# 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.

## Key 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.