Stochastic Schroedinger equations and applications to Ehrenfest-type theorems
Abstract
We study stochastic evolution equations describing the dynamics of open quantum systems. First, using resolvent approximations, we obtain a sufficient condition for regularity of solutions to linear stochastic Schroedinger equations driven by cylindrical Brownian motions applying to many physical systems. Then, we establish well-posedness and norm conservation property of a wide class of open quantum systems described in position representation. Moreover, we prove Ehrenfest-type theorems that describe the evolution of the mean value of quantum observables in open systems. Finally, we give a new criterion for existence and uniqueness of weak solutions to non-linear stochastic Schroedinger equations. We apply our results to physical systems such as fluctuating ion traps and quantum measurement processes of position.
Cite
@article{arxiv.1207.2939,
title = {Stochastic Schroedinger equations and applications to Ehrenfest-type theorems},
author = {Franco Fagnola and Carlos M. Mora},
journal= {arXiv preprint arXiv:1207.2939},
year = {2014}
}