Langevin dynamics with a tilted periodic potential

Abstract

We study a Langevin equation for a particle moving in a periodic potential in the presence of viscosity $\gamma$ and subject to a further external field $\alpha$. For a suitable choice of the parameters $\alpha$ and $\gamma$ the related deterministic dynamics yields heteroclinic orbits. In such a regime, in absence of stochastic noise both confined and unbounded orbits coexist. We prove that, with the inclusion of an arbitrarly small noise only the confined orbits survive in a sub-exponential time scale.

38 pages, 6 figures

References in corpus (2)

• Pathwise description of dynamic pitchfork bifurcations with additive noise
• From ballistic to diffusive behavior in periodic potentials

Cited by in corpus (1)

• On the waiting time distribution for continuous stochastic systems