Non-Markovian Dissipative Semiclassical Propagator of the Wigner Function

Abstract

We construct the Feynman and Vernon' theory of the influence functional in phase space using Marinov path-integrals. Based on this result we construct the phase-space version of the celebrated Ullersma-Caldeira-Leggett model, which allows us to derive the semiclassical propagating function of the Wigner function. We show that semiclassical propagation is done by pairs of deterministic coupled non-classical trajectories whose corresponding equations of motion contain memory terms which explicitly indicate the presence of non-Markovian effects. An alternative stochastic formulation is also discussed.