Path-integral approach to a semiclassical stochastic description of quantum dissipative systems

Abstract

The competition between coherence and relaxation in dissipative quantum systems is studied. For the spin-boson model, we previously obtained [J. Chem. Phys., in press] an expression for the system's equilibrium density matrix when the bath can be treated classically, and equations of motion when, in addition, the parameter coupling the system states, V, is large. The dynamical influence of the bath is then representable as a stochastic process that incorporates the feedback of the system into the bath. In this work, we use path integral methods to explore our approach in the context of a system described by a potential energy surface. An effective stochastic Hamiltonian for the system is found. Using the discrete variable representation, we obtain a set of stochastic integro-differential equations for the matrix elements of the reduced system density operator. The two-state approximation is explored numerically and the results are compared with those obtained with other methods.