The position non Markovian master equation

In this paper, we derive the non Markovian master equation (NMME) that correspond to position non Markovian stochastic Schrodinger equation (PNMSSE) in linear and non linear cases. In this case, using Nivokov property we derive four formulas of (NMME) for linear and non linear cases respectively. The functional derivative operator may depend on time and independent with respect to noise. Here, we determine the functional derivative of statistical operator. When the functional derivative operator depends on time and noise, one can calculate the perturbation and post Markovian perturbation for the functional operator, which exists in position non Markovian equation of motion (PNMEM). In order to explain our theory, we present a simple non Markovian example. Finally, we give the conclusion and the plan for future works. (C) 2016 Published by Elsevier Ltd.