Semiclassical theory of energy diffusive escape

Institut fu¨r Theoretische Physik, Universit¨at Ulm, Albert-Einstein-Allee 11, 89069 Ulm, Germany(Dated: August 11, 2009)Thermal escape out of a metastable well is considered in the weak friction regime, where the bot-tleneck for decay is energy diffusion, and at lower temperatures, where quantum tunneling becomesrelevant. Within a systematic semiclassical formalism an extension of the classical diffusion equationis derived starting from a quantum mechanical master equation. In contrast to previous approachesfinite barrier transmission also affects transition probabilities. The decay rate is obtained fromthe stationary non-equilibrium solution and captures the intimate interplay between thermal andquantum fluctuations above the crossover to the deep quantum regime.I. INTRODUCTION