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.

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

References in corpus (7)

• Introduction to decoherence theory
• Theory of decoherence in a matter wave Talbot-Lau interferometer
• Master equation for a quantum particle in a gas
• Decoherence in a Talbot Lau interferometer: the influence of molecular scattering
• On the quantum description of Einstein's Brownian motion
• Monitoring approach to open quantum dynamics using scattering theory
• Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check

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• Monitoring derivation of the quantum linear Boltzmann equation
• Quantum Angular Momentum Diffusion of Rigid Bodies
• Fermi's golden rule, the origin and breakdown of Markovian master equations, and the relationship between oscillator baths and the random matrix model
• The Wigner Function of Ground State and One-Dimensional Numerics
• Stochastic simulation algorithm for the quantum linear Boltzmann equation
• Kinetic description of quantum Brownian motion
• Collisional decoherence of a tracer particle moving in one dimension
• Broken Detailed Balance and Entropy Production in CPTP Quantum Brownian Motion