Muon diffusion and quantum-motional narrowing

We study the motional narrowing of a spin-(1/2) particle, diffusing in a solid with random magnetic fields at sites. At high temperatures, where the particle performs random walk between sites, the spin relaxes according to the well-known classical theory of motional narrowing. At low temperatures, where the particle is delocalized, we show that the classical theory breaks down. In this quantum regime we show that the tunneling amplitude sets the scale for spin relaxation, but not the diffusion rate as previously thought