Relaxation dynamics of a quantum Brownian particle in an ideal gas

Abstract

We show how the quantum analog of the Fokker-Planck equation for describing Brownian motion can be obtained as the diffusive limit of the quantum linear Boltzmann equation. The latter describes the quantum dynamics of a tracer particle in a dilute, ideal gas by means of a translation-covariant master equation. We discuss the type of approximations required to obtain the generalized form of the Caldeira-Leggett master equation, along with their physical justification. Microscopic expressions for the diffusion and relaxation coefficients are obtained by analyzing the limiting form of the equation in both the Schroedinger and the Heisenberg picture.

arXiv comment15 pages; to appear in Eur. Phys. J. Special Topics (2007)

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• Stochastic simulation algorithm for the quantum linear Boltzmann equation
• The Wigner Function of Ground State and One-Dimensional Numerics
• Quantum friction
• Comment on "Quantum linear Boltzmann equation with finite intercollision time"
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• Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion
• Collisional decoherence of a tracer particle moving in one dimension