Quantum Kramers' equation for energy diffusion and barrier crossing dynamics in the low friction regime

摘要

Based on a true phase space probability distribution function and an ensembleaveraging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)]a non-Markovian quantum Kramers' equation to derive the quantum ratecoefficient for barrier crossing due to thermal activation and tunneling in theintermediate to strong friction regime. We complement and extend this approachto weak friction regime to derive quantum Kramers' equation in energy space andthe rate of decay from a metastable well. The theory is valid for arbitrarytemperature and noise correlation. We show that depending on the nature of thepotential there may be a net reduction of the total quantum rate below itscorresponding classical value which is in conformity with earlier observation.The method is independent of path integral approaches and takes care of quantumeffects to all orders.