Quantum motional narrowing

Abstract

We study the motional narrowing of a spin-1/2 particle diffusing in a solid with random magnetic fields at sites. The crystal environment is modeled in a simple way interpolating between zero temperature and high temperatures. A two-site problem is solved exactly and the findings are in accordance with expectation. In the N-site problem the low temperature spin relaxation is found to be in striking contrast to the classical theory of motional narrowing. The relation to pSR experiments is discussed.

Muon Diffusion and Quantum-Motional Narrowing

“…The essential question is now whether the spin still relaxes according to (11) in the quantum regime such that the diffusion coefficient can be directly extracted from pSR-measurements. We have not managed to solve the integral (8) exactly for y < W. An approximate analytical calculation [18] yielded the y + 0 value -Lo (0, O)/W = 0.5, 1.63, 1.06 in d = 1,2,3, respectively. We have also computed L, (0,O) numerically in d = 2.…”

“…We have also calculated the spin relaxation at zero temperature, by means of a second-order cumulant expansion [18]. That calculation also resulted in a lifetime Finally consider the pSR-experiment on KC1 [5].…”