Non-Gaussian spin dephasing

We address spin dephasing induced by stochastic transitions between different precession frequencies. A very famous analytical approximation is the Gaussian approximation presented by [Anderson and Weiss, Rev. Mod. Phys. 25, 269 (1953)]. It states that independent from the transition dynamics, a Gaussian frequency distribution implies a Gaussian distribution of the phase angles, which provides a simple analytical result for the transverse magnetization decay. In contrast we find that (i) the assumption of Gaussian dephasing restricts the stochastic dynamics to a very limited class (ii) the Anderson-Weiss model is applicable only in a special case of fluctuations, i.e., if and only if the Green's function G(ω2,ω1,Δt) describing the transition probability between two frequencies ω1→ω2 is Gaussian, and (iii) the exact time course of magnetization decay is dependent on the relaxation time in the motional narrowing limit and the correlation time describing the correlation function of the local frequencies. In contrast to previous publications, we conclude that a Gaussian equilibrium distribution of local frequencies does not imply a Gaussian-distributed phase angle. The general theory is illustrated by calculating the Green's function of the transition dynamics for a stochastic process in the strong collision approximation. The result is highly relevant for describing relaxation processes in the presence of local field inhomogeneities