QUASI-CLASSICAL EQUATIONS OF MOTION FOR NONLINEAR BROWNIAN SYSTEMS

Following the formalism of Gell-Mann and Hartle, phenomenological equations of motion are derived from the decoherence functional of quantum mechanics, using a path-integral description. This is done explicitly for the case of a system interacting with a ''bath'' of harmonic oscillators whose individual motions are neglected. The results are compared to the equations derived from the purely classical theory. The case of linear interactions is treated exactly, and nonlinear interactions are also compared, using classical and quantum perturbation theory.