Semiclassical theory of energy diffusive escape

TL;DR

This paper develops a semiclassical framework to describe thermal escape from metastable states, incorporating quantum tunneling effects and energy diffusion, bridging classical and quantum regimes.

Contribution

It introduces an extended semiclassical diffusion equation derived from quantum master equations, accounting for finite barrier transmission effects.

Findings

Decay rate captures thermal and quantum fluctuation interplay

Finite barrier transmission influences transition probabilities

Framework applicable across classical to deep quantum regimes

Abstract

Thermal escape out of a metastable well is considered in the weak friction regime, where the bottleneck for decay is energy diffusion, and at lower temperatures, where quantum tunneling becomes relevant. Within a systematic semiclassical formalism an extension of the classical diffusion equation is derived starting from a quantum mechanical master equation. In contrast to previous approaches finite barrier transmission also affects transition probabilities. The decay rate is obtained from the stationary non-equilibrium solution and captures the intimate interplay between thermal and quantum fluctuations above the crossover to the deep quantum regime.