Quantum Bernoulli noises approach to quantum master equations and applications to Ehrenfest-type theorems
Abstract
This paper investigates the regularity properties of quantum master equations with unbounded coefficients within the space of square-integrable complex-valued Bernoulli functionals. Initially, we demonstrate the existence of a unique regular solution to the linear stochastic Schrödinger equation driven by cylindrical Brownian motions. Subsequently, we establish the existence of regular solutions for the autonomous linear quantum master equation and provide a probabilistic representation of this solution in terms of the stochastic Schrödinger equation. Finally, by taking the expectation of some observables with respect to the solution of the quantum master equation, we derive a system of differential equations that describe the evolution of the mean values of certain quantum observables.
