Empirical information on quantum diffusion

The applicability of the quantum theory of diffusion to experiments on muon motion in selected metals is examined. Thereby the conventional picture of immediate self-trapping of the muon is employed. Small-polaron hopping of muons at intermediate temperatures seems to be established. There are indications for coherent diffusion in several metals at low temperatures. The quantitative behavior of the diffusion coefficient or transfer rate at low temperatures found in Al and Cu is in disgreement with the theoretical predictions.Many discussions with O. Hartmann, E. Karlsson, L.O. Norlin, T.O. Niinikoski, D. Richter, J.M. Welter, and A. Yaouanc are grateful acknowledged.