2002•Journal of Physics A Mathematical and GeneralOpen access

Langevin equation with back-reaction

Petr Chvosta, František Slanina

Abstract

We investigate a simple model of an overdamped Brownian particle in a harmonic potential. The dynamics is described by a Langevin equation with a two-valued stochastic force. The properties of the Langevin force are controlled through a back-reaction mechanism by the particle dynamics. Our analysis reveals two quite different dynamical regimes. The low-temperature regime exhibits a dynamically induced ergodicity breaking. However, an arbitrarily small periodic perturbation is capable of bringing the system back to ergodicity.

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Key concepts: Ergodicity, Langevin equation, Brownian dynamics, Langevin dynamics, Brownian motion, Statistical physics, Physics, Perturbation (astronomy)