Note on the quantum recurrence theorem
Abstract
An essential step in the proof of the quantum recurrence theorem is shown to follow from the Poincaré recurrence theorem of classical mechanics.Received 30 November 1977DOI:https://doi.org/10.1103/PhysRevA.18.2379©1978 American Physical Society
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For systems with a continuum spectrum, the survival probability of an arbitrary initial state vanishes identically at t→∞.
“For systems with a continuum spectrum, Fock and Krylov showed that the survival probability of an arbitrary initial state vanishes identically at t → ∞ [26].”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [26]
The survival probability S(t) vanishes at infinity as a consequence of the Riemann-Lebesgue lemma.
“That S ( t ) vanishes at infinity as a consequence of the Rieman-Lebesgue lemma [26].”
From Scrambling the spectral form factor: Unitarity constraints and exact results (2017) · cites this paper as [26]
Cites
Probability and Related Topics in Physical Sciences.
Busch, K. A., Kac, M., Uhlenbeck, G. E., Hibbs, A. R., & van der Pol, B. (1960) · American Mathematical Monthly · doi:10.2307/2309209 · Cited by 817 · see citing works
Bocchieri, P., & Loinger, A. (1957) · Physical Review · doi:10.1103/physrev.107.337 · Cited by 288 · see citing works
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Disturbing Implications of a Cosmological Constant
Dyson, L., Kleban, M., & Susskind, L. (2002) · Journal of High Energy Physics · doi:10.1088/1126-6708/2002/10/011 · Cited by 338 · see citing works
Scrambling the spectral form factor: Unitarity constraints and exact results
del Campo, A., Molina-Vilaplana, J., & Sonner, J. (2017) · Physical Review D · doi:10.1103/physrevd.95.126008 · Cited by 133 · see citing works
- Authors
- Schulman, L. S.
- Affiliations
- Technion – Israel Institute of Technology (IL)
- Corresponding author
- Schulman, L. S.
- ORCID
- Schulman, L. S.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1978-11-01
- Volume
- 18
- Issue
- 5
- Pages
- 2379-2380
- ISSN
- 0556-2791 (ISSN-L)
- OpenAlex
- W2019450960
- Cited by
- 74
- References
- 2
- Citations by year
- 2026: 6 · 2025: 5 · 2024: 5 · 2023: 2 · 2022: 3 · 2021: 4 · 2019: 1 · 2018: 3 · 2017: 7 · 2016: 6 · 2015: 4 · 2014: 3 · 2013: 4 · 2012: 3
- FWCI
- 0.00
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Keywords
- Poincaré recurrence theorem, classical mechanics, quantum mechanics
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