Scanning tunneling microscopy observations of long hops in the diffusion of Pb atoms on Ge surfaces are explained by the model of a Brownian particle in a periodic potential. The classical turnover theory for barrier crossing predicts a large correlated hopping probability in the underdamped limit, consistent with experiment and in agreement with simulations. The corresponding quantum theory predicts that in the underdamped limit the rate is dominated by tunneling. This causes the quantum correlated hopping probability to vanish in this limit and may be thought of as a new form of quantum localization.

• Received 15 December 1992

DOI:https://doi.org/10.1103/PhysRevLett.70.3299