Decoherence, chaos, and the correspondence principle
Open accessAbstract
We present evidence that decoherence can produce a smooth quantum-to-classical transition in nonlinear dynamical systems. High-resolution tracking of quantum and classical evolutions reveals differences in expectation values of corresponding observables. Solutions of master equations demonstrate that decoherence destroys quantum interference in Wigner distributions and washes out fine structure in classical distributions, bringing the two closer together. Correspondence between quantum and classical expectation values is also reestablished.
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Even in the chaotic case, for some examples, the evolution of W_red(q,p,t) approximates the evolution of a classical phase-space distribution W_class(q,p,t), where both distributions rapidly delocalise.
“On the other hand, at least for some examples it can be shown that, even in the chaotic case, the evolution of W red ( q, p, t ) approximates the evolution of a classical phase-space distribution W class ( q, p, t ) (a Liouville flow with a diffusive contribution from the environment), where both distributions rapidly delocalise (Habib et al . 1998; Zurek 2003, pp. 745-47).”
From De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial? (2008) · cites this paper as Habib et al. 1998
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Cites
On the generators of quantum dynamical semigroups
Lindblad, G. (1976) · Communications in Mathematical Physics · doi:10.1007/bf01608499 · Cited by 7,548 · see citing works
Hu, B. L., Paz, J. P., & Zhang, Y. (1992) · Physical Review D · doi:10.1103/physrevd.45.2843 · Cited by 996 · see citing works
Consistent interpretations of quantum mechanics
Omnès, R. (1992) · Reviews of Modern Physics · doi:10.1103/revmodphys.64.339 · Cited by 648 · see citing works
Preferred States, Predictability, Classicality and the Environment-Induced Decoherence
Zurek, W. H. (1993) · Progress of Theoretical Physics · doi:10.1143/ptp/89.2.281 · Cited by 525 · see citing works
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Research works printed but not linked: 4
- [2]G. Casati et al , in Stochastic Behavior in Classical and Quantum Hamiltonian Systems , G. Casati and J. Ford, eds. (Springer, New York, 1979); F. Haake, M. Ku´ s, and R. Scharf, Z. Phys. B 65 , 381 (1987); J. Ford and G. Mantica, Am. J. Phys. 60 , 1086 (1992); see also G. Casati and B. Chirikov, Quantum Chaos (Cambridge University Press, Cambridge, 1995).
- [6]W. H. Zurek and J. P. Paz, in Quantum Measurements, Irreversibility, and the Physics of Information , P. Busch et al , eds. (World Scientific, Singapore, 1993); Phys. Rev. Lett. 72 , 2508 (1994); Physica D83 , 300 (1995).
- [8]W. H. Zurek, Phys. Rev. D 26 , 1982 (1982); Phys. Today 44 , 36 (1991); Prog. Theor. Phys. 89 , 281 (1993); E. Joos and H. D. Zeh, Z. Phys. B 59 , 223 (1985); R. Omn´ es, Rev. Mod. Phys. 64 , 339 (1992); M. Gell-Mann and J. B. Hartle, Phys. Rev. D 47 , 3345 (1993); D. Giulini et al Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, New York, 1996).
- [12]G. Lindblad, Commun. Math. Phys. 48 , 119 (1976); A. O. Caldeira and A. J. Leggett, Physica 121A , 587 (1983); W. G. Unruh and W. H. Zurek, Phys. Rev. D 40 , 1071 (1989); B. L. Hu, J. P. Paz, and Y. H. Zhang, ibid 45 , 2843 (1992); D. F. Walls and G. J. Milburn, Quantum Optics (Springer, New York, 1994).
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De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?
Valentini, A. (2008) · arXiv · doi:10.48550/arxiv.0811.0810
“p;t) approximates the evolution of a classical phase-space distribution W class(q;p;t) (a Liouville ow with a diusive contribution from the environment), where both distributions rapidly delocalise (Habib et al. 1998; Zurek 2003, pp. 745{47).14 In pilot-wave theory, a mixed quantum state is described by a preferred de…”
Background
- Authors
- Habib, S., Shizume, K., & Zurek, W. H.
- Affiliations
- Los Alamos National Laboratory (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1998-05-18
- Volume
- 80
- Issue
- 20
- Pages
- 4361-4365
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2036196303
- Cited by
- 252
- References
- 4
- Citations by year
- 2026: 7 · 2025: 7 · 2024: 12 · 2023: 7 · 2022: 3 · 2021: 5 · 2020: 4 · 2019: 9 · 2018: 9 · 2017: 8 · 2016: 6 · 2015: 5 · 2014: 7 · 2013: 9 · 2012: 5
- FWCI
- 11.68
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- 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 Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- decoherence, quantum-to-classical transition, nonlinear dynamical systems, chaos, correspondence principle, Wigner function, quantum interference, master equation, classical limit, expectation values
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