Langevin dynamics with space-time periodic nonequilibrium forcing

Abstract

We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and Martinez. In the hyperbolic scaling, a nontrivial average velocity can be observed even if the external forcing vanishes in average. More surprisingly, an average velocity in the direction opposite to the forcing may develop at the linear response level -- a phenomenon called negative mobility. The diffusive limit of the non-equilibrium Langevin dynamics is also studied using the general methodology of central limit theorems for additive functionals of Markov processes. To apply this methodology, which is based on the study of appropriate Poisson equations, we extend recent results on pointwise estimates of the resolvent of the generator associated with the Langevin dynamics. Our theoretical results are illustrated by numerical simulations of a two-dimensional system.

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• The computation of averages from equilibrium and nonequilibrium Langevin molecular dynamics
• Level 2.5 large deviations for continuous time Markov chains with time periodic rates
• Frequency and field-dependent response of confined electrolytes from Brownian dynamics simulations
• Error Analysis of Modified Langevin Dynamics
• Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions
• Ergodic properties of quasi-Markovian generalized Langevin equations with configuration dependent noise and non-conservative force
• Convergence of Nonequilibrium Langevin Dynamics for Planar Flows