Some results on the quantum dynamics of a particle in a Markovian potential

Abstract

We consider the quantum dynamics of a particle in a time dependent potentialV(t), assuming it to be a Markovian random function of time. We derive a formula for the density matrix at timet averaged over the realisations of the potential. We then obtain a kind of RAGE theorem for the time evolution of compact observables, and some information on the phase space behaviour of the system.