A semiclassical theory for the diffusion of a particle moving on a periodic potential, coupled to a dissipative heat bath, is presented. The resulting expressions for the diffusion coefficient, mean squared path length, and hopping length distribution are valid for memory friction and provide a theory which goes uniformly from the underdamped to the strongly damped limit. In the underdamped limit, quantum tunneling and reflection cause the quantum diffusion coefficient to be lower than the classical, leading to an inverse isotope effect; the diffusion of D atoms should be faster than the diffusion of H atoms.

• Received 9 February 1994

DOI:https://doi.org/10.1103/PhysRevE.49.5098