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.
Publié le : 1985-07-05
Classification:
quantum mechanics,
random potential,
disordered system,
scattering theory,
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph],
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph],
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[MATH.MATH-QA]Mathematics [math]/Quantum Algebra [math.QA],
[MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP]
@article{hal-00005467,
author = {Pillet, Claude-Alain},
title = {Some results on the quantum dynamics of a particle in a Markovian potential},
journal = {HAL},
volume = {1985},
number = {0},
year = {1985},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00005467}
}
Pillet, Claude-Alain. Some results on the quantum dynamics of a particle in a Markovian potential. HAL, Tome 1985 (1985) no. 0, . http://gdmltest.u-ga.fr/item/hal-00005467/