A heisenberg equation-of-motion derivation of stochastic Schrödinger equations for non-Markovian open systems

A method is presented by which the stochastic Schrödinger equation can be derived for systems coupled to a reservoir in cases in which the system-reservoir interaction is non-Markovian, and under the condition that the initial system reservoir state is decorrelated. The method is based on a Heisenberg equation of motion approach applied in conjunction with a technique of dealing with system-reservoir interactions introduced by Mollow in his treatment of the AC Stark effect. The general Diósi-Strunz stochastic Schrödinger equation is regained, but the method developed here offers a different perspective on obtaining the final form of this equation for specific applications. The method is illustrated for a damped two level atom, a driven damped harmonic oscillator, and quantum Brownian motion.