Relaxation in charge-transfer systems with very large tunnel splitting: A semiclassical stochastic approach

Electron transfer in strongly coupled systems, appropriate to mixed-valence compounds, is studied to explore the competition between electronic coherence and dissipation. A set of stochastic equations is derived for a spin-boson Hamiltonian with large tunneling coupling matrix element ~adiabatic regime! and strong system-bath-coupling. The bath dynamics is treated classically while the quantum character of the system is maintained. The bath dynamics is affected by the system dynamics, the effect being included by a mean-field description, valid for the adiabatic regime. Numerical solutions of the stochastic equations are presented and compared with exact quantum mechanical results. The numerical implementation of the method is straightforward and the long-time behavior of the system can be accessed. Analytic equilibrium solutions for the adiabatic regime are obtained, and we find good agreement between the long-time solution of the stochastic equations and these equilibrium solutions. We examine the dependence of the electronic population on the initial preparation of the bath and find that the proportion between oscillation ~coherence! and decay ~dissipation! is quite sensitive to this initial condition.