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

Claude-Alain Pillet (1, 2, 3)

1 CPT - Centre de Physique Théorique - UMR 6207
2 Intitut für Theoretische Physik
3 CPT - Centre de Physique Théorique - UMR 7332

We consider the quantum dynamics of a particle in a time dependent potential V(t) assuming it to be a Markovian random function of time. We derive a formula for the density matrix at time t 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.

Mots clés: quantum mechanics; random potential; disordered system; scattering theory

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Algèbres quantiques [math.QA]; Théorie spectrale [math.SP]

Claude-Alain Pillet. Some results on the quantum dynamics of a particle in a Markovian potential. Communications in Mathematical Physics, 1985, 102, pp.237-254. ⟨10.1007/BF01229379⟩. ⟨hal-00005467⟩