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.
Keywords
PhysicsFokker–Planck equationStatistical physicsStochastic differential equationGaussianMarkov processQuantum mechanicsGaussian noiseNoise (video)White noiseQuantumDifferential equationClassical mechanicsMathematics
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Publication Info
- Year
- 1991
- Type
- article
- Volume
- 43
- Issue
- 8
- Pages
- 4131-4142
- Citations
- 212
- Access
- Closed
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Cite This
Yoshitaka Tanimura,
Peter G. Wolynes
(1991).
Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bath.
Physical Review A
, 43
(8)
, 4131-4142.
https://doi.org/10.1103/physreva.43.4131
Identifiers
- DOI
- 10.1103/physreva.43.4131