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From Quantum Dynamics to the Canonical Distribution: General Picture and a Rigorous Example
Open accessAbstract
Derivation of the canonical (or Boltzmann) distribution based only on quantum dynamics is discussed. Consider a closed system which consists of a mutually interacting subsystem and a heat bath, and assume that the whole system is initially in a pure state (which can be far from equilibrium) with small energy fluctuation. Under the ``hypothesis of equal weights for eigenstates,'' we derive the canonical distribution in the sense that, at sufficiently large and typical time, the (instantaneous) quantum mechanical expectation value of an arbitrary operator of the subsystem is almost equal to the desired canonical expectation value. We present a class of examples in which the above derivation can be rigorously established without any unproven hypotheses.
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Cited by
Many-Body Localization and Thermalization in Quantum Statistical Mechanics
Nandkishore, R., & Huse, D. A. (2015) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031214-014726 · Cited by 2,376
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics
D'Alessio, L., Kafri, Y., Polkovnikov, A., & Rigol, M. (2016) · Advances in Physics · doi:10.1080/00018732.2016.1198134 · Cited by 2,330
Quantum many-body systems out of equilibrium
Eisert, J., Friesdorf, M., & Gogolin, C. (2015) · Nature Physics · doi:10.1038/nphys3215 · Cited by 1,255
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
Goldstein, S., Lebowitz, J. L., Tumulka, R., & Zanghì, N. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.050403 · Cited by 709
Metadata
- Authors
- Tasaki, H.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1998-02-16
- Volume
- 80
- Issue
- 7
- Pages
- 1373-1376
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2093300793
- Cited by
- 425
- References
- 9
- FWCI
- 1.42
- Type
- journal article
- Language
- en
- Open access
- green
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