Dissipation in a quantum-mechanical system

We consider a model of a dissipative quantum-mechanical system consisting of weakly coupled quantum and classical subsystems. The classical subsystem is assumed to be infinite, and thus serves as a means to transfer the energy of the quantum subsystem to the infinity (actually, to dissipate the energy). The quantum-classical coupling is treated in the spirit of the mean-field approximation. Solving the equations for the classical subsystem explicitly an effective dissipative Schrödinger equation for the quantum subsystem is obtained. The proposed method is illustrated by calculating the shape of the nonlinear resonance.