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Автор: Grafiati

Опубліковано: 7 вересня 2023

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1

ALBEVERIO, SERGIO, LUDWIK DABROWSKI, and SHAO-MING FEI. "A REMARK ON ONE-DIMENSIONAL MANY-BODY PROBLEMS WITH POINT INTERACTIONS." International Journal of Modern Physics B 14, no. 07 (March 20, 2000): 721–27. http://dx.doi.org/10.1142/s0217979200000601.

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The integrability of one-dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.

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2

Herrera, William J., Herbert Vinck-Posada, and Shirley Gómez Páez. "Green's functions in quantum mechanics courses." American Journal of Physics 90, no. 10 (October 2022): 763–69. http://dx.doi.org/10.1119/5.0065733.

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The use of Green's functions is valuable when solving problems in electrodynamics, solid-state physics, and many-body physics. However, its role in quantum mechanics is often limited to the context of scattering by a central force. This work shows how Green's functions can be used in other examples in quantum mechanics courses. In particular, we introduce time-independent Green's functions and the Dyson equation to solve problems with an external potential. We calculate the reflection and transmission coefficients of scattering by a Dirac delta barrier and the energy levels and local density of states of the infinite square well potential.

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3

Wu, Yueyang. "A New Simple Method of Simulating One Dimensional Quantum Problem Based on Lattice Point Concepts." Highlights in Science, Engineering and Technology 38 (March 16, 2023): 461–69. http://dx.doi.org/10.54097/hset.v38i.5868.

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One-dimensional quantum problems have always been an important issue in various branches of quantum mechanics fields, and many quantum models can be idealized as one-dimensional potential profiles. Therefore, it is necessary to investigates the way to deal with and calculate the problems. This paper proposes a new and simple method for simulation and calculation of one-dimensional quantum problems. To be specific, by representing continuous X values by a series of discrete lattice points, the Hamiltonian matrix is constructed for the system in the way of dealing with monomer and many-body problems, so as to simply calculate the energy level distribution and draw the wave function image. In terms of simulating one-dimensional infinite deep potential well, one-dimensional finite deep potential well, one-dimensional multi-potential well and other one-dimensional quantum systems with this method, this paper shows that the method is accurate and practical. Compared with other methods for one-dimensional quantum problems, this paper also presents the superiority of this method. To deal with the problem based on such a method can save the computation cost and time cost, which is more convenient to study the one-dimensional quantum problem in the future. These results shed light on studying complex one-dimensional quantum problems conveniently.

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4

Meisinger, Peter N., and Michael C. Ogilvie. "PT symmetry in classical and quantum statistical mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (April 28, 2013): 20120058. http://dx.doi.org/10.1098/rsta.2012.0058.

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-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside the conventional equilibrium statistical mechanics of Hermitian systems. -symmetric models form a natural class where the partition function is necessarily real, but not necessarily positive. The correlation functions of these models display a much richer set of behaviours than Hermitian systems, displaying sinusoidally modulated exponential decay, as in a dense fluid, or even sinusoidal modulation without decay. Classical spin models with -symmetry include Z( N ) models with a complex magnetic field, the chiral Potts model and the anisotropic next-nearest-neighbour Ising model. Quantum many-body problems with a non-zero chemical potential have a natural -symmetric representation related to the sign problem. Two-dimensional quantum chromodynamics with heavy quarks at non-zero chemical potential can be solved by diagonalizing an appropriate -symmetric Hamiltonian.

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5

Wu, Yusen, and Jingbo B. Wang. "Estimating Gibbs partition function with quantum Clifford sampling." Quantum Science and Technology 7, no. 2 (February 14, 2022): 025006. http://dx.doi.org/10.1088/2058-9565/ac47f0.

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Abstract The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum systems and phenomena. However, for interacting many-body quantum systems, its calculation generally involves summing over an exponential number of terms and can thus quickly grow to be intractable. Accurately and efficiently estimating the partition function of its corresponding system Hamiltonian then becomes the key in solving quantum many-body problems. In this paper we develop a hybrid quantum–classical algorithm to estimate the partition function, utilising a novel quantum Clifford sampling technique. Note that previous works on the estimation of partition functions require O ( 1 / ϵ Δ ) -depth quantum circuits (Srinivasan et al 2021 IEEE Int. Conf. on Quantum Computing and Engineering (QCE) pp 112–22; Montanaro 2015 Proc. R. Soc. A 471 20150301), where Δ is the minimum spectral gap of stochastic matrices and ϵ is the multiplicative error. Our algorithm requires only a shallow O ( 1 ) -depth quantum circuit, repeated O ( n / ϵ 2 ) times, to provide a comparable ϵ approximation. Shallow-depth quantum circuits are considered vitally important for currently available noisy intermediate-scale quantum devices.

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6

KUZEMSKY, A. L. "BOGOLIUBOV'S VISION: QUASIAVERAGES AND BROKEN SYMMETRY TO QUANTUM PROTECTORATE AND EMERGENCE." International Journal of Modern Physics B 24, no. 08 (March 30, 2010): 835–935. http://dx.doi.org/10.1142/s0217979210055378.

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In the present interdisciplinary review, we focus on the applications of the symmetry principles to quantum and statistical physics in connection with some other branches of science. The profound and innovative idea of quasiaverages formulated by N. N. Bogoliubov, gives the so-called macro-objectivation of the degeneracy in the domain of quantum statistical mechanics, quantum field theory and quantum physics in general. We discuss the complementary unifying ideas of modern physics, namely: spontaneous symmetry breaking, quantum protectorate and emergence. The interrelation of the concepts of symmetry breaking, quasiaverages and quantum protectorate was analyzed in the context of quantum theory and statistical physics. The chief purposes of this paper were to demonstrate the connection and interrelation of these conceptual advances of the many-body physics and to try to show explicitly that those concepts, though different in details, have certain common features. Several problems in the field of statistical physics of complex materials and systems (e.g., the chirality of molecules) and the foundations of the microscopic theory of magnetism and superconductivity were discussed in relation to these ideas.

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7

Sattath, Or, Siddhardh C. Morampudi, Chris R. Laumann, and Roderich Moessner. "When a local Hamiltonian must be frustration-free." Proceedings of the National Academy of Sciences 113, no. 23 (May 19, 2016): 6433–37. http://dx.doi.org/10.1073/pnas.1519833113.

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A broad range of quantum optimization problems can be phrased as the question of whether a specific system has a ground state at zero energy, i.e., whether its Hamiltonian is frustration-free. Frustration-free Hamiltonians, in turn, play a central role for constructing and understanding new phases of matter in quantum many-body physics. Unfortunately, determining whether this is the case is known to be a complexity-theoretically intractable problem. This makes it highly desirable to search for efficient heuristics and algorithms to, at least, partially answer this question. Here we prove a general criterion—a sufficient condition—under which a local Hamiltonian is guaranteed to be frustration-free by lifting Shearer’s theorem from classical probability theory to the quantum world. Remarkably, evaluating this condition proceeds via a fully classical analysis of a hardcore lattice gas at negative fugacity on the Hamiltonian’s interaction graph, which, as a statistical mechanics problem, is of interest in its own right. We concretely apply this criterion to local Hamiltonians on various regular lattices, while bringing to bear the tools of spin glass physics that permit us to obtain new bounds on the satisfiable to unsatisfiable transition in random quantum satisfiability. We are then led to natural conjectures for when such bounds will be tight, as well as to a novel notion of universality for these computer science problems. Besides providing concrete algorithms leading to detailed and quantitative insights, this work underscores the power of marrying classical statistical mechanics with quantum computation and complexity theory.

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8

Holland, Peter. "Uniting the wave and the particle in quantum mechanics." Quantum Studies: Mathematics and Foundations 7, no. 1 (October 5, 2019): 155–78. http://dx.doi.org/10.1007/s40509-019-00207-4.

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Abstract We present a unified field theory of wave and particle in quantum mechanics. This emerges from an investigation of three weaknesses in the de Broglie–Bohm theory: its reliance on the quantum probability formula to justify the particle-guidance equation; its insouciance regarding the absence of reciprocal action of the particle on the guiding wavefunction; and its lack of a unified model to represent its inseparable components. Following the author’s previous work, these problems are examined within an analytical framework by requiring that the wave–particle composite exhibits no observable differences with a quantum system. This scheme is implemented by appealing to symmetries (global gauge and spacetime translations) and imposing equality of the corresponding conserved Noether densities (matter, energy, and momentum) with their Schrödinger counterparts. In conjunction with the condition of time-reversal covariance, this implies the de Broglie–Bohm law for the particle where the quantum potential mediates the wave–particle interaction (we also show how the time-reversal assumption may be replaced by a statistical condition). The method clarifies the nature of the composite’s mass, and its energy and momentum conservation laws. Our principal result is the unification of the Schrödinger equation and the de Broglie–Bohm law in a single inhomogeneous equation whose solution amalgamates the wavefunction and a singular soliton model of the particle in a unified spacetime field. The wavefunction suffers no reaction from the particle since it is the homogeneous part of the unified field to whose source the particle contributes via the quantum potential. The theory is extended to many-body systems. We review de Broglie’s objections to the pilot-wave theory and suggest that our field-theoretic description provides a realization of his hitherto unfulfilled ‘double solution’ programme. A revised set of postulates for the de Broglie–Bohm theory is proposed in which the unified field is taken as the basic descriptive element of a physical system.

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9

Yung, Man-Hong, Xun Gao, and Joonsuk Huh. "Universal bound on sampling bosons in linear optics and its computational implications." National Science Review 6, no. 4 (April 9, 2019): 719–29. http://dx.doi.org/10.1093/nsr/nwz048.

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ABSTRACT In linear optics, photons are scattered in a network through passive optical elements including beam splitters and phase shifters, leading to many intriguing applications in physics, such as Mach–Zehnder interferometry, the Hong–Ou–Mandel effect, and tests of fundamental quantum mechanics. Here we present the fundamental limit in the transition amplitudes of bosons, applicable to all physical linear optical networks. Apart from boson sampling, this transition bound results in many other interesting applications, including behaviors of Bose–Einstein condensates (BEC) in optical networks, counterparts of Hong–Ou–Mandel effects for multiple photons, and approximating permanents of matrices. In addition, this general bound implies the existence of a polynomial-time randomized algorithm for estimating the transition amplitudes of bosons, which represents a solution to an open problem raised by Aaronson and Hance (Quantum Inf Comput 2012; 14: 541–59). Consequently, this bound implies that computational decision problems encoded in linear optics, prepared and detected in the Fock basis, can be solved efficiently by classical computers within additive errors. Furthermore, our result also leads to a classical sampling algorithm that can be applied to calculate the many-body wave functions and the S-matrix of bosonic particles.

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10

Movassagh, Ramis, and Peter W. Shor. "Supercritical entanglement in local systems: Counterexample to the area law for quantum matter." Proceedings of the National Academy of Sciences 113, no. 47 (November 7, 2016): 13278–82. http://dx.doi.org/10.1073/pnas.1605716113.

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Quantum entanglement is the most surprising feature of quantum mechanics. Entanglement is simultaneously responsible for the difficulty of simulating quantum matter on a classical computer and the exponential speedups afforded by quantum computers. Ground states of quantum many-body systems typically satisfy an “area law”: The amount of entanglement between a subsystem and the rest of the system is proportional to the area of the boundary. A system that obeys an area law has less entanglement and can be simulated more efficiently than a generic quantum state whose entanglement could be proportional to the total system’s size. Moreover, an area law provides useful information about the low-energy physics of the system. It is widely believed that for physically reasonable quantum systems, the area law cannot be violated by more than a logarithmic factor in the system’s size. We introduce a class of exactly solvable one-dimensional physical models which we can prove have exponentially more entanglement than suggested by the area law, and violate the area law by a square-root factor. This work suggests that simple quantum matter is richer and can provide much more quantum resources (i.e., entanglement) than expected. In addition to using recent advances in quantum information and condensed matter theory, we have drawn upon various branches of mathematics such as combinatorics of random walks, Brownian excursions, and fractional matching theory. We hope that the techniques developed herein may be useful for other problems in physics as well.

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11

Lestienne, Rémy. "In Support of Whitehead’s Time." KronoScope 18, no. 1 (April 2, 2018): 29–45. http://dx.doi.org/10.1163/15685241-12341400.

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Abstract In 1911, Alfred North Whitehead has a brainstorm: if we deny the reality of the instant, many problems of the philosophy of nature seem solved. His metaphysics, however, will wait until his moving to Harvard, in 1924, to mature. Besides his denial of the instants of time and the replacement of the concept of time by that of “process,” Whitehead articulates new concepts (concrescence, prehension) to account for the crystallization of successive empirical realities, the solidarity between events, the permanence of objects, and their deterministic behavior altogether. His views of nature fit well with both quantum mechanics and relativity theories, although not in the details of the latter. But one of his largely unnoticed merits, in my view, is to reopen the question of free will in the mind-body problem.

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12

Aguirre-Téllez, Cristian Andrés, and José Barba-Ortega. "Breve argumentación didáctica de la mecánica cuántica de muchos cuerpos." Respuestas 22, no. 1 (January 1, 2017): 29. http://dx.doi.org/10.22463/0122820x.817.

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El problema general en mecánica cuántica está basado en la solución de una ecuación en valores propios de un operador dado (en una representación adecuada), generalmente dicho operador es el Hamiltoniano que da cuenta de la interacción energética (salvo que dependa del tiempo) del sistema en cuestión. La solución de la ecuación de Schrödinger permite escribir el comportamiento dinámico del sistema sometido a ciertas restricciones. Sin embargo, la solución analítica de esta ecuación es viable solo en sistemas simples, cuando el sistema se describe desde la interacción de muchas partículas (problema electrónico-base de la construcción de sistemas cuánticos complejos aplicable a la descripción de moléculas, sólidos y sistemas cuánticos interactuantes en general.) la solución de la ecuación de Schrödinger del sistema no se puede realizar vía método analítico; con lo cual existe una forma más global de enfrentar dicho problema, el método auto consistente; mediante el cual se puede solucionar sistemas complejos de muchos cuerpos. Es así que en el presente paper presentamos una comparación entre el sistema auto consistente y algunas variantes que existen, con el método analítico en sistemas demuchos cuerpos y como opera dicho método, esto aplicado a un problema de dos cuerpos con interacción Coulombiana, ya que este problema presenta solución analítica y ha sido extensamente estudiado; esto con la finalidad de que los estudiantes interesados en la materia comprendan como se abordan problemas vía métodos auto consistentes y como opera este método, ya que en la literatura pocas veces se presenta el algoritmo de solución mediante este método.Palabras clave: Mecánica Cuántica, Método Auto-Consistente, problema de dos cuerpos.AbstractThe general problem in quantum mechanics is based on the solution of an equation in eigenvalues of a given operator (in a suitable representation), generally said operator is the Hamiltonian that accounts for the energy interaction (unless it depends on the time) of the system in question. The solution of the Schrodinger equation allows writing the dynamic behavior of the system subject to certain restrictions. however, the analytical solution of this equation is feasible only in simple systems, when the system is described from the interaction of many particles (electronic problem- basis of the construction of complex quantum systems applicable to the description of molecules, solids and interacting quantum systems in general.), the solution of the Schrödinger equation of the system can´t be performed via analytical method; with which there is a more global way of facing this problem, the self-consistent method; through which complex systems of many bodies can be solved. thus, in the present paper we present a comparison between the self-consistent system and some variants that exist, with the analytical method in systems of many bodies and how this method operates, this applied to a problem of two bodies with Coulombian interaction, since this problem presents an analytical solution and has been extensively studied; this in order that students interested in the subject understand how problems are addressed through self-consistent methods and how this method operates, since in the literature rarely the solution algorithm is presented by this method.Keywords: Quantum mechanics, Self Consistent Field, Two body problem.

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13

Gujrati, Purushottam Das. "Foundations of Nonequilibrium Statistical Mechanics in Extended State Space." Foundations 3, no. 3 (August 23, 2023): 419–548. http://dx.doi.org/10.3390/foundations3030030.

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The review provides a pedagogical but comprehensive introduction to the foundations of a recently proposed statistical mechanics (μNEQT) of a stable nonequilibrium thermodynamic body, which may be either isolated or interacting. It is an extension of the well-established equilibrium statistical mechanics by considering microstates mk in an extended state space in which macrostates (obtained by ensemble averaging A^) are uniquely specified so they share many properties of stable equilibrium macrostates. The extension requires an appropriate extended state space, three distinct infinitessimals dα=(d,de,di) operating on various quantities q during a process, and the concept of reduction. The mechanical process quantities (no stochasticity) like macrowork are given by A^dαq, but the stochastic quantities C^αq like macroheat emerge from the commutator C^α of dα and A^. Under the very common assumptions of quasi-additivity and quasi-independence, exchange microquantities deqk such as exchange microwork and microheat become nonfluctuating over mk as will be explained, a fact that does not seem to have been appreciated so far in diverse branches of modern statistical thermodynamics (fluctuation theorems, quantum thermodynamics, stochastic thermodynamics, etc.) that all use exchange quantities. In contrast, dqk and diqk are always fluctuating. There is no analog of the first law for a microstate as the latter is a purely mechanical construct. The second law emerges as a consequence of the stability of the system, and cannot be violated unless stability is abandoned. There is also an important thermodynamic identity diQ≡diW≥0 with important physical implications as it generalizes the well-known result of Count Rumford and the Gouy-Stodola theorem of classical thermodynamics. The μNEQT has far-reaching consequences with new results, and presents a new understanding of thermodynamics even of an isolated system at the microstate level, which has been an unsolved problem. We end the review by applying it to three different problems of fundamental interest.

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14

Wall, Michael L., Arghavan Safavi-Naini, and Martin Gärttner. "Many-body quantum mechanics." XRDS: Crossroads, The ACM Magazine for Students 23, no. 1 (September 20, 2016): 25–29. http://dx.doi.org/10.1145/2983537.

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15

Gómez-Ullate, D., A. González-López, and M. A. Rodríguez. "New algebraic quantum many-body problems." Journal of Physics A: Mathematical and General 33, no. 41 (October 5, 2000): 7305–35. http://dx.doi.org/10.1088/0305-4470/33/41/305.

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16

Popov, Yu V., and C. Dal Cappello. "Theoretical developments in (e,2e) studies of excited states and in (e,3e) spectroscopy." Canadian Journal of Physics 74, no. 11-12 (November 1, 1996): 843–49. http://dx.doi.org/10.1139/p96-120.

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The theory of single and double ionization of atoms deals with one of the most difficult problems in quantum mechanics: the scattering of a few charged particles. A large number of different (e,2e) experiments and theoretical calculations have helped us to understand the main physical mechanisms and their effect on the shape of triple differential cross section (TDCS). Recently the first deeply asymmetric (e,2e) experiments, leaving the residual ion in an excited state (which we indicate in this paper by (e,2e)*), and (e,3e) experiments have been performed. These offer new challenges to the theory. A very preliminary survey of main theoretical methods currently used to explain the experimental measurements is presented here. It will be shown that small differences in the choice of initial and final state models employed by different authors lead to large effects in both the shape and absolute size of the TDCS in the case of excitation ionization, even if these models give almost identical results for the (e,2e) case. A few physical mechanisms contributing to the (e,2e)* process are discussed in this paper. Special attention is given to the multichannel close-coupling method. (e,3e) experiments allow us to study the final state wave function with two continuum electrons. We obtain two unexpected results. First, we found that the two-step mechanism contribution is comparable and even bigger than that of shake-off. Second, the algorithms exploiting the angular decompositions of many-body continuum wave functions do not work in the case of long-range potentials; this is a result of the failure of the widely used diagonalization approximations in this case. The physical considerations that support these and other results are presented in this paper.

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17

Otsuki, Junya, Masayuki Ohzeki, Hiroshi Shinaoka, and Kazuyoshi Yoshimi. "Sparse Modeling in Quantum Many-Body Problems." Journal of the Physical Society of Japan 89, no. 1 (January 15, 2020): 012001. http://dx.doi.org/10.7566/jpsj.89.012001.

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18

Turbiner, A. V. "Quantum many-body problems and perturbation theory." Physics of Atomic Nuclei 65, no. 6 (June 2002): 1135–43. http://dx.doi.org/10.1134/1.1490123.

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19

Bravyi, Sergey, David Gosset, Robert König, and Kristan Temme. "Approximation algorithms for quantum many-body problems." Journal of Mathematical Physics 60, no. 3 (March 2019): 032203. http://dx.doi.org/10.1063/1.5085428.

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20

Saito, Hiroki. "Human-Machine Collaboration in Quantum Many-Body Problems." JPSJ News and Comments 17 (January 15, 2020): 06. http://dx.doi.org/10.7566/jpsjnc.17.06.

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21

Yan, Mu-Lin, and Bao-Heng Zhao. "Solvable quantum many-body problems in two dimensions." Physics Letters A 168, no. 1 (August 1992): 25–27. http://dx.doi.org/10.1016/0375-9601(92)90323-e.

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22

Gavreev, M. A., I. A. Luchnikov, and A. K. Fedorov. "Tensor Networks in Many-body Quantum Control Problems." Physics in Higher Education 29, no. 1 (2023): 14–17. http://dx.doi.org/10.54965/16093143_2023_29_s1_14.

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23

White, Steven R. "Numerical canonical transformation approach to quantum many-body problems." Journal of Chemical Physics 117, no. 16 (October 22, 2002): 7472–82. http://dx.doi.org/10.1063/1.1508370.

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24

CARDY, JOHN. "EXACT RESULTS FOR MANY-BODY PROBLEMS USING FEW-BODY METHODS." International Journal of Modern Physics B 20, no. 19 (July 30, 2006): 2595–602. http://dx.doi.org/10.1142/s0217979206035072.

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Recently there has been developed a new approach to the study of critical quantum systems in 1+1 dimensions which reduces them to problems in one-dimensional Brownian motion. This goes under the name of stochastic, or Schramm, Loewner Evolution (SLE). I review some of the recent progress in this area, from the point of view of many-body theory. Connections to random matrices also emerge.

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25

GU, YING-QIU. "NEW APPROACH TO N-BODY RELATIVISTIC QUANTUM MECHANICS." International Journal of Modern Physics A 22, no. 11 (April 30, 2007): 2007–19. http://dx.doi.org/10.1142/s0217751x07036233.

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In this paper, we propose a new approach to the relativistic quantum mechanics for many-body, which is a self-consistent system constructed by juxtaposed but mutually coupled nonlinear Dirac's equations. The classical approximation of this approach provides the exact Newtonian dynamics for many-body, and the nonrelativistic approximation gives the complete Schrödinger equation for many-body.

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26

Nandkishore, Rahul, and David A. Huse. "Many-Body Localization and Thermalization in Quantum Statistical Mechanics." Annual Review of Condensed Matter Physics 6, no. 1 (March 2015): 15–38. http://dx.doi.org/10.1146/annurev-conmatphys-031214-014726.

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27

Wyllard, Niclas. "(Super)conformal many-body quantum mechanics with extended supersymmetry." Journal of Mathematical Physics 41, no. 5 (May 2000): 2826–38. http://dx.doi.org/10.1063/1.533273.

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28

Lev, F. M. "On the many-body problem in relativistic quantum mechanics." Nuclear Physics A 433, no. 4 (February 1985): 605–18. http://dx.doi.org/10.1016/0375-9474(85)90020-x.

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29

Lindner, U. "To Applicability of Hamilton's Equations in Quantum Many-Body Problems." physica status solidi (b) 141, no. 1 (May 1, 1987): 263–68. http://dx.doi.org/10.1002/pssb.2221410126.

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30

Lewin, Mathieu, Phan Thành Nam, and Nicolas Rougerie. "Derivation of nonlinear Gibbs measures from many-body quantum mechanics." Journal de l’École polytechnique — Mathématiques 2 (2015): 65–115. http://dx.doi.org/10.5802/jep.18.

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31

Feldman, Joel, and Eugene Trubowitz. "Renormalization in classical mechanics and many body quantum field theory." Journal d'Analyse Mathématique 58, no. 1 (December 1992): 213–47. http://dx.doi.org/10.1007/bf02790365.

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32

Larder, B., D. O. Gericke, S. Richardson, P. Mabey, T. G. White, and G. Gregori. "Fast nonadiabatic dynamics of many-body quantum systems." Science Advances 5, no. 11 (November 2019): eaaw1634. http://dx.doi.org/10.1126/sciadv.aaw1634.

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Анотація:

Modeling many-body quantum systems with strong interactions is one of the core challenges of modern physics. A range of methods has been developed to approach this task, each with its own idiosyncrasies, approximations, and realm of applicability. However, there remain many problems that are intractable for existing methods. In particular, many approaches face a huge computational barrier when modeling large numbers of coupled electrons and ions at finite temperature. Here, we address this shortfall with a new approach to modeling many-body quantum systems. On the basis of the Bohmian trajectory formalism, our new method treats the full particle dynamics with a considerable increase in computational speed. As a result, we are able to perform large-scale simulations of coupled electron-ion systems without using the adiabatic Born-Oppenheimer approximation.

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33

Evangelista, Francesco A. "A driven similarity renormalization group approach to quantum many-body problems." Journal of Chemical Physics 141, no. 5 (August 7, 2014): 054109. http://dx.doi.org/10.1063/1.4890660.

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34

Emsiz, E., E. M. Opdam, and J. V. Stokman. "Trigonometric Cherednik algebra at critical level and quantum many-body problems." Selecta Mathematica 14, no. 3-4 (March 14, 2009): 571–605. http://dx.doi.org/10.1007/s00029-009-0516-y.

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35

Chakrabarti, Barnali. "Use of supersymmetric isospectral formalism to realistic quantum many-body problems." Pramana 73, no. 2 (August 2009): 405–16. http://dx.doi.org/10.1007/s12043-009-0132-6.

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36

Batchelor, M. T. "Beautiful Models: 70 Years of Exactly Solved Quantum Many-Body Problems." Journal of Physics A: Mathematical and General 38, no. 14 (March 22, 2005): 3245–46. http://dx.doi.org/10.1088/0305-4470/38/14/b03.

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37

Cherednik, I. "Integration of Quantum Many-Body Problems by Affine Knizhnik-Zamolodchikov Equations." Advances in Mathematics 106, no. 1 (June 1994): 65–95. http://dx.doi.org/10.1006/aima.1994.1049.

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38

Bányai, Ladislaus Alexander, and Mircea Bundaru. "About Non-relativistic Quantum Mechanics and Electromagnetism." Recent Progress in Materials 04, no. 04 (December 8, 2022): 1–19. http://dx.doi.org/10.21926/rpm.2204027.

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Анотація:

We describe here the coherent formulation of electromagnetism in the non-relativistic quantum-mechanical many-body theory of interacting charged particles. We use the mathematical frame of the field theory and its quantization in the spirit of the quantum electrodynamics (QED). This is necessary because a manifold of misinterpretations emerged especially regarding the magnetic field and gauge invariance. The situation was determined by the historical development of quantum mechanics, starting from the Schrödinger equation of a single particle in the presence of given electromagnetic fields, followed by the many-body theories of many charged identical particles having just Coulomb interactions. Our approach to the non-relativistic QED emphasizes the role of the gauge-invariance and of the external fields. We develop further the approximation of this theory allowing a closed description of the interacting charged particles without photons. The resulting Hamiltonian coincides with the quantized version of the Darwin Hamiltonian containing besides the Coulomb also a current-current diamagnetic interaction. We show on some examples the importance of this extension of the many-body theory.

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39

Novo, Leonardo, Juani Bermejo-Vega, and Raúl García-Patrón. "Quantum advantage from energy measurements of many-body quantum systems." Quantum 5 (June 2, 2021): 465. http://dx.doi.org/10.22331/q-2021-06-02-465.

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Анотація:

The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). In this work, we investigate whether quantum advantage demonstrations can be achieved for more physically-motivated sampling problems, related to measurements of physical observables. We focus on the problem of sampling the outcomes of an energy measurement, performed on a simple-to-prepare product quantum state – a problem we refer to as energy sampling. For different regimes of measurement resolution and measurement errors, we provide complexity theoretic arguments showing that the existence of efficient classical algorithms for energy sampling is unlikely. In particular, we describe a family of Hamiltonians with nearest-neighbour interactions on a 2D lattice that can be efficiently measured with high resolution using a quantum circuit of commuting gates (IQP circuit), whereas an efficient classical simulation of this process should be impossible. In this high resolution regime, which can only be achieved for Hamiltonians that can be exponentially fast-forwarded, it is possible to use current theoretical tools tying quantum advantage statements to a polynomial-hierarchy collapse whereas for lower resolution measurements such arguments fail. Nevertheless, we show that efficient classical algorithms for low-resolution energy sampling can still be ruled out if we assume that quantum computers are strictly more powerful than classical ones. We believe our work brings a new perspective to the problem of demonstrating quantum advantage and leads to interesting new questions in Hamiltonian complexity.

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40

Zhang, Zhidong. "Topological Quantum Statistical Mechanics and Topological Quantum Field Theories." Symmetry 14, no. 2 (February 4, 2022): 323. http://dx.doi.org/10.3390/sym14020323.

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The Ising model describes a many-body interacting spin (or particle) system, which can be utilized to imitate the fundamental forces of nature. Although it is the simplest many-body interacting system of spins (or particles) with Z2 symmetry, the phenomena revealed in Ising systems may afford us lessons for other types of interactions in nature. In this work, we first focus on the mathematical structure of the three-dimensional (3D) Ising model. In the Clifford algebraic representation, many internal factors exist in the transfer matrices of the 3D Ising model, which are ascribed to the topology of the 3D space and the many-body interactions of spins. They result in the nonlocality, the nontrivial topological structure, as well as the long-range entanglement between spins in the 3D Ising model. We review briefly the exact solution of the ferromagnetic 3D Ising model at the zero magnetic field, which was derived in our previous work. Then, the framework of topological quantum statistical mechanics is established, with respect to the mathematical aspects (topology, algebra, and geometry) and physical features (the contribution of topology to physics, Jordan–von Neumann–Wigner framework, time average, ensemble average, and quantum mechanical average). This is accomplished by generalizations of our findings and observations in the 3D Ising models. Finally, the results are generalized to topological quantum field theories, in consideration of relationships between quantum statistical mechanics and quantum field theories. It is found that these theories must be set up within the Jordan–von Neumann–Wigner framework, and the ergodic hypothesis is violated at the finite temperature. It is necessary to account the time average of the ensemble average and the quantum mechanical average in the topological quantum statistical mechanics and to introduce the parameter space of complex time (and complex temperature) in the topological quantum field theories. We find that a topological phase transition occurs near the infinite temperature (or the zero temperature) in models in the topological quantum statistical mechanics and the topological quantum field theories, which visualizes a symmetrical breaking of time inverse symmetry.

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41

Colcelli, A., G. Mussardo, G. Sierra, and A. Trombettoni. "Free fall of a quantum many-body system." American Journal of Physics 90, no. 11 (November 2022): 833–40. http://dx.doi.org/10.1119/10.0013427.

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Анотація:

The quantum version of the free fall problem is a topic often skipped in undergraduate quantum mechanics courses, because its discussion usually requires wavepackets built on the Airy functions—a difficult computation. Here, on the contrary, we show that the problem can be nicely simplified both for a single particle and for general many-body systems by making use of a gauge transformation that corresponds to a change of reference frame from the laboratory frame to the one comoving with the falling system. Using this approach, the quantum mechanics problem of a particle in an external gravitational potential reduces to a much simpler one where there is no longer any gravitational potential in the Schrödinger equation. It is instructive to see that the same procedure can be used for many-body systems subjected to an external gravitational potential and a two-body interparticle potential that is a function of the distance between the particles. This topic provides a helpful and pedagogical example of a quantum many-body system whose dynamics can be analytically described in simple terms.

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42

Watanabe, Hiroshi C., Maximilian Kubillus, Tomáš Kubař, Robert Stach, Boris Mizaikoff, and Hiroshi Ishikita. "Cation solvation with quantum chemical effects modeled by a size-consistent multi-partitioning quantum mechanics/molecular mechanics method." Physical Chemistry Chemical Physics 19, no. 27 (2017): 17985–97. http://dx.doi.org/10.1039/c7cp01708a.

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43

Shigeta, Yasuteru, Tomoya Inui, Takeshi Baba, Katsuki Okuno, Hiroyuki Kuwabara, Ryohei Kishi, and Masayoshi Nakano. "Quantal cumulant mechanics and dynamics for multidimensional quantum many-body clusters." International Journal of Quantum Chemistry 113, no. 3 (March 14, 2012): 348–55. http://dx.doi.org/10.1002/qua.24052.

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44

Calogero, F. "Partially solvable quantum many-body problems in D-dimensional space (D=1,2,3,…)." Journal of Mathematical Physics 40, no. 9 (September 1999): 4208–26. http://dx.doi.org/10.1063/1.532961.

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45

Lavagno, A., and P. Quarati. "Classical and quantum non-extensive statistics effects in nuclear many-body problems." Chaos, Solitons & Fractals 13, no. 3 (March 2002): 569–80. http://dx.doi.org/10.1016/s0960-0779(01)00040-6.

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46

Li, Ying, Ze-Yao Han, Chao-Jian Li, Jin Lü, Xiao Yuan, and Bu-Jiao Wu. "Review on quantum advantages of sampling problems." Acta Physica Sinica 70, no. 21 (2021): 210201. http://dx.doi.org/10.7498/aps.70.20211428.

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Анотація:

Exploiting the coherence and entanglement of quantum many-qubit states, quantum computing can significantly surpass classical algorithms, making it possible to factor large numbers, solve linear equations, simulate many-body quantum systems, etc., in a reasonable time. With the rapid development of quantum computing hardware, many attention has been drawn to explore how quantum computers could go beyond the limit of classical computation. Owing to the need of a universal fault-tolerant quantum computer for many existing quantum algorithms, such as Shor’s factoring algorithm, and considering the limit of near-term quantum devices with small qubit numbers and short coherence times, many recent works focused on the exploration of demonstrating quantum advantages using noisy intermediate-scaled quantum devices and shallow circuits, and hence some sampling problems have been proposed as the candidates for quantum advantage demonstration. This review summarizes quantum advantage problems that are realizable on current quantum hardware. We focus on two notable problems—random circuit simulation and boson sampling—and consider recent theoretical and experimental progresses. After the respective demonstrations of these two types of quantum advantages on superconducting and optical quantum platforms, we expect current and near-term quantum devices could be employed for demonstrating quantum advantages in general problems.

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47

Bender, Carl M., Maarten DeKieviet, and S. P. Klevansky. "PT quantum mechanics." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 371, no. 1989 (April 28, 2013): 20120523. http://dx.doi.org/10.1098/rsta.2012.0523.

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-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on -symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a -symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the phase transition can now be understood intuitively without resorting to sophisticated mathe- matics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter–antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of -synthetic materials are being developed, and the phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of -symmetric quantum mechanics.

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48

Freericks, J. K., B. K. Nikolić, and O. Frieder. "The nonequilibrium quantum many-body problem as a paradigm for extreme data science." International Journal of Modern Physics B 28, no. 31 (December 8, 2014): 1430021. http://dx.doi.org/10.1142/s0217979214300217.

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Анотація:

Generating big data pervades much of physics. But some problems, which we call extreme data problems, are too large to be treated within big data science. The nonequilibrium quantum many-body problem on a lattice is just such a problem, where the Hilbert space grows exponentially with system size and rapidly becomes too large to fit on any computer (and can be effectively thought of as an infinite-sized data set). Nevertheless, much progress has been made with computational methods on this problem, which serve as a paradigm for how one can approach and attack extreme data problems. In addition, viewing these physics problems from a computer-science perspective leads to new approaches that can be tried to solve more accurately and for longer times. We review a number of these different ideas here.

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49

Goihl, Marcel, Mathis Friesdorf, Albert H. Werner, Winton Brown, and Jens Eisert. "Experimentally Accessible Witnesses of Many-Body Localization." Quantum Reports 1, no. 1 (June 17, 2019): 50–62. http://dx.doi.org/10.3390/quantum1010006.

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The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.

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50

Ohmori, Kenji, Guido Pupillo, Joseph Thywissen, and Matthias Weidemüller. "Call for papers: addressing quantum many-body problems with cold atoms and molecules." Journal of Physics B: Atomic, Molecular and Optical Physics 49, no. 10 (April 25, 2016): 100201. http://dx.doi.org/10.1088/0953-4075/49/10/100201.

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