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Entropy
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Thermalization in Isolated Quantum Systems
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Thermalization in Isolated Quantum Systems

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 July 2019) | Viewed by 16710

Special Issue Editors

Prof. Dr. Vladimir Zelevinsky

E-Mail Website1 Website2
Guest Editor
Department of Physics and Astronomy and Facility for Rare Isotope Beams, Michigan State University, East Lansing, MI 48824-1321, USA
Interests: quantum many-body theory; nuclear structure; chaos and non-linear dynamics; fundamental symmetries in nuclei; open quantum systems; mesons in nuclei
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Felix Izrailev

E-Mail Website1 Website2
Guest Editor
1. Instituto de Fisica, Benemérita Universidad Autónoma de Puebla, Puebla 72570, Pue, Mexico
2. Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824-1321, USA

Special Issue Information

Dear Colleagues,

The field of mesoscopic physics is going through rapid development with contributions from many subfields of science including atomic, molecular and nuclear physics, condensed matter physics on the micro- and nano-scale, biophysics and quantum information. In all cases, we have to deal with relatively small systems of interacting constituents where statistical features are clearly emerging being described in terms of temperature, entropy, etc., while at the same time one still can study, theoretically and experimentally, individual quantum states.

If traditional statistical physics usually considered statistical ensembles in the limit of infinitely large volume and particle number, and the equilibrium thermalization was reached due to the interaction with a thermostat, in a small system with a finite number of particles thermal equilibrium is established as a result of interparticle interactions which, at high level density, leads to chaotic mixing of simple many-body configurations. Historically this follows the line from Boltzmann to Landau and Lifshitz who stressed in their Statistical Physics that statistical properties can be observed and studied on the level of individual quantum states. This direction of science addresses the emergence of thermodynamic phenomena from quantum mechanics and quantum chaos creating in a sense a new paradigm of statistical mechanics.

This emerging field encompasses different bright ideas and very wide practical applications; its interdisciplinary character leads to different viewpoints and illuminating discussions. We, therefore, solicit contribution to this Special Issue on a new branch of quantum physics and its applications.

Prof. Dr. Vladimir Zelevinsky
Prof. Dr. Felix Izrailev
Guest Editors

Manuscript Submission Information

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Quantum and classical chaos
  • Thermalization in isolated quantum systems
  • Quantum signatures of thermalization
  • Strength functions and thermalization
  • Statistics of particles in quantum thermalized systems
  • Quantum thermalization and collective phenomena
  • Pecularities of small systems
  • Various definitions of entropy and temperature
  • Thermalization in open systems
  • Time development of thermalization
  • Relaxation to equilibrium
  • Experimental observation of quantum thermalization
  • Quench dynamics
  • Fluctuations in isolated systems

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Published Papers (4 papers)

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Research

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27 pages, 4175 KiB  
Article
The Correlation Production in Thermodynamics
by Sheng-Wen Li
Entropy 2019, 21(2), 111; https://doi.org/10.3390/e21020111 - 24 Jan 2019
Cited by 7 | Viewed by 4065
Abstract
Macroscopic many-body systems always exhibit irreversible behaviors. However, in principle, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville equation, guarantees that the entropy of an isolated system does not change with time, which is quite [...] Read more.
Macroscopic many-body systems always exhibit irreversible behaviors. However, in principle, the underlying microscopic dynamics of the many-body system, either the (quantum) von Neumann or (classical) Liouville equation, guarantees that the entropy of an isolated system does not change with time, which is quite confusing compared with the macroscopic irreversibility. We notice that indeed the macroscopic entropy increase in standard thermodynamics is associated with the correlation production inside the full ensemble state of the whole system. In open systems, the irreversible entropy production of the open system can be proved to be equivalent with the correlation production between the open system and its environment. During the free diffusion of an isolated ideal gas, the correlation between the spatial and momentum distributions is increasing monotonically, and it could well reproduce the entropy increase result in standard thermodynamics. In the presence of particle collisions, the single-particle distribution always approaches the Maxwell-Boltzmann distribution as its steady state, and its entropy increase indeed indicates the correlation production between the particles. In all these examples, the total entropy of the whole isolated system keeps constant, while the correlation production reproduces the irreversible entropy increase in the standard macroscopic thermodynamics. In this sense, the macroscopic irreversibility and the microscopic reversibility no longer contradict with each other. Full article
(This article belongs to the Special Issue Thermalization in Isolated Quantum Systems)
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21 pages, 848 KiB  
Article
Chaotic Dynamics in a Quantum Fermi–Pasta–Ulam Problem
by Alexander L. Burin, Andrii O. Maksymov, Ma’ayan Schmidt and Il’ya Ya. Polishchuk
Entropy 2019, 21(1), 51; https://doi.org/10.3390/e21010051 - 10 Jan 2019
Cited by 9 | Viewed by 4226
Abstract
We investigate the emergence of chaotic dynamics in a quantum Fermi—Pasta—Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy [...] Read more.
We investigate the emergence of chaotic dynamics in a quantum Fermi—Pasta—Ulam problem for anharmonic vibrations in atomic chains applying semi-quantitative analysis of resonant interactions complemented by exact diagonalization numerical studies. The crossover energy separating chaotic high energy phase and localized (integrable) low energy phase is estimated. It decreases inversely proportionally to the number of atoms until approaching the quantum regime where this dependence saturates. The chaotic behavior appears at lower energies in systems with free or fixed ends boundary conditions compared to periodic systems. The applications of the theory to realistic molecules are discussed. Full article
(This article belongs to the Special Issue Thermalization in Isolated Quantum Systems)
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15 pages, 668 KiB  
Article
New Equilibrium Ensembles for Isolated Quantum Systems
by Fabio Anza
Entropy 2018, 20(10), 744; https://doi.org/10.3390/e20100744 - 29 Sep 2018
Cited by 2 | Viewed by 2920
Abstract
The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called “diagonal ensemble” ρ DE . Building on the intuition [...] Read more.
The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called “diagonal ensemble” ρ DE . Building on the intuition provided by Jaynes’ maximum entropy principle, in this paper we present a novel technique to generate progressively better approximations to ρ DE . As an example, we write down a hierarchical set of ensembles which can be used to describe the equilibrium physics of small isolated quantum systems, going beyond the “thermal ansatz” of Gibbs ensembles. Full article
(This article belongs to the Special Issue Thermalization in Isolated Quantum Systems)
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Review

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22 pages, 1491 KiB  
Review
Random k-Body Ensembles for Chaos and Thermalization in Isolated Systems
by Venkata Krishna Brahmam Kota and Narendra D. Chavda
Entropy 2018, 20(7), 541; https://doi.org/10.3390/e20070541 - 20 Jul 2018
Cited by 9 | Viewed by 4586
Abstract
Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) [...] Read more.
Embedded ensembles or random matrix ensembles generated by k-body interactions acting in many-particle spaces are now well established to be paradigmatic models for many-body chaos and thermalization in isolated finite quantum (fermion or boson) systems. In this article, briefly discussed are (i) various embedded ensembles with Lie algebraic symmetries for fermion and boson systems and their extensions (for Majorana fermions, with point group symmetries etc.); (ii) results generated by these ensembles for various aspects of chaos, thermalization and statistical relaxation, including the role of q-hermite polynomials in k-body ensembles; and (iii) analyses of numerical and experimental data for level fluctuations for trapped boson systems and results for statistical relaxation and decoherence in these systems with close relations to results from embedded ensembles. Full article
(This article belongs to the Special Issue Thermalization in Isolated Quantum Systems)
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