Nonmonotonic behavior of mobility in a multidimensional overdamped periodic system

The mobility motion of an overdamped particle subjected to a thermal white noise in a multidimensional coupled periodic potential tilted by a constant force is studied. An approximate expression for the mean velocity of the particle is obtained on the assumption that nontransport variables play the roles of parameters, and the theoretical prediction is compared with a Langevin simulation. It is observed that the two-dimensional mean velocity can be a nonmonotonic function of the temperature when the curvature of the potential at the barriers is less than that at local minima. Moreover, the peak of mean velocity drifts toward low temperatures and becomes sharper if a third degree of freedom is introduced.