Resonant diffusion in periodic systems with memory

The diffusion coefficient D in a periodic potential with exponentially decaying memory friction is studied by the matrix-continued-fraction method. It is shown that, at sufficiently high static friction, D presents a maximum as a function of the memory decay parameter. This maximum is due to the interplay between two oscillatory motions, the first induced by the periodic potential and the second by the memory. The maximum appears when the frequencies of these motions are in resonance.