Corrections to Einstein's relation for Brownian motion in a tilted periodic potential

Abstract

In this paper we revisit the problem of Brownian motion in a tilted periodic potential. We use homogenization theory to derive general formulas for the effective velocity and the effective diffusion tensor that are valid for arbitrary tilts. Furthermore, we obtain power series expansions for the velocity and the diffusion coefficient as functions of the external forcing. Thus, we provide systematic corrections to Einstein's formula and to linear response theory. Our theoretical results are supported by extensive numerical simulations. For our numerical experiments we use a novel spectral numerical method that leads to a very efficient and accurate calculation of the effective velocity and the effective diffusion tensor.

29 pages, 7 figures, submitted to the Journal of Statistical Physics

References in corpus (1)

• The modified Sutherland--Einstein relation for diffusive nonequilibria

Cited by in corpus (10)

• Diffusion in a biased washboard potential revisited
• Error Analysis of Modified Langevin Dynamics
• Arcsine Law and Multistable Brownian Dynamics in a Tilted Periodic Potential
• Langevin dynamics with space-time periodic nonequilibrium forcing
• Noise-induced transitions in rugged energy landscapes
• Numerical Methods for Computing Effective Transport Properties of Flashing Brownian Motors
• Velocity multistability vs ergodicity breaking in a biased periodic potential
• Numerical computations of geometric ergodicity for stochastic dynamics
• Mass transport in Fokker-Planck equations with tilted periodic potential
• Conundrum of weak noise limit for diffusion in a tilted periodic potential