Spin depolarization by random walks in lattice gases

Abstract

The transverse spin depolarization of spin particles that perform tracer diffusion in lattice gases is studied. The lattice gas particles are noninteracting except that double occupancy of lattice sites is forbidden. The depolarization function P(t) is discussed for a model in which random local spin–rotation frequencies taken from a Gaussian probability distribution of width σ are associated with the lattice sites. The results of simulations of P(t) in dimensions d=1, 2, and 3 are compared with recent results for simple, uncorrelated random walks and analyzed by scaling expressions. In d=2 and 3, the dependence of the decay constant of the observed exponential polarization decay on σ and c, the concentration of the lattice gas particles, can be described by a simple scaling law involving the tracer-diffusion correlation factor. In d=1, where the tracer diffusion is anomalously slow, a faster than simple-exponential decay is found at large times t. A theory based on the scaling behavior of the distribution of sites visited in d=1 allows for a qualitative understanding of the observed polarization decay.