Simulated glaze ice shapes included the LEWICE and spoiler ice shapes to represent 9-min and 22.5-min ice accretions. Additional test variables included Reynolds number and elevator deflection. Lift, drag, hinge moment coefficients as well as boundary layer velocity profiles were obtained. The experimental results showed substantial degradation in aerodynamic performance of the airfoils and the swept horizontal tail due to the simulated ice shapes. For the two-dimensional airfoils, the largest aerodynamic penalties were obtained when the 3-in spoiler-ice, which was representative of 45-min glaze ice accretions, was set normal to the chord. Scale and Reynolds effects were not significant for lift and drag. However, pitching moments and pressure distributions showed great sensitivity to Reynolds number and geometric scaling. For the threedimensional study with the swept finite tail, the 22.5-min ice shapes resulted in greater aerodynamic performance degradation than the 9-min ice shapes. The addition of 24
Yang, Taiseung; Spilker, Robert L
2007-06-01
A three-dimensional (3D) contact finite element formulation has been developed for biological soft tissue-to-tissue contact analysis. The linear biphasic theory of Mow, Holmes, and Lai (1984, J. Biomech., 17(5), pp. 377-394) based on continuum mixture theory, is adopted to describe the hydrated soft tissue as a continuum of solid and fluid phases. Four contact continuity conditions derived for biphasic mixtures by Hou et al. (1989, ASME J. Biomech. Eng., 111(1), pp. 78-87) are introduced on the assumed contact surface, and a weighted residual method has been used to derive a mixed velocity-pressure finite element contact formulation. The Lagrange multiplier method is used to enforce two of the four contact continuity conditions, while the other two conditions are introduced directly into the weighted residual statement. Alternate formulations are possible, which differ in the choice of continuity conditions that are enforced with Lagrange multipliers. Primary attention is focused on a formulation that enforces the normal solid traction and relative fluid flow continuity conditions on the contact surface using Lagrange multipliers. An alternate approach, in which the multipliers enforce normal solid traction and pressure continuity conditions, is also discussed. The contact nonlinearity is treated with an iterative algorithm, where the assumed area is either extended or reduced based on the validity of the solution relative to contact conditions. The resulting first-order system of equations is solved in time using the generalized finite difference scheme. The formulation is validated by a series of increasingly complex canonical problems, including the confined and unconfined compression, the Hertz contact problem, and two biphasic indentation tests. As a clinical demonstration of the capability of the contact analysis, the gleno-humeral joint contact of human shoulders is analyzed using an idealized 3D geometry. In the joint, both glenoid and humeral head
Energy Technology Data Exchange (ETDEWEB)
Kim, D.W. [Yonsei Univ., Seoul (Korea, Republic of)
1994-09-01
In this study impedance changes due to aortic expansion, blood and lung resistivity changes during systole were calculated for various electrode configurations in impedance cardiography using a three-dimensional finite element thoracic model. For the aortic expansion the aorta between the potential electrodes in the model was expanded for the increase of blood volume, 30ml. The blood volume increase in aorta was calculated with the basal impedance(Z) and the impedance change({Delta}Z) found from the finite element code using the formula, vol={rho}(L/Z){sup 2}{Delta}Z relating impedance change and blood volume change. The aortic expansions were simulated for six electrode configurations including the conventional one and then the blood volumes were calculated using the formula above to investigate which one was closer to the actual blood velum increase of 30ml. It was calculated to be 24ml for the conventional configuration. For the other five ones, they were all closer to 30ml than the conventional one. From the results above it can be also concluded that the impedance change in impedance cardiography is approximately proportional to the blood volume change in large arteries. (author). 10 refs., 3 figs.
Calibration of dimensional change in finite element models using AGR moderator brick measurements
Energy Technology Data Exchange (ETDEWEB)
McNally, K., E-mail: kevin.mcnally@hsl.gsi.gov.uk [Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN (United Kingdom); Hall, G. [NGRG, School of MACE, University of Manchester, Manchester M13 9PL (United Kingdom); Tan, E. [Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN (United Kingdom); Marsden, B.J. [NGRG, School of MACE, University of Manchester, Manchester M13 9PL (United Kingdom); Warren, N. [Health and Safety Laboratory, Harpur Hill, Buxton, Derbyshire SK17 9JN (United Kingdom)
2014-08-01
Physically based models, resolved using the finite element (FE) method, are often used to model changes in geometry and the associated stress fields of graphite moderator bricks within a reactor. These models require inputs that describe the loading conditions (field variables), and coded relationships describing the behaviour of material properties. Historically, behaviour on material properties have been obtained from Materials Test Reactor (MTR) experiments, however data relating to samples trepanned from operating reactors are increasingly being used to improve models. Geometry measurements from operating reactors offer the potential for improving the coded relationship for dimensional change in FE models. A non-linear mixed-effect model is presented for calibrating the parameters of FE models that are sensitive to mid-brick diameter, using channel geometry measurements obtained from inspection campaigns. The work makes use of a novel technique: the development of a Bayesian emulator, which is a surrogate for the FE model. The use of an emulator allows the influence of the inputs to the finite element model to be evaluated, and delivers a substantial reduction in the computational burden of calibration.
Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach
Ou, Yangxin; Chen, Yuntian
2015-01-01
We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into a series of independent 2D problems (2.5D), which reduces the computational cost. Moreover, the reduced 2D problems can be extremely accurate, compared to its 3D counterpart. Our method can precisely quantify the total emission rates, as well as the fraction of emission rates into different modal channels for waveguides with arbitrary cross-sections. We compare our method with dyadic Green's function for the light emission in single mode metallic nanowire, which yields an excellent agreement. This method is applied in multi-mode waveguides, as well as multi-core waveguides. We further show that our method has the full capability of including dipole orientations, as illustrated via a rotating dipole, which leads to unidirectional excitation of guide modes. The 2.5D Finite El...
Fourier finite element modeling of light emission in waveguides: 2.5-dimensional FEM approach.
Ou, Yangxin; Pardo, David; Chen, Yuntian
2015-11-16
We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into a series of independent 2D problems (2.5D), which reduces the computational cost. Moreover, the reduced 2D problems can be extremely accurate, compared to its 3D counterpart. Our method can precisely quantify the total emission rates, as well as the fraction of emission rates into different modal channels for waveguides with arbitrary cross-sections. We compare our method with dyadic Green's function for the light emission in single mode metallic nanowire, which yields an excellent agreement. This method is applied in multi-mode waveguides, as well as multi-core waveguides. We further show that our method has the full capability of including dipole orientations, as illustrated via a rotating dipole, which leads to unidirectional excitation of guide modes. The 2.5D Finite Element Method (FEM) approach proposed here can be applied for various waveguides, thus it is useful to interface single-photon single-emitter in nano-structures, as well as for other scenarios involving coupled waveguide-emitters.
Finite current stationary states of random walks on one-dimensional lattices with aperiodic disorder
Miki, Hiroshi
2016-11-01
Stationary states of random walks with finite induced drift velocity on one-dimensional lattices with aperiodic disorder are investigated by scaling analysis. Three aperiodic sequences, the Thue-Morse (TM), the paperfolding (PF), and the Rudin-Shapiro (RS) sequences, are used to construct the aperiodic disorder. These are binary sequences, composed of two symbols A and B, and the ratio of the number of As to that of Bs converges to unity in the infinite sequence length limit, but their effects on diffusional behavior are different. For the TM model, the stationary distribution is extended, as in the case without current, and the drift velocity is independent of the system size. For the PF model and the RS model, as the system size increases, the hierarchical and fractal structure and the localized structure, respectively, are broken by a finite current and changed to an extended distribution if the system size becomes larger than a certain threshold value. Correspondingly, the drift velocity is saturated in a large system while in a small system it decreases as the system size increases.
High Performance Computing of Three-Dimensional Finite Element Codes on a 64-bit Machine
Directory of Open Access Journals (Sweden)
M.P Raju
2012-01-01
Full Text Available Three dimensional Navier-Stokes finite element formulations require huge computational power in terms of memory and CPU time. Recent developments in sparse direct solvers have significantly reduced the memory and computational time of direct solution methods. The objective of this study is twofold. First is to evaluate the performance of various state-of-the-art sequential sparse direct solvers in the context of finite element formulation of fluid flow problems. Second is to examine the merit in upgrading from 32 bit machine to a 64 bit machine with larger RAM capacity in terms of its capacity to solve larger problems. The choice of a direct solver is dependent on its computational time and its in-core memory requirements. Here four different solvers, UMFPACK, MUMPS, HSL_MA78 and PARDISO are compared. The performances of these solvers with respect to the computational time and memory requirements on a 64-bit windows server machine with 16GB RAM is evaluated.
Effects of finite pulse width on two-dimensional Fourier transform electron spin resonance
Liang, Zhichun; Crepeau, Richard H.; Freed, Jack H.
2005-12-01
Two-dimensional (2D) Fourier transform ESR techniques, such as 2D-ELDOR, have considerably improved the resolution of ESR in studies of molecular dynamics in complex fluids such as liquid crystals and membrane vesicles and in spin labeled polymers and peptides. A well-developed theory based on the stochastic Liouville equation (SLE) has been successfully employed to analyze these experiments. However, one fundamental assumption has been utilized to simplify the complex analysis, viz. the pulses have been treated as ideal non-selective ones, which therefore provide uniform irradiation of the whole spectrum. In actual experiments, the pulses are of finite width causing deviations from the theoretical predictions, a problem that is exacerbated by experiments performed at higher frequencies. In the present paper we provide a method to deal with the full SLE including the explicit role of the molecular dynamics, the spin Hamiltonian and the radiation field during the pulse. The computations are rendered more manageable by utilizing the Trotter formula, which is adapted to handle this SLE in what we call a "Split Super-Operator" method. Examples are given for different motional regimes, which show how 2D-ELDOR spectra are affected by the finite pulse widths. The theory shows good agreement with 2D-ELDOR experiments performed as a function of pulse width.
A Reduced Three Dimensional Model for SAW Sensors Using Finite Element Analysis.
El Gowini, Mohamed M; Moussa, Walied A
2009-01-01
A major problem that often arises in modeling Micro Electro Mechanical Systems (MEMS) such as Surface Acoustic Wave (SAW) sensors using Finite Element Analysis (FEA) is the extensive computational capacity required. In this study a new approach is adopted to significantly reduce the computational capacity needed for analyzing the response of a SAW sensor using the finite element (FE) method. The approach is based on the plane wave solution where the properties of the wave vary in two dimensions and are uniform along the thickness of the device. The plane wave solution therefore allows the thickness of the SAW device model to be minimized; the model is referred to as a Reduced 3D Model (R3D). Various configurations of this novel R3D model are developed and compared with theoretical and experimental frequency data and the results show very good agreement. In addition, two-dimensional (2D) models with similar configurations to the R3D are developed for comparison since the 2D approach is widely adopted in the literature as a computationally inexpensive approach to model SAW sensors using the FE method. Results illustrate that the R3D model is capable of capturing the SAW response more accurately than the 2D model; this is demonstrated by comparison of centre frequency and insertion loss values. These results are very encouraging and indicate that the R3D model is capable of capturing the MEMS-based SAW sensor response without being computationally expensive.
A Reduced Three Dimensional Model for SAW Sensors Using Finite Element Analysis
Directory of Open Access Journals (Sweden)
Mohamed M. El Gowini
2009-12-01
Full Text Available A major problem that often arises in modeling Micro Electro Mechanical Systems (MEMS such as Surface Acoustic Wave (SAW sensors using Finite Element Analysis (FEA is the extensive computational capacity required. In this study a new approach is adopted to significantly reduce the computational capacity needed for analyzing the response of a SAW sensor using the finite element (FE method. The approach is based on the plane wave solution where the properties of the wave vary in two dimensions and are uniform along the thickness of the device. The plane wave solution therefore allows the thickness of the SAW device model to be minimized; the model is referred to as a Reduced 3D Model (R3D. Various configurations of this novel R3D model are developed and compared with theoretical and experimental frequency data and the results show very good agreement. In addition, two-dimensional (2D models with similar configurations to the R3D are developed for comparison since the 2D approach is widely adopted in the literature as a computationally inexpensive approach to model SAW sensors using the FE method. Results illustrate that the R3D model is capable of capturing the SAW response more accurately than the 2D model; this is demonstrated by comparison of centre frequency and insertion loss values. These results are very encouraging and indicate that the R3D model is capable of capturing the MEMS-based SAW sensor response without being computationally expensive.
A one-dimensional mixed porohyperelastic transport swelling finite element model with growth.
Harper, J L; Simon, B R; Vande Geest, J P
2014-01-01
A one-dimensional, large-strain, mixed porohyperelastic transport and swelling (MPHETS) finite element model was developed in MATLAB and incorporated with a well-known growth model for soft tissues to allow the model to grow (increase in length) or shrink (decrease in length) at constant material density. By using the finite element model to determine the deformation and stress state, it is possible to implement different growth laws in the program in the future to simulate how soft tissues grow and behave when exposed to various stimuli (e.g. mechanical, chemical, or electrical). The essential assumptions needed to use the MPHETS model with growth are clearly identified and explained in this paper. The primary assumption in this work, however, is that the stress upon which growth acts is the stress in the solid skeleton, i.e. the effective stress, S(eff). It is shown that significantly different amounts of growth are experienced for the same loading conditions when using a porohyperelastic model as compared to a purely solid model. In one particular example, approximately 51% less total growth occurred in the MPHETS model than in the solid model even though both problems were subjected to the same external loading. This work represents a first step in developing more sophisticated models capable of capturing the complex mechanical and biochemical environment in growing and remodeling tissues.
Institute of Scientific and Technical Information of China (English)
Jun Liu; Zheng Nan; Ping Yi
2012-01-01
In the last decade,three dimensional discontinuous deformation analyses (3D DDA) has attracted more and more attention of researchers and geotechnical engineers worldwide.The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation,which would cause block expansion under rigid body rotation and thus limit its capability to model block deformation.In this paper,3D DDA is coupled with tetrahedron finite elements to tackle these two problems.Tetrahedron is the simplest in the 3D domain and makes it easy to implement automatic discretization,even for complex topology shape.Furthermore,element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly.The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested.Validation is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes,i.e.,wedge failure.Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases.Finally,a complex rockslide example demonstrates the robustness and versatility of the coupled method.
Finite-time scaling via linear driving: application to the two-dimensional Potts model.
Huang, Xianzhi; Gong, Shurong; Zhong, Fan; Fan, Shuangli
2010-04-01
We apply finite-time scaling to the q-state Potts model with q=3 and 4 on two-dimensional lattices to determine its critical properties. This consists in applying to the model a linearly varying external field that couples to one of its q states to manipulate its dynamics in the vicinity of its criticality and that drives the system out of equilibrium and thus produces hysteresis and in defining an order parameter other than the usual one and a nonequilibrium susceptibility to extract coercive fields. From the finite-time scaling of the order parameter, the coercivity, and the hysteresis area and its derivative, we are able to determine systematically both static and dynamic critical exponents as well as the critical temperature. The static critical exponents obtained in general and the magnetic exponent delta in particular agree reasonably with the conjectured ones. The dynamic critical exponents obtained appear to confirm the proposed dynamic weak universality but unlikely to agree with recent short-time dynamic results for q=4. Our results also suggest an alternative way to characterize the weak universality.
A three-dimensional finite element model for biomechanical analysis of the hip.
Chen, Guang-Xing; Yang, Liu; Li, Kai; He, Rui; Yang, Bin; Zhan, Yan; Wang, Zhi-Jun; Yu, Bing-Nin; Jian, Zhe
2013-11-01
The objective of this study was to construct a three-dimensional (3D) finite element model of the hip. The images of the hip were obtained from Chinese visible human dataset. The hip model includes acetabular bone, cartilage, labrum, and bone. The cartilage of femoral head was constructed using the AutoCAD and Solidworks software. The hip model was imported into ABAQUS analysis system. The contact surface of the hip joint was meshed. To verify the model, the single leg peak force was loaded, and contact area of the cartilage and labrum of the hip and pressure distribution in these structures were observed. The constructed 3D hip model reflected the real hip anatomy. Further, this model reflected biomechanical behavior similar to previous studies. In conclusion, this 3D finite element hip model avoids the disadvantages of other construction methods, such as imprecision of cartilage construction and the absence of labrum. Further, it provides basic data critical for accurately modeling normal and abnormal loads, and the effects of abnormal loads on the hip.
Spectral properties of quasi-one-dimensional conductors with a finite transverse band dispersion
Energy Technology Data Exchange (ETDEWEB)
Losic, Z Bonacic; Zupanovic, P [Department of Physics, Faculty of Natural Sciences, Mathematics and Kinesiology, University of Split, Teslina 12, 21000 Split (Croatia); Bjelis, A [Department of Physics, Faculty of Science, University of Zagreb, POB 162, 10001 Zagreb (Croatia)], E-mail: agicz@pmfst.hr, E-mail: bjelis@phy.hr
2008-08-13
We determine the one-particle spectral function and the corresponding derived quantities for the conducting chain lattice with finite inter-chain hopping t{sub perpendicular} and three-dimensional long-range Coulomb electron-electron interaction. The standard G{sub 0}W{sub 0} approximation is used. It is shown that, due to the optical character of the anisotropic plasmon dispersion caused by the finite t{sub perpendicular}, a low energy quasi-particle {delta}-peak appears in the spectral function in addition to the hump present at energies of the order of the plasmon energy. Particular attention is devoted to the continuous crossover from the non-Fermi liquid regime to the Fermi liquid regime with increasing t{sub perpendicular}. It is shown that the spectral weight of the hump transfers to the quasi-particle as the optical gap in the plasmon dispersion increases together with t{sub perpendicular}, with the quasi-particle residuum Z behaving like -ln t{sub perpendicular}){sup -1} in the limit t{sub perpendicular} {yields}0. Our approach is appropriate for the wide range of energy scales given by the plasmon energy and the width of the conduction band, and is complementary to the Luttinger liquid techniques that are limited to the low energy regime close to the Fermi surface.
Creating cat states in one-dimensional quantum walks using delocalized initial states
Zhang, Wei-Wei; Goyal, Sandeep K.; Gao, Fei; Sanders, Barry C.; Simon, Christoph
2016-09-01
Cat states are coherent quantum superpositions of macroscopically distinct states and are useful for understanding the boundary between the classical and the quantum world. Due to their macroscopic nature, cat states are difficult to prepare in physical systems. We propose a method to create cat states in one-dimensional quantum walks using delocalized initial states of the walker. Since the quantum walks can be performed on any quantum system, our proposal enables a platform-independent realization of the cat states. We further show that the linear dispersion relation of the effective quantum walk Hamiltonian, which governs the dynamics of the delocalized states, is responsible for the formation of the cat states. We analyze the robustness of these states against environmental interactions and present methods to control and manipulate the cat states in the photonic implementation of quantum walks.
Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor
Branny, Artur; Kumar, Santosh; Proux, Raphaël; Gerardot, Brian D
2017-01-01
An outstanding challenge in quantum photonics is scalability, which requires positioning of single quantum emitters in a deterministic fashion. Site positioning progress has been made in established platforms including defects in diamond and self-assembled quantum dots, albeit often with compromised coherence and optical quality. The emergence of single quantum emitters in layered transition metal dichalcogenide semiconductors offers new opportunities to construct a scalable quantum architecture. Here, using nanoscale strain engineering, we deterministically achieve a two-dimensional lattice of quantum emitters in an atomically thin semiconductor. We create point-like strain perturbations in mono- and bi-layer WSe2 which locally modify the band-gap, leading to efficient funnelling of excitons towards isolated strain-tuned quantum emitters that exhibit high-purity single photon emission. We achieve near unity emitter creation probability and a mean positioning accuracy of 120±32 nm, which may be improved with further optimization of the nanopillar dimensions. PMID:28530219
Deterministic strain-induced arrays of quantum emitters in a two-dimensional semiconductor
Branny, Artur; Kumar, Santosh; Proux, Raphaël; Gerardot, Brian D.
2017-05-01
An outstanding challenge in quantum photonics is scalability, which requires positioning of single quantum emitters in a deterministic fashion. Site positioning progress has been made in established platforms including defects in diamond and self-assembled quantum dots, albeit often with compromised coherence and optical quality. The emergence of single quantum emitters in layered transition metal dichalcogenide semiconductors offers new opportunities to construct a scalable quantum architecture. Here, using nanoscale strain engineering, we deterministically achieve a two-dimensional lattice of quantum emitters in an atomically thin semiconductor. We create point-like strain perturbations in mono- and bi-layer WSe2 which locally modify the band-gap, leading to efficient funnelling of excitons towards isolated strain-tuned quantum emitters that exhibit high-purity single photon emission. We achieve near unity emitter creation probability and a mean positioning accuracy of 120+/-32 nm, which may be improved with further optimization of the nanopillar dimensions.
Non-linear excitation of quantum emitters in two-dimensional hexagonal boron nitride
Schell, Andreas W; Takashima, Hideaki; Takeuchi, Shigeki; Aharonovich, Igor
2016-01-01
Two-photon absorption is an important non-linear process employed for high resolution bio-imaging and non-linear optics. In this work we realize two-photon excitation of a quantum emitter embedded in a two-dimensional material. We examine defects in hexagonal boron nitride and show that the emitters exhibit similar spectral and quantum properties under one-photon and two-photon excitation. Furthermore, our findings are important to deploy two-dimensional hexagonal boron nitride for quantum non-linear photonic applications.
Quantum mechanics in a space with a finite number of points
Arik, Metin; Ildes, Medine
2016-04-01
We define a deformed kinetic energy operator for a discrete position space with a finite number of points. The structure may be either periodic or nonperiodic with well-defined end points. It is shown that for the nonperiodic case the translation operator becomes nonunitary due to the end points. This uniquely defines an algebra that has the desired unique representation. Energy eigenvalues and energy wave functions for both cases are found. As expected, in the continuum limit the solution for the nonperiodic case becomes the same as the solution of an infinite one-dimensional square well and the periodic case solution becomes the same as the solution of a particle in a box with periodic boundary conditions.
On-chip generation of high-dimensional entangled quantum states and their coherent control
Kues, Michael; Reimer, Christian; Roztocki, Piotr; Cortés, Luis Romero; Sciara, Stefania; Wetzel, Benjamin; Zhang, Yanbing; Cino, Alfonso; Chu, Sai T.; Little, Brent E.; Moss, David J.; Caspani, Lucia; Azaña, José; Morandotti, Roberto
2017-06-01
Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics, for increasing the sensitivity of quantum imaging schemes, for improving the robustness and key rate of quantum communication protocols, for enabling a richer variety of quantum simulations, and for achieving more efficient and error-tolerant quantum computation. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.
On-chip generation of high-dimensional entangled quantum states and their coherent control.
Kues, Michael; Reimer, Christian; Roztocki, Piotr; Cortés, Luis Romero; Sciara, Stefania; Wetzel, Benjamin; Zhang, Yanbing; Cino, Alfonso; Chu, Sai T; Little, Brent E; Moss, David J; Caspani, Lucia; Azaña, José; Morandotti, Roberto
2017-06-28
Optical quantum states based on entangled photons are essential for solving questions in fundamental physics and are at the heart of quantum information science. Specifically, the realization of high-dimensional states (D-level quantum systems, that is, qudits, with D > 2) and their control are necessary for fundamental investigations of quantum mechanics, for increasing the sensitivity of quantum imaging schemes, for improving the robustness and key rate of quantum communication protocols, for enabling a richer variety of quantum simulations, and for achieving more efficient and error-tolerant quantum computation. Integrated photonics has recently become a leading platform for the compact, cost-efficient, and stable generation and processing of non-classical optical states. However, so far, integrated entangled quantum sources have been limited to qubits (D = 2). Here we demonstrate on-chip generation of entangled qudit states, where the photons are created in a coherent superposition of multiple high-purity frequency modes. In particular, we confirm the realization of a quantum system with at least one hundred dimensions, formed by two entangled qudits with D = 10. Furthermore, using state-of-the-art, yet off-the-shelf telecommunications components, we introduce a coherent manipulation platform with which to control frequency-entangled states, capable of performing deterministic high-dimensional gate operations. We validate this platform by measuring Bell inequality violations and performing quantum state tomography. Our work enables the generation and processing of high-dimensional quantum states in a single spatial mode.