Unstable decay and state selection

TL;DR

This paper develops a general, accurate method using path-integral techniques to determine the probabilities of state selection in stochastic systems starting from unstable states, especially when multiple metastable states are involved.

Contribution

It introduces a simple, broadly applicable formula for state-selection probabilities in stochastic systems with unstable initial states.

Findings

Derived accurate formulas for state-selection probabilities

Applicable to a wide range of stochastic systems

Provides a new analytical tool for metastable state analysis

Abstract

We consider the problem of state selection for a stochastic system, initially in an unstable stationary state, when multiple metastable states compete for occupation. Using path-integral techniques we derive remarkably simple and accurate formulas for state-selection probabilities. The method is sufficiently general that it is applicable to a wide variety of problems.