Non-Markovian stochastic Liouville equation and its Markovian representation

Abstract

The non-Markovian variant of the stochastic Liouville equation (SLE) is studied within the continuous time random walk approach (CTRWA). The CTRWA-based non-Markovian SLE is shown to be equivalently represented by the corresponding conventional Markovian SLE. This Markovian representation provides a rigorous method for deriving the non-Markovian SLE and allows for a physically clear interpretation of the specific features of this SLE. It also enables one to develop convenient non-Markovian models useful for applications, some of which are discussed in detail. Special attention is given to the discussion of anomalous long-tailed CTRW processes and non-Markovian SLE. The obtained results are applied to the analysis of the effect of rate fluctuations on chemical reaction kinetics. It is shown, in particular, that the anomalous fluctuations not only influence the reaction rate but also change the reaction kinetics itself.