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

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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 (September 20, 2016): 25–29. http://dx.doi.org/10.1145/2983537.

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2

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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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 (November 7, 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 entropy. A more accurate description requires different frameworks, namely, statistical mechanics and quantum physics to explore in depth the microscopic properties of physical systems and relate them to their macroscopic properties. These frameworks also allow to go beyond equilibrium situations. Given the notably increasing complexity of mathematical models to study realistic systems, and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models show limitations in scope or applicability. On the other hand, machine learning, i.e., data-driven, methods prove to be increasingly efficient for the study of complex quantum systems. Deep neural networks, in particular, have been successfully applied to many-body quantum dynamics simulations and to quantum matter phase characterization. In the present work, we show how to use a variational autoencoder (VAE)—a state-of-the-art tool in the field of deep learning for the simulation of probability distributions of complex systems. More precisely, we transform a quantum mechanical problem of many-body state reconstruction into a statistical problem, suitable for VAE, by using informationally complete positive operator-valued measure. We show, with the paradigmatic quantum Ising model in a transverse magnetic field, that the ground-state physics, such as, e.g., magnetization and other mean values of observables, of a whole class of quantum many-body systems can be reconstructed by using VAE learning of tomographic data for different parameters of the Hamiltonian, and even if the system undergoes a quantum phase transition. We also discuss challenges related to our approach as entropy calculations pose particular difficulties.

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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 (November 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 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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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 (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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6

FRÖHLICH, J., and U. M. STUDER. "GAUGE INVARIANCE IN NON-RELATIVISTIC MANY-BODY THEORY." International Journal of Modern Physics B 06, no. 11n12 (June 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 (March 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 (May 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 (February 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 (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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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 (June 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 work out the full Magnus expansion. We numerically show that it is possible to have superquadratic scaling of a nonstandard phase term, arising from the modification to the commutation relations, with coupled mechanical oscillators.

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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 (March 10, 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 (December 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 (January 20, 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 (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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18

Orth, Andreas. "Quantum mechanical resonance and limiting absorption: The many body problem." Communications in Mathematical Physics 126, no. 3 (January 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 (December 3, 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–Gaussian ensemble—a single parameter model of level statistics proposed recently in the context of disordered many-body systems. Moreover, the Pechukas–Yukawa distribution is also only slightly inferior to the two-parameter β–h ansatz shown earlier to reproduce level statistics of physical systems remarkably well.

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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 (January 22, 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 (July 15, 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 (March 9, 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 limits. On the other hand, in the strong dipole-dipole coupling limit, the single peak in the Kerr intensity splits into two peaks. The splitting of the Kerr spectrum is due to the creation of dressed states in the plasmonic nanohybrids within the strong dipole-dipole interaction. Further, we found that the Kerr nonlinearity is also enhanced due to the interaction between the surface plasmon polaritons and excitons of the quantum emitters. Next, we predicted the spontaneous decay rates are enhanced due to the dipole-dipole coupling. The enhancement of the Kerr intensity due to the surface plasmon polaritons can be used to fabricate nanosensors. The splitting of one peak (ON) two peaks (OFF) can be used to fabricate the nanoswitches for nanotechnology and nanomedical applications.

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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 (December 8, 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, 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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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 (June 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 (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

Elze, Hans-Thomas. "Qubit exchange interactions from permutations of classical bits." International Journal of Quantum Information 17, no. 08 (December 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 (October 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 (January 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 (January 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 (March 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 (March 14, 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 (March 17, 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 (October 30, 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/ N , up to logarithmic corrections. In the transition region, the single-site eigenstate entanglement entropies exhibit bimodal distributions, so that localized bits are either ‘on’ (strongly entangled) or ‘off’ (weakly entangled) in eigenstates. The clusters of ‘on’ bits vary significantly between eigenstates of the same sample, which provides evidence for a heterogeneous discontinuous transition out of the localized phase in single-site observables. We obtain these results by perturbative mapping to bond percolation on the hypercube at small J and by numerical exact diagonalization of the full many-body system. Our results support the arguments that the MBL phase is unstable in systems with short-range interactions and quenched randomness in dimensions d that are high but finite. This article is part of the themed issue ‘Breakdown of ergodicity in quantum systems: from solids to synthetic matter’.

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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 (April 15, 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, namely Be, Li−, and B+. This unique choice spans three classes—a neutral atom, an anion, and a cation. We have employed the unitary coupled-cluster ansätz to perform a rigorous analysis of two very important factors that could affect the precision of the simulations of electron correlation effects within a basis, namely mapping and backend simulator. We carry out our all-electron calculations with four such basis sets. The results obtained are compared with those calculated by using the full configuration interaction, traditional coupled-cluster and the unitary coupled-cluster methods, on a classical computer, to assess the precision of our results. A salient feature of the study involves a detailed analysis to find the number of shots (the number of times a variational quantum eigensolver algorithm is repeated to build statistics) required for calculations with IBM Qiskit’s QASM simulator backend, which mimics an ideal quantum computer. When more qubits become available, our study will serve as among the first steps taken towards computing other properties of interest to various applications such as new physics beyond the Standard Model of elementary particles and atomic clocks using the variational quantum eigensolver algorithm.

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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 two cases is found to be related to the different values of the shift exponent which governs the behavior of the critical line in the vicinity of the zero-temperature critical point. The observation of different values of the shift-exponent and of the related critical exponents along thermodynamic paths within the typical V-shaped region in the phase diagram may be interpreted as a signature of emerging quantum critical fluctuations.

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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 (May 29, 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 (August 21, 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 (September 15, 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 means to characterize both stable and unstable fixed points: divergent fidelity temperature for unstable fixed points and zero-fidelity temperature and (locally) maximal fidelity entropy for stable fixed points. In addition, fidelity entropy behaves differently at an unstable fixed point for topological phase transitions and at a stable fixed point for topological quantum states of matter. A detailed analysis of fidelity mechanical-state functions is presented for six fundamental models—the quantum spin-1/2 XY model, the transverse-field quantum Ising model in a longitudinal field, the quantum spin-1/2 XYZ model, the quantum spin-1/2 XXZ model in a magnetic field, the quantum spin-1 XYZ model, and the spin-1/2 Kitaev model on a honeycomb lattice for illustrative purposes. We also present an argument to justify why the thermodynamic, psychological/computational, and cosmological arrows of time should align with each other, with the psychological/computational arrow of time being singled out as a master arrow of time.

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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 (December 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 is prohibitive. We show here that a single special twist angle can be found using the transition structure factor, which provides the same benefit as twist averaging with one or two orders of magnitude reduction in computational time. We demonstrate that this not only works for metal systems but also is applicable to a broader range of materials, including insulators and semiconductors.

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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 (March 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 (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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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 (March 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) interactions is in order, are often unsatisfactory or partially missing in DFT models of water. In this review, we discuss the modeling of water and aqueous systems based on DFT and provide a comprehensive description of a general theoretical/computational framework for the development of data-driven many-body potentials from DFT reference data. This framework, coined MB-DFT, readily enables efficient many-body molecular dynamics (MD) simulations of small molecules, in both gas and condensed phases, while preserving the accuracy of the underlying DFT model. Theoretical considerations are emphasized, including the role that the delocalization error plays in MB-DFT potentials of water and the possibility to elevate DFT and MB-DFT to near-chemical-accuracy through a density-corrected formalism. The development of the MB-DFT framework is described in detail, along with its application in MB-MD simulations and recent extension to the modeling of reactive processes in solution within a quantum mechanics/MB molecular mechanics (QM/MB-MM) scheme, using water as a prototypical solvent. Finally, we identify open challenges and discuss future directions for MB-DFT and QM/MB-MM simulations in condensed phases.

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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 (November 21, 2007): 194101. http://dx.doi.org/10.1063/1.2778428.

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Elze, Hans-Thomas. "Multipartite cellular automata and the superposition principle." International Journal of Quantum Information 14, no. 04 (June 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 continuum limit. Presently, we show, in particular, how such automata can form “multipartite” systems consistently with the tensor product structures of non-relativistic many-body QM, while maintaining the linearity of dynamics. Consequently, the superposition principle is fully operative already on the level of these primordial discrete deterministic automata, including the essential quantum effects of interference and entanglement.

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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 (December 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 contrast to commonly used pairwise approaches, many-body effects substantially decrease the relative stability of native states in the absence of water. Upon solvation, the protein-water dispersion interaction counteracts this effect and stabilizes native conformations and transition states. These observations arise from the highly delocalized and collective character of the interactions, suggesting a remarkable persistence of electron correlation through aqueous environments and providing the basis for long-range interaction mechanisms in biomolecular systems.

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Kourehpaz, Mahdi, Stefan Donsa, Fabian Lackner, Joachim Burgdörfer, and Iva Březinová. "Canonical Density Matrices from Eigenstates of Mixed Systems." Entropy 24, no. 12 (November 29, 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 properties provided the eigenstate thermalization hypothesis holds, which requires the system to be quantum-chaotic. In the present paper, we study the emergence of thermal states in the regime of a quantum analog of a mixed phase space. Specifically, we study the emergence of the canonical density matrix of an impurity upon reduction from isolated energy eigenstates of a large but finite quantum system the impurity is embedded in. Our system can be tuned by means of a single parameter from quantum integrability to quantum chaos and corresponds in between to a system with mixed quantum phase space. We show that the probability for finding a canonical density matrix when reducing the ensemble of energy eigenstates of the finite many-body system can be quantitatively controlled and tuned by the degree of quantum chaos present. For the transition from quantum integrability to quantum chaos, we find a continuous and universal (i.e., size-independent) relation between the fraction of canonical eigenstates and the degree of chaoticity as measured by the Brody parameter or the Shannon entropy.

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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 (July 26, 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’s principle. We also demonstrate that our model is able to describe linear quantum-mechanical systems with shape-changing external potentials.

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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 in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

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