Long jumps in the strong-collision model

The jump-length probability distribution for a classical particle diffusing in a periodic potential is calculated in the framework of a strong-collision model, where each collision of the particle with the thermal bath reequilibrates the velocity. Exact numerical results are obtained by the matrix-continued-fraction method, and two different analytical approximations are developed. In the first approximations it is assumed that an activated particle is always retrapped in the cell where it suffers the first collision; in the second approximation it is assumed that only the collisions giving a final total energy which is lower than the activation barrier are effective for retrapping. This second analytical approximation is in excellent agreement with the numerical data.