Scanning tunnelling microscopic observations of long hops in the diffusion of Pb atoms on Ge surfaces were explained by the model for a Brownian particle in a periodic potential. The classical turnover theory for barrier-crossing predicted the occurrence of a large correlated hopping probability in the underdamped limit. This was consistent with experiment and was in agreement with simulations. The corresponding quantum theory predicted that, in the underdamped limit, the rate was dominated by tunnelling. This caused the quantum correlated hopping probability to vanish in this limit, and could be envisaged to be a new form of quantum localization.

E.Pollak, J.Bader, B.J.Berne, P.Talkner: Physical Review Letters, 1993, 70[21], 3299-302