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Cited by 3,175Quantum chaos and dynamical systemsQuantum many-body systemsStatistical Mechanics and Entropy

Chaos and quantum thermalization

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Srednicki, Mark·1994·Physical Review E
DOI 10.1103/physreve.50.888
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Abstract

We show that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture. Berry's conjecture is expected to hold only if the corresponding classical system is chaotic, and essentially states that the energy eigenfunctions behave as if they were Gaussian random variables. We review the existing evidence, and show that previously neglected effects substantially strengthen the case for Berry's conjecture. We study a rarefied hard-sphere gas as an explicit example of a many-body system which is known to be classically chaotic, and show that an energy eigenstate which obeys Berry's conjecture predicts a Maxwell-Boltzmann, Bose-Einstein, or Fermi-Dirac distribution for the momentum of each constituent particle, depending on whether the wave functions are taken to be nonsymmetric, completely symmetric, or completely antisymmetric functions of the positions of the particles. We call this phenomenon eigenstate thermalization. We show that a generic initial state will approach thermal equilibrium at least as fast as O(\ensuremath{\Elzxh}/\ensuremath{\Delta})${\mathit{t}}^{\mathrm{\ensuremath{-}}1}$, where \ensuremath{\Delta} is the uncertainty in the total energy of the gas. This result holds for an individual initial state; in contrast to the classical theory, no averaging over an ensemble of initial states is needed. We argue that these results constitute a sound foundation for quantum statistical mechanics.

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Crossref · 10.1103/physreve.50.888

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  • The factor of implies that can be understood from the point of view of the eigenstate thermalization hypothesis (ETH).

    “where the factor of implies that can be understood from the point of view of the eigenstate thermalization hypothesis (ETH) (Deutsch 1991; Srednicki 1994), as emphasized in Saad (2019), Jafferis et al. (2022a, 2022b).26”

    From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Srednicki 1994

  • By ETH one expects the squared energy matrix elements to be smooth functions of the energy for sufficiently simple operators with zero one-point-function.

    “For sufficiently simple operators that have zero one-point-function,36 by ETH one expects the squared energy matrix elements to be smooth functions of the energy (Deutsch 1991; Srednicki 1994).”

    From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Srednicki 1994

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Authors
Srednicki, M.
Affiliations
University of California, Santa Barbara (US)
Corresponding author
Srednicki, Mark
ORCID
Srednicki, Mark
Venue
Physical Review E
Publisher
American Physical Society (APS)
Published
1994-08-01
Volume
50
Issue
2
Pages
888-901
ISSN
  • 1063-651X (ISSN-L)
  • 1095-3787
DOI
10.1103/physreve.50.888
OpenAlex
W2034251480
Cited by
3,175
References
0
Citations by year
2026: 188 · 2025: 313 · 2024: 272 · 2023: 272 · 2022: 275 · 2021: 267 · 2020: 303 · 2019: 248 · 2018: 216 · 2017: 187 · 2016: 165 · 2015: 137 · 2014: 88 · 2013: 58 · 2012: 48
FWCI
3.21
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University)
Topics
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
Keywords
quantum thermalization, eigenstate thermalization, quantum chaos, isolated quantum systems, energy eigenfunctions, Gaussian random variables, Maxwell-Boltzmann distribution, Bose-Einstein distribution, Fermi-Dirac distribution, thermal equilibrium, convergence rate, quantum statistical mechanics

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