Diffusion coefficient in periodic and random potentials

Transport and diffusion of particles on modulated surfaces is a nonequilibrium problem which is receiving a great deal of attention due to its technological applications, but analytical calculations are scarce. In earlier work, we developed a perturbative approach to begin to provide an analytic platform for predictions about particle trajectories over such surfaces. In some temperature and forcing regimes, we successfully reproduced results for average particle velocities obtained from numerical simulations. In this paper, we extend the perturbation theory to the calculation of higher moments, in particular the diffusion tensor and the skewness. Numerical simulations are used to check the domain of validity of the perturbative approach.