Non-Markovian stochastic Schrodinger equation

We report a study of a stochastic Schrodinger equation corresponding to the Redfield master equation with slipped initial conditions, which describes the dynamics of a slow subsystem weakly coupled to a fast thermal bath. Using the projection-operator method of Feshbach, we derive a non-Markovian stochastic Schrodinger equation of the generalized Langevin type, which simulates the time evolution of the quantum wave functions of the subsystem driven by the fluctuating bath. For delta-correlated baths, the non-Markovian stochastic Schrodinger equation reduces to the previously derived Markovian one. Numerical methods are proposed to simulate the time evolution under our non-Markovian stochastic Schrodinger equation. These methods are illustrated with the spin-boson model. (C) 1999 American Institute of Physics. [S0021-9606(99)50237-7].