## Preprint 2010-10

## Carlos M. Mora:

### Regularity of solutions to quantum master equations: A stochastic approach

### Abstract:

We develop the connections between stochastic processes and operator theory to describe the evolution of open quantum systems. Using stochastic Schrodinger equations, we study Markovian quantum master equations (QMEs for short) whose coefficients involve unbounded operators. QMEs are operator evolution equations that govern the dynamics of the density operators, which are positive operators of trace 1. Let the initial density operator be regular in the sense that the expected values with respect to it of a large class of unbounded operators are well-defined. Then we prove, under general conditions, that the solution of the QME remains regular all the time. Our analysis is mainly based on probabilistic representations of solutions to QMEs and adjoint quantum master equations (AQMEs). As by-products we obtain probabilistic interpretations of regular solutions to QMEs and the uniqueness of the solution for the AQME.

This preprint gave rise to the following definitive publication(s):

**Carlos M. MORA: ***Regularity of solutions to quantum master equations: A stochastic approach*. Annals of Applied Probability, vol. 41, 3B, pp. 1978-2012, (2013).