Rare Transition Events in Nonequilibrium Systems with State-Dependent Noise: Application to Stochastic Current Switching in Semiconductor Superlattices

TL;DR

This paper develops a geometric method to analyze rare noise-induced transitions in nonequilibrium systems with state-dependent noise, applying it to electronic transport in semiconductor superlattices to understand switching behavior near bifurcations.

Contribution

It introduces a generalized algorithm for computing maximum likelihood transition paths in systems with state-dependent noise, extending previous mathematical frameworks.

Findings

Mean lifetime scales as log< T > ∝ |V_th - V|^{3/2} near bifurcation

Method successfully applied to model of semiconductor superlattices

Provides insights into electric field transition mechanisms

Abstract

Using recent mathematical advances, a geometric approach to rare noise-driven transition events in nonequilibrium systems is given, and an algorithm for computing the maximum likelihood transition curve is generalized to the case of state-dependent noise. It is applied to a model of electronic transport in semiconductor superlattices to investigate transitions between metastable electric field distributions. When the applied voltage $V$ is varied near a saddle-node bifurcation at $V_th$, the mean life time $<T>$ of the initial metastable state is shown to scale like $log<T> \propto |V_th - V|^{3/2}$ as $V\to V_th$.