Coherent states via decoherence.
Open accessAbstract
The rate at which pure initial states deteriorate into mixtures is computed for a harmonic oscillator interacting with an environment in thermal equilibrium. The decoherence process resulting from this interaction selects a set of states characterized by maximal stability (or minimal loss of predictive power) which can be quantified by the rate of increase in either linear or statistical entropy. In the weak coupling limit, coherent states are shown to produce the least entropy, thus becoming the natural counterparts of classical points in phase space.
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For some elementary systems, such as a harmonic oscillator, the motion of a narrowly-localised packet W_red(q,p,t) can trace out a thin 'tube' approximating a classical trajectory in phase space.
“For some elementary systems, such as a harmonic oscillator, the motion of a narrowly-localised packet W red ( q, p, t ) can trace out a thin 'tube' approximating a classical trajectory in phase space (Zurek et al . 1993).”
From De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial? (2008) · cites this paper as Zurek et al. 1993
The introduction (p. 1187) describes a stable Gaussian wave packet in an isolated harmonic oscillator and relates coherent states to classical points in phase space. This supports the harmonic-oscillator example, but the passages do not describe a reduced phase-space packet W_red(q,p,t) tracing a thin tube around a classical trajectory. (LLM, conf=0.78)
Experimental — accuracy not yet measuredThe linearised entropy is a computationally convenient but accurate approach to measure coherence.
“Alternatively, the linearised entropy is a computationally convenient but accurate approach to measure coherence 58,59 .”
From An open quantum systems approach to proton tunnelling in DNA (2022) · cites this paper as [58]
The opening passage (p. 1187) says the rate of increase in linear entropy can quantify stability during decoherence, supporting its use as a measure of coherence loss in the harmonic-oscillator model. It does not say linear entropy is computationally convenient or establish its accuracy as a general measure; the nearby statement about mathematical convenience refers to coherent states, not entropy. (LLM, conf=0.82)
Experimental — accuracy not yet measured
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Cites
Hu, B. L., Paz, J. P., & Zhang, Y. (1992) · Physical Review D · doi:10.1103/physrevd.45.2843 · Cited by 996 · see citing works
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Decoherence, the measurement problem, and interpretations of quantum mechanics
Schlosshauer, M. (2005) · Reviews of Modern Physics · doi:10.1103/revmodphys.76.1267 · Cited by 1,443 · see citing works
Importance of quantum decoherence in brain processes
Tegmark, M. (2000) · Physical Review E · doi:10.1103/physreve.61.4194 · Cited by 776 · see citing works
Dynamics of Loschmidt echoes and fidelity decay
Gorin, T., Prosen, T., Seligman, T. H., & Žnidarič, M. (2006) · Physics Reports · doi:10.1016/j.physrep.2006.09.003 · Cited by 623 · see citing works
Zurek, W. H. (2009) · Nature Physics · doi:10.1038/nphys1202 · Cited by 564 · see citing works
Self-citationPreferred 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
Self-citationConsciousness as a state of matter
Tegmark, M. (2015) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2015.03.014 · Cited by 183 · see citing works
An open quantum systems approach to proton tunnelling in DNA
Slocombe, L., Sacchi, M., & Al-Khalili, J. (2022) · Communications Physics · doi:10.1038/s42005-022-00881-8 · Cited by 122 · see citing works
Apparent wave function collapse caused by scattering
Tegmark, M. (1993) · Foundations of Physics Letters · doi:10.1007/bf00662807 · Cited by 87 · see citing works
Plaga, R. (1997) · Foundations of Physics · doi:10.1007/bf02550677 · Cited by 18 · see citing works
De Broglie-Bohm Pilot-Wave Theory: Many Worlds in Denial?
Valentini, A. (2008) · arXiv · doi:10.48550/arxiv.0811.0810
“For some elementary systems, such as a harmonic oscillator, the motion of a narrowly-localised packet Wred(q, p, t) can trace out a thin ‘tube’ approximating a classical trajectory in phase space (Zurek et al. 1993).”
Background
- Authors
- Zurek, W. H., Habib, S., & Paz, J. P.
- Affiliations
- Los Alamos National Laboratory (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 1993-03-01
- Volume
- 70
- Issue
- 9
- Pages
- 1187-1190
- ISSN
- 0031-9007 (ISSN-L)
- OpenAlex
- W2047856422
- Cited by
- 679
- References
- 1
- Citations by year
- 2026: 7 · 2025: 11 · 2024: 10 · 2023: 17 · 2022: 31 · 2021: 18 · 2020: 34 · 2019: 13 · 2018: 15 · 2017: 20 · 2016: 15 · 2015: 16 · 2014: 17 · 2013: 21 · 2012: 21
- FWCI
- 14.24
- Type
- journal article
- Language
- en
- Open access
- green
- zenodo.org
- Licence
- public-domain
- link.aps.org/licenses/aps-default-license (vor)
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- Zenodo (CERN European Organization for Nuclear Research) (submittedVersion, public-domain)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Quantum chaos and dynamical systems
- Keywords
- coherent states, decoherence, harmonic oscillator, open quantum systems, thermal environment, weak coupling, linear entropy, statistical entropy
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