Stochastic Schroedinger equations and applications to Ehrenfest-type theorems

TL;DR

This paper develops mathematical tools for analyzing open quantum systems using stochastic Schroedinger equations, establishing conditions for solution regularity, well-posedness, and Ehrenfest-type theorems, with applications to physical systems like ion traps.

Contribution

It introduces new criteria for solution existence and uniqueness in stochastic Schroedinger equations and applies these to physical quantum systems.

Findings

Established regularity conditions for solutions to linear stochastic Schroedinger equations.

Proved well-posedness and norm conservation for a broad class of open quantum systems.

Derived Ehrenfest-type theorems describing the evolution of quantum observables.

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.