Inertial effects and long-term transport properties of particle motion in washboard potential

The motion of non-interacting Brownian particles in the washboard potential is investigated in inertial regimes, when the overdamped approximation does not yield accurate predictions. The analysis is based on homogenization methods, deriving closed-form expressions for the long-term transport properties, i.e. effective velocity and diffusion coefficient. Different reduced models of increasing complexity, improving the overdamped approximation, are developed starting from the basic assumption that the velocity variable can be split into an “almost” deterministic and a fully stochastic contribution. The almost deterministic velocity term can be estimated from a fully deterministic or from a stochastic slow inertial manifold. The latter approach provides accurate predictions for all the asymptotic transport properties.