Relaxation dynamics of a quantum Brownian particle in an ideal gas
Dipartimento di Fisica dell'Università di Milano and INFN, Sezione di Milano, via Celoria 16, 20133 Milan, Italy
2 Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 Munich, Germany
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 Schrödinger and the Heisenberg picture.
© EDP Sciences, Springer-Verlag, 2007