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Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bath
Abstract
The quantum Fokker-Planck equation for a Gaussian-Markovian bath is deduced by applying a method proposed by Tanimura and Kubo [J. Phys. Soc. Jpn. 58, 101 (1989)]. The results are expressed in the form of simultaneous differential equations in terms of density operators and can treat strong system-bath interactions where the correlated effects of the noise play an important role. The classical Fokker-Planck equation for a Gaussian-Markovian noise is obtained by performing the Wigner transformation, and its equilibrium state is shown to be the Maxwell-Boltzmann distribution. The method is convenient for numerical studies. Calculations for quantum-system harmonic oscillators and the double-well potential problems are demonstrated for cases of Gaussian-white noise and Gaussian-Markovian noise.
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“The set of hierarchy equations derived here provides an exact treatment of decoherence, and employs neither the rotating-wave, Born, nor Markovian approximations.”
From Quantum speed limits in open systems: Non-Markovian dynamics without rotating-wave approximation (2015) · cites this paper as [21]
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Metadata
- Authors
- Tanimura, Y., & Wolynes, P. G.
- Affiliations
- University of Illinois Urbana-Champaign (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 1991-04-01
- Volume
- 43
- Issue
- 8
- Pages
- 4131-4142
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W1976387111
- Cited by
- 224
- References
- 25
- Citations by year
- 2026: 6 · 2025: 8 · 2024: 8 · 2023: 7 · 2022: 5 · 2021: 10 · 2020: 9 · 2019: 12 · 2018: 9 · 2017: 5 · 2016: 13 · 2015: 9 · 2014: 9 · 2013: 10 · 2012: 5
- FWCI
- 1.83
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- PubMed (publishedVersion)
- Topics
- 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
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
- Keywords
- quantum Fokker-Planck equation, system-bath interaction, Wigner transformation, density matrix, correlated noise, Maxwell-Boltzmann distribution, harmonic oscillator, double-well potential, Gaussian white noise, open quantum systems
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