Minimal irreversible quantum mechanics. The decay of unstable states

Brownian motion is modelled by a harmonic oscillator (Brownian particle) in teracting with a continuous set of uncoupled harmonic oscillators. The inte raction is linear in the coordinates and the momenta. The model has an anal ytical solution that is used to study the time evolution of the reduced den sity operator. It is derived in a closed form, in the one-particle sector o f the model. The irreversible behavior of the Brownian particle is describe d by a reduced density matrix. (C) 2000 Published by Elsevier Science B.V. All rights reserved.