Quantum diffusion of positive muons and muonium atoms

The diffusion properties of the positive muon (μ+) and muonium (Mu) as light isotopes of protons and atomic hydrogen in crystalline solids are reported. It is demonstrated that they are excellently described as quantum tunneling of small polarons interacting with a phonon/electron bath. As one of the most dramatic manifestations of the quantum nature, the tunneling probability increases with decreasing temperature, which is in sharp contrast with the case of thermally activated diffusion. Moreover, the recent experimental study at very low temperature (below 0.1 K) strongly suggests that Mu is in a delocalized state analogous to the Bloch state for conduction electrons.