Quantum Smoluchowski equation: A systematic study

Abstract

The strong friction regime at low temperatures is analyzed systematically starting from the formally exact path integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher order quantum corrections to the original quantum Smoluchowski equation [PRL 87, 086802 (2001), PRL 101, 11903 (2008)] can be derived. Drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them. It is shown that the inclusion of higher order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly.