Quantum statistical mechanics in a closed system
Abstract
A closed quantum-mechanical system with a large number of degrees of freedom does not necessarily give time averages in agreement with the microcanonical distribution. For systems where the different degrees of freedom are uncoupled, situations are discussed that show a violation of the usual statistical-mechanical rules. By adding a finite but very small perturbation in the form of a random matrix, it is shown that the results of quantum statistical mechanics are recovered. Expectation values in energy eigenstates for this perturbed system are also discussed, and deviations from the microcanonical result are shown to become exponentially small in the number of degrees of freedom.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
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 Deutsch 1991
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 Deutsch 1991
Cited by
Sorted by citations
Exploring the many-body localization transition in two dimensions
Choi, J.-Y., Hild, S., Zeiher, J., Schauß, P., Rubio-Abadal, A., Yefsah, T., Khemani, V., Huse, D. A., Bloch, I., & Gross, C. (2016) · Science · doi:10.1126/science.aaf8834 · Cited by 979 · see citing works
Programmable Quantum Simulations of Spin Systems with Trapped Ions
Monroe, C., Campbell, W. C., Duan, L. M., Gong, Z. X., Gorshkov, A. V., Hess, P., Islam, R., Kim, K., Linke, N., Pagano, G., et al. (2019) · arXiv · doi:10.48550/arxiv.1912.07845 · Cited by 806
Quantum mechanical evolution towards thermal equilibrium
Linden, N., Popescu, S., Short, A. J., & Winter, A. (2009) · Physical Review E · doi:10.1103/physreve.79.061103 · Cited by 625 · see citing works
Black holes and random matrices
Cotler, J. S., Gur-Ari, G., Hanada, M., Polchinski, J., Saad, P., Shenker, S. H., Stanford, D., Streicher, A., & Tezuka, M. (2017) · Journal of High Energy Physics · doi:10.1007/jhep05(2017)118 · Cited by 562 · see citing works
Jerusalem lectures on black holes and quantum information
Harlow, D. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.015002 · Cited by 480 · see citing works
Universality of long-distance AdS physics from the CFT bootstrap
Fitzpatrick, A. L., Kaplan, J., & Walters, M. T. (2014) · Journal of High Energy Physics · doi:10.1007/jhep08(2014)145 · Cited by 397 · see citing works
An infalling observer in AdS/CFT
Papadodimas, K., & Raju, S. (2013) · Journal of High Energy Physics · doi:10.1007/jhep10(2013)212 · Cited by 335 · see citing works
Information scrambling in quantum circuits
Mi, X., Roushan, P., Quintana, C., Mandrà, S., Marshall, J., Neill, C., Arute, F., Arya, K., Atalaya, J., Babbush, R., et al. (2021) · Science · doi:10.1126/science.abg5029 · Cited by 283 · see citing works
Gauge-Gravity Duality and the Black Hole Interior
Marolf, D., & Polchinski, J. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.171301 · Cited by 260 · see citing works
Lessons from the Information Paradox
Raju, S. (2020) · arXiv · doi:10.48550/arxiv.2012.05770 · Cited by 234
Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity
Mertens, T. G., & Turiaci, G. J. (2023) · Living Reviews in Relativity · doi:10.1007/s41114-023-00046-1 · Cited by 181 · see citing works
Eigenstate Thermalization and Disorder Averaging in Gravity
Pollack, J., Rozali, M., Sully, J., & Wakeham, D. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.021601 · Cited by 116 · see citing works
Spread of entanglement in a Sachdev-Ye-Kitaev chain
Gu, Y., Lucas, A., & Qi, X.-L. (2017) · Journal of High Energy Physics · doi:10.1007/jhep09(2017)120 · Cited by 109 · see citing works
Learning the Alpha-bits of black holes
Hayden, P., & Penington, G. (2019) · Journal of High Energy Physics · doi:10.1007/jhep12(2019)007 · Cited by 125 · see citing works
Entanglement Entropies of Equilibrated Pure States in Quantum Many-Body Systems and Gravity
Liu, H., & Vardhan, S. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.010344 · Cited by 77 · see citing works
Product spectrum ansatz and the simplicity of thermal states
Martyn, J., & Swingle, B. (2019) · Physical Review A · doi:10.1103/physreva.100.032107 · Cited by 66 · see citing works
Power-law decay exponents: A dynamical criterion for predicting thermalization
Távora, M., Torres-Herrera, E. J., & Santos, L. F. (2017) · Physical Review A · doi:10.1103/physreva.95.013604 · Cited by 53 · see citing works
- Authors
- Deutsch, J. M.
- Affiliations
- University of California, Santa Cruz (US)
- Corresponding author
- Deutsch, J. M.
- ORCID
- Deutsch, J. M.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1991-02-01
- Volume
- 43
- Issue
- 4
- Pages
- 2046-2049
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2086612234
- Cited by
- 2,860
- References
- 0
- Citations by year
- 2026: 167 · 2025: 283 · 2024: 239 · 2023: 246 · 2022: 247 · 2021: 252 · 2020: 276 · 2019: 223 · 2018: 204 · 2017: 180 · 2016: 153 · 2015: 121 · 2014: 85 · 2013: 56 · 2012: 37
- FWCI
- 1.28
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- quantum statistical mechanics, microcanonical distribution, time averages, closed quantum systems, energy eigenstates, expectation values
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
