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 p
article is obtained on the assumption that nontransport variables play the
roles of parameters, and the theoretical prediction is compared with a Lang
evin simulation. It is observed that the two-dimensional mean velocity can
be a nonmonotonic function of the temperature when the curvature of the pot
ential at the barriers is less than that at local minima. Moreover, the pea
k of mean velocity drifts toward low temperatures and becomes sharper if a
third degree of freedom is introduced.