Stochastic resonance in multidimensional periodic potential

We study the mobility and diffusion of an underdamped Brownian particle moving in a two-dimensional (2D) periodic potential which subjects to a thermal white noise and a weak external driving force. Both the signal power amplification and the diffusion rate are calculated via Langevin simulations. It is shown that the stochastic resonance (SR) can be observed in the two dimension, namely, the output quantities as functions of the temperature show a nonmonotonic behavior, however, the SR cannot be obtained in the one dimension (1D). In the 2D potential, the height of dynamical barrier is decreased effectively along the direction of transport if the curvature of the potential at the barrier is less than that at the local minima. This leads to the SR condition being obeyed, i.e., the Kramers frequency over the barrier roughly matches the frequency of external signal.