Optimum Paths for Systems Subject to Internal Noise

TL;DR

This paper develops a path-integral framework to analyze the stochastic dynamics of systems with internal coloured noise, revealing unique singular behaviors in the overdamped limit and generalizing to various noise types.

Contribution

It introduces a novel path-integral formulation for internal coloured noise and characterizes the optimal paths via third order differential equations, highlighting singular overdamped limits.

Findings

Optimal paths are governed by third order differential equations.

Overdamped limit is singular for systems with internal coloured noise.

Formalism applies to various noise processes beyond exponential correlation.

Abstract

We formulate the stochastic dynamics of a particle subject to internal non-white (coloured) noise in terms of path-integrals. In the simplest case, where the noise is exponentially correlated, the weak-noise limit is characterised by optimum paths which are given by third order differential equations. In contrast to systems subject to white noise or external coloured noise, the overdamped limit for these systems is singular. We analyse the origin of this behaviour. The whole formalism is generalised to more general noise processes and the essential features are shown to be similar to the exponentially correlated case.