QUANTUM BROWNIAN-MOTION

We study the behavior of a subsystem (harmonic oscillator) in contact with a thermal reservoir (finite set of uncoupled harmonic oscillators ). We solve exactly the eigenvalue problem and obtain the temporal evo lution of the dynamical variables of interest. We show how the subsyst em goes to equilibrium and give quantitative estimates of the Poincare recurrence times. We study the behavior of the subsystem mean occupat ion number in the limit of a dense bath and compare it with the expect ed exponential decay law.