Optimum Paths for Systems Subject to Internal Noise

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.