APPROXIMATE ANALYTICAL SOLUTION OF THE JUMP RATE PROBLEM IN A SYMMETRICAL WELL WITH SPATIALLY VARYING FRICTION

The jump rate problem for a particle in a periodic potential is studie d by an analytical solution of the Klein-Kramers equation. The very ge neral case of a position-dependent friction is considered. The low-fri ction solution is obtained extending to the symmetric well the Wiener- Hopf method developed by Mel'nikov and Meshkov in the study of the esc ape rate from a metastable well with position-independent friction. An analytical expression for the jump rate, valid in the whole damping r ange, is obtained by a multiplicative bridging formula. Explicit resul ts are presented for a cosine potential and a cosine friction and the low and high damping limits are discussed.