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Journal articles on the topic 'Many-body quantum mechanic'

Author: Grafiati

Published: 11 March 2023

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1

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

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2

Shigeta, Yasuteru, Tomoya Inui, Takeshi Baba, et al. "Quantal cumulant mechanics and dynamics for multidimensional quantum many-body clusters." International Journal of Quantum Chemistry 113, no. 3 (2012): 348–55. http://dx.doi.org/10.1002/qua.24052.

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3

Luchnikov, Ilia A., Alexander Ryzhov, Pieter-Jan Stas, Sergey N. Filippov, and Henni Ouerdane. "Variational Autoencoder Reconstruction of Complex Many-Body Physics." Entropy 21, no. 11 (2019): 1091. http://dx.doi.org/10.3390/e21111091.

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Thermodynamics is a theory of principles that permits a basic description of the macroscopic properties of a rich variety of complex systems from traditional ones, such as crystalline solids, gases, liquids, and thermal machines, to more intricate systems such as living organisms and black holes to name a few. Physical quantities of interest, or equilibrium state variables, are linked together in equations of state to give information on the studied system, including phase transitions, as energy in the forms of work and heat, and/or matter are exchanged with its environment, thus generating en

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4

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

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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 gravitat

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5

Goihl, Marcel, Mathis Friesdorf, Albert H. Werner, Winton Brown, and Jens Eisert. "Experimentally Accessible Witnesses of Many-Body Localization." Quantum Reports 1, no. 1 (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 wor

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6

FRÖHLICH, J., and U. M. STUDER. "GAUGE INVARIANCE IN NON-RELATIVISTIC MANY-BODY THEORY." International Journal of Modern Physics B 06, no. 11n12 (1992): 2201–8. http://dx.doi.org/10.1142/s0217979292001092.

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We review some recent results on the physics of two-dimensional, incompressible electron and spin liquids. These results follow from Ward identities reflecting the U(1) em × SU(2) spin -gauge invariance of non-relativistic quantum mechanics. They describe a variety of generalized quantized Hall effects.

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7

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

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8

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

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9

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

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10

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 (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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11

Chevalier, Hadrien, Hyukjoon Kwon, Kiran E. Khosla, Igor Pikovski, and M. S. Kim. "Many-body probes for quantum features of spacetime." AVS Quantum Science 4, no. 2 (2022): 021402. http://dx.doi.org/10.1116/5.0079675.

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Many theories of quantum gravity can be understood as imposing a minimum length scale the signatures of which can potentially be seen in precise table top experiments. In this work, we inspect the capacity for correlated many-body systems to probe non-classicalities of spacetime through modifications of the commutation relations. We find an analytic derivation of the dynamics for a single mode light field interacting with a single mechanical oscillator and with coupled oscillators to first order corrections to the commutation relations. Our solution is valid for any coupling function as we wor

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12

Avery, John. "Many-dimensional hydrogenlike wave functions and the quantum mechanical many-body problem." International Journal of Quantum Chemistry 30, S20 (1986): 57–63. http://dx.doi.org/10.1002/qua.560300708.

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13

Avery, J., D. Z. Goodson, and D. R. Herschbach. "Dimensional scaling and the quantum mechanical many-body problem." Theoretica Chimica Acta 81, no. 1-2 (1991): 1–20. http://dx.doi.org/10.1007/bf01113374.

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14

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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15

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

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16

Lieb, Elliott H. "Some of the Early History of Exactly Soluble Models." International Journal of Modern Physics B 11, no. 01n02 (1997): 3–10. http://dx.doi.org/10.1142/s0217979297000034.

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17

Zhang, Zhidong. "Topological Quantum Statistical Mechanics and Topological Quantum Field Theories." Symmetry 14, no. 2 (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 topolo

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18

Orth, Andreas. "Quantum mechanical resonance and limiting absorption: The many body problem." Communications in Mathematical Physics 126, no. 3 (1990): 559–73. http://dx.doi.org/10.1007/bf02125700.

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19

De, Bitan, Piotr Sierant, and Jakub Zakrzewski. "On intermediate statistics across many-body localization transition." Journal of Physics A: Mathematical and Theoretical 55, no. 1 (2021): 014001. http://dx.doi.org/10.1088/1751-8121/ac39cd.

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Abstract The level statistics in the transition between delocalized and localized phases of many body interacting systems is considered. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically via Monte Carlo method. The resulting higher order spacing ratios are compared with data coming from different quantum many body systems. It is found that this Pechukas–Yukawa distribution compares favorably with β–Gaussia

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20

Macrì, Tommaso, and Fabio Cinti. "Many-Body Physics of Low-Density Dipolar Bosons in Box Potentials." Condensed Matter 4, no. 1 (2019): 17. http://dx.doi.org/10.3390/condmat4010017.

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Crystallization is a generic phenomenon in classical and quantum mechanics arising in a variety of physical systems. In this work, we focus on a specific platform, ultracold dipolar bosons, which can be realized in experiments with dilute gases. We reviewed the relevant ingredients leading to crystallization, namely the interplay of contact and dipole–dipole interactions and system density, as well as the numerical algorithm employed. We characterized the many-body phases investigating correlations and superfluidity.

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21

Kunz, A. Barry, Jie Meng, and John M. Vail. "Quantum-mechanical cluster-lattice interaction in crystal simulation: Many-body effects." Physical Review B 38, no. 2 (1988): 1064–66. http://dx.doi.org/10.1103/physrevb.38.1064.

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22

Singh, Mahi R. "A Review of Many-Body Interactions in Linear and Nonlinear Plasmonic Nanohybrids." Symmetry 13, no. 3 (2021): 445. http://dx.doi.org/10.3390/sym13030445.

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In this review article, we discuss the many-body interactions in plasmonic nanohybrids made of an ensemble of quantum emitters and metallic nanoparticles. A theory of the linear and nonlinear optical emission intensity was developed by using the many-body quantum mechanical density matrix method. The ensemble of quantum emitters and metallic nanoparticles interact with each other via the dipole-dipole interaction. Surfaces plasmon polaritons are located near to the surface of the metallic nanoparticles. We showed that the nonlinear Kerr intensity enhances due to the weak dipole-dipole coupling

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23

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

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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, fo

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24

Bányai, Ladislaus Alexander. "The Non-Relativistic Many-Body Quantum-Mechanical Hamiltonian with Diamagnetic Current-Current Interaction." International Journal of Theoretical Physics 60, no. 6 (2021): 2236–43. http://dx.doi.org/10.1007/s10773-021-04842-9.

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AbstractWe extend the standard solid-state quantum mechanical Hamiltonian containing only Coulomb interactions between the charged particles by inclusion of the (transverse) current-current diamagnetic interaction starting from the non-relativistic QED restricted to the states without photons and neglecting the retardation in the photon propagator. This derivation is supplemented with a derivation of an analogous result along the non-rigorous old classical Darwin-Landau-Lifshitz argumentation within the physical Coulomb gauge.

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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 (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

Elze, Hans-Thomas. "Qubit exchange interactions from permutations of classical bits." International Journal of Quantum Information 17, no. 08 (2019): 1941003. http://dx.doi.org/10.1142/s021974991941003x.

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In order to prepare for the introduction of dynamical many-body and, eventually, field theoretical models, we show here that quantum mechanical exchange interactions in a three-spin chain can emerge from the deterministic dynamics of three classical Ising spins. States of the latter form an ontological basis, which will be discussed with reference to the ontology proposed in the Cellular Automaton Interpretation of Quantum Mechanics by ’t[Formula: see text]Hooft. Our result illustrates a new Baker–Campbell–Hausdorff (BCH) formula with terminating series expansion.

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27

Loeffler, Hannes H., Jorge Iglesias Yagüe, and Bernd M. Rode. "Many-Body Effects in Combined Quantum Mechanical/Molecular Mechanical Simulations of the Hydrated Manganous Ion." Journal of Physical Chemistry A 106, no. 41 (2002): 9529–32. http://dx.doi.org/10.1021/jp020443k.

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28

Kim, M. R., C. Tong, S. K. Kim, M. S. Son, D. H. Shin, and J. K. Rhee. "Many-body effects on the ground-state energy in semiconductor quantum wells." Materials Science and Engineering: B 106, no. 2 (2004): 177–81. http://dx.doi.org/10.1016/j.mseb.2003.09.021.

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29

Zhang, Ruiqin, and Conghao Deng. "Exact solutions of the Schrödinger equation for some quantum-mechanical many-body systems." Physical Review A 47, no. 1 (1993): 71–77. http://dx.doi.org/10.1103/physreva.47.71.

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30

Hagedorn, George A. "Scattering Theory for Many-Body Quantum Mechanical Systems–Rigorous Results (Israel Michael Sigal)." SIAM Review 27, no. 1 (1985): 103. http://dx.doi.org/10.1137/1027030.

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31

Chemla, D. S., and J. Shah. "Ultrafast dynamics of many-body processes and fundamental quantum mechanical phenomena in semiconductors." Proceedings of the National Academy of Sciences 97, no. 6 (2000): 2437–44. http://dx.doi.org/10.1073/pnas.97.6.2437.

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32

Sahni, Viraht, and Manoj K. Harbola. "Quantum-Mechanical interpretation of the local many-body potential of density-functional theory." International Journal of Quantum Chemistry 38, S24 (1990): 569–84. http://dx.doi.org/10.1002/qua.560382456.

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33

Ponte, Pedro, C. R. Laumann, David A. Huse, and A. Chandran. "Thermal inclusions: how one spin can destroy a many-body localized phase." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 375, no. 2108 (2017): 20160428. http://dx.doi.org/10.1098/rsta.2016.0428.

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Many-body localized (MBL) systems lie outside the framework of statistical mechanics, as they fail to equilibrate under their own quantum dynamics. Even basic features of MBL systems, such as their stability to thermal inclusions and the nature of the dynamical transition to thermalizing behaviour, remain poorly understood. We study a simple central spin model to address these questions: a two-level system interacting with strength J with N ≫1 localized bits subject to random fields. On increasing J , the system transitions from an MBL to a delocalized phase on the vanishing scale J c ( N )∼1/

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34

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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35

Sumeet, Srinivasa Prasannaa V, Bhanu Pratap Das, and Bijaya Kumar Sahoo. "Assessing the Precision of Quantum Simulation of Many-Body Effects in Atomic Systems Using the Variational Quantum Eigensolver Algorithm." Quantum Reports 4, no. 2 (2022): 173–92. http://dx.doi.org/10.3390/quantum4020012.

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The emerging field of quantum simulation of many-body systems is widely recognized as a very important application of quantum computing. A crucial step towards its realization in the context of many-electron systems requires a rigorous quantum mechanical treatment of the different interactions. In this pilot study, we investigate the physical effects beyond the mean-field approximation, known as electron correlation, in the ground state energies of atomic systems using the classical-quantum hybrid variational quantum eigensolver algorithm. To this end, we consider three isoelectronic species,

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36

Campana, L. S., A. Cavallo, L. De Cesare, U. Esposito, and A. Naddeo. "Thermodynamics of the Classical Planar Ferromagnet Close to the Zero-Temperature Critical Point: A Many-Body Approach." Advances in Condensed Matter Physics 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/619513.

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We explore the low-temperature thermodynamic properties and crossovers of ad-dimensional classical planar Heisenberg ferromagnet in a longitudinal magnetic field close to its field-induced zero-temperature critical point by employing the two-time Green’s function formalism in classical statistical mechanics. By means of a classical Callen-like method for the magnetization and the Tyablikov-like decoupling procedure, we obtain, for anyd, a low-temperature critical scenario which is quite similar to the one found for the quantum counterpart. Remarkably, ford>2the discrimination between the tw

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37

Conte, Adriano Mosca, Emiliano Ippoliti, Rodolfo Del Sole, Paolo Carloni, and Olivia Pulci. "Many-Body Perturbation Theory Extended to the Quantum Mechanics/Molecular Mechanics Approach: Application to Indole in Water Solution." Journal of Chemical Theory and Computation 5, no. 7 (2009): 1822–28. http://dx.doi.org/10.1021/ct800528e.

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38

Sellier, Jean Michel, and Kristina G. Kapanova. "A study of entangled systems in the many-body signed particle formulation of quantum mechanics." International Journal of Quantum Chemistry 117, no. 23 (2017): e25447. http://dx.doi.org/10.1002/qua.25447.

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39

Zhou, Huan-Qiang, Qian-Qian Shi, and Yan-Wei Dai. "Fidelity Mechanics: Analogues of the Four Thermodynamic Laws and Landauer’s Principle." Entropy 24, no. 9 (2022): 1306. http://dx.doi.org/10.3390/e24091306.

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Fidelity mechanics is formalized as a framework for investigating critical phenomena in quantum many-body systems. Fidelity temperature is introduced for quantifying quantum fluctuations, which, together with fidelity entropy and fidelity internal energy, constitute three basic state functions in fidelity mechanics, thus enabling us to formulate analogues of the four thermodynamic laws and Landauer’s principle at zero temperature. Fidelity flows, which are irreversible, are defined and may be interpreted as an alternative form of renormalization group flows. Thus, fidelity mechanics offers a m

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40

Mihm, Tina N., Tobias Schäfer, Sai Kumar Ramadugu, Laura Weiler, Andreas Grüneis, and James J. Shepherd. "A shortcut to the thermodynamic limit for quantum many-body calculations of metals." Nature Computational Science 1, no. 12 (2021): 801–8. http://dx.doi.org/10.1038/s43588-021-00165-1.

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AbstractComputationally efficient and accurate quantum mechanical approximations to solve the many-electron Schrödinger equation are crucial for computational materials science. Methods such as coupled cluster theory show potential for widespread adoption if computational cost bottlenecks can be removed. For example, extremely dense k-point grids are required to model long-range electronic correlation effects, particularly for metals. Although these grids can be made more effective by averaging calculations over an offset (or twist angle), the resultant cost in time for coupled cluster theory

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41

Watanabe, Hiroshi C., Misa Banno, and Minoru Sakurai. "An adaptive quantum mechanics/molecular mechanics method for the infrared spectrum of water: incorporation of the quantum effect between solute and solvent." Physical Chemistry Chemical Physics 18, no. 10 (2016): 7318–33. http://dx.doi.org/10.1039/c5cp07136d.

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Quantum effects in solute–solvent interactions, such as the many-body effect and the dipole-induced dipole, are known to be critical factors influencing the infrared spectra of species in the liquid phase.

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42

Howland, James S. "SCATTERING THEORY FOR MANY-BODY QUANTUM MECHANICAL SYSTEMS Rigorous Results (Lecture Notes in Mathematics, 1011)." Bulletin of the London Mathematical Society 17, no. 2 (1985): 202–3. http://dx.doi.org/10.1112/blms/17.2.202.

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43

Herrera, William J., Herbert Vinck-Posada, and Shirley Gómez Páez. "Green's functions in quantum mechanics courses." American Journal of Physics 90, no. 10 (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 o

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44

Palos, Etienne, Saswata Dasgupta, Eleftherios Lambros, and Francesco Paesani. "Data-driven many-body potentials from density functional theory for aqueous phase chemistry." Chemical Physics Reviews 4, no. 1 (2023): 011301. http://dx.doi.org/10.1063/5.0129613.

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Density functional theory (DFT) has been applied to modeling molecular interactions in water for over three decades. The ubiquity of water in chemical and biological processes demands a unified understanding of its physics, from the single molecule to the thermodynamic limit and everything in between. Recent advances in the development of data-driven and machine-learning potentials have accelerated simulation of water and aqueous systems with DFT accuracy. However, anomalous properties of water in the condensed phase, where a rigorous treatment of both local and non-local many-body (MB) intera

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45

Giese, Timothy J., and Darrin M. York. "Charge-dependent model for many-body polarization, exchange, and dispersion interactions in hybrid quantum mechanical∕molecular mechanical calculations." Journal of Chemical Physics 127, no. 19 (2007): 194101. http://dx.doi.org/10.1063/1.2778428.

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46

Elze, Hans-Thomas. "Multipartite cellular automata and the superposition principle." International Journal of Quantum Information 14, no. 04 (2016): 1640001. http://dx.doi.org/10.1142/s0219749916400013.

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Cellular automata (CA) can show well known features of quantum mechanics (QM), such as a linear updating rule that resembles a discretized form of the Schrödinger equation together with its conservation laws. Surprisingly, a whole class of “natural” Hamiltonian CA, which are based entirely on integer-valued variables and couplings and derived from an action principle, can be mapped reversibly to continuum models with the help of sampling theory. This results in “deformed” quantum mechanical models with a finite discreteness scale l, which for [Formula: see text] reproduce the familiar continuu

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47

Stöhr, Martin, and Alexandre Tkatchenko. "Quantum mechanics of proteins in explicit water: The role of plasmon-like solute-solvent interactions." Science Advances 5, no. 12 (2019): eaax0024. http://dx.doi.org/10.1126/sciadv.aax0024.

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Quantum-mechanical van der Waals dispersion interactions play an essential role in intraprotein and protein-water interactions—the two main factors affecting the structure and dynamics of proteins in water. Typically, these interactions are only treated phenomenologically, via pairwise potential terms in classical force fields. Here, we use an explicit quantum-mechanical approach of density-functional tight-binding combined with the many-body dispersion formalism and demonstrate the relevance of many-body van der Waals forces both to protein energetics and to protein-water interactions. In con

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48

Kourehpaz, Mahdi, Stefan Donsa, Fabian Lackner, Joachim Burgdörfer, and Iva Březinová. "Canonical Density Matrices from Eigenstates of Mixed Systems." Entropy 24, no. 12 (2022): 1740. http://dx.doi.org/10.3390/e24121740.

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One key issue of the foundation of statistical mechanics is the emergence of equilibrium ensembles in isolated and closed quantum systems. Recently, it was predicted that in the thermodynamic (N→∞) limit of large quantum many-body systems, canonical density matrices emerge for small subsystems from almost all pure states. This notion of canonical typicality is assumed to originate from the entanglement between subsystem and environment and the resulting intrinsic quantum complexity of the many-body state. For individual eigenstates, it has been shown that local observables show thermal propert

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49

Zloshchastiev, Konstantin G. "On the Dynamical Nature of Nonlinear Coupling of Logarithmic Quantum Wave Equation, Everett-Hirschman Entropy and Temperature." Zeitschrift für Naturforschung A 73, no. 7 (2018): 619–28. http://dx.doi.org/10.1515/zna-2018-0096.

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AbstractWe study the dynamical behavior of the nonlinear coupling of a logarithmic quantum wave equation. Using the statistical mechanical arguments for a large class of many-body systems, this coupling is shown to be related to temperature, which is a thermodynamic conjugate to the Everett-Hirschman’s quantum information entropy. A combined quantum-mechanical and field-theoretical model is proposed, which leads to a logarithmic equation with variable nonlinear coupling. We study its properties and present arguments regarding its nature and interpretation, including the connection to Landauer’

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50

Buividovich, Pavel, Masanori Hanada, and Andreas Schäfer. "Real-time dynamics of matrix quantum mechanics beyond the classical approximation." EPJ Web of Conferences 175 (2018): 08006. http://dx.doi.org/10.1051/epjconf/201817508006.

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We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are

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