Mean field approximation for the stochastic Schrödinger equation

Abstract

A stochastic mean-field (SMF) approach to nonadiabatic molecular simulations is introduced. Based on the quantum-classical mean-field approximation, SMF extents the classical model of the environment to incorporate its quantum properties. SMF differs from the ordinary mean-field method by the presence of additional terms in the Schrödinger equation that are due to the system-environment interaction. SMF resolves the two major drawbacks of mixed quantum-classical models. First, decoherence effects in the quantum subsystem are rigorously included. Present in all open systems, decoherence is crucial for nonadiabatic transitions taking place in condensed media. Second, the correct branching of the quantum-classical trajectories is achieved. In earlier approaches, the correct branching of the trajectories was attained via ad hoc surface hopping procedures, which experienced the hop rejection problem and could produce unfavorable classical trajectories in regions of nonadiabatic transitions depending on the quantum basis. It is shown that the correct branching of the trajectories is a direct consequence of decoherence. It is argued that the hop rejection problem disappears in SMF. The decoherence operator is discussed in detail, and the properties of the SMF method are illustrated with model simulations.