Quantum Smoluchowski equation for driven systems
arXiv:0904.0950 · doi:10.1103/PhysRevE.80.042101
Abstract
We consider a driven quantum harmonic oscillator strongly coupled to a heat bath. Starting from the exact quantum Langevin equation, we use a Green's function approach to determine the corresponding semiclassical equation for the Wigner phase space distribution. In the limit of high friction, we apply Brinkman's method to derive the quantum Smoluchowski equation for the probability distribution in position space. We further determine the range of validity of the equation and discuss the special case of a Brownian parametric oscillator.
4 pages
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- On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
- Low-temperature quantum fluctuations in overdamped ratchets
- Heat transport in overdamped quantum systems