Measurement of persistence in 1D diffusion

Abstract

Using a novel NMR scheme we observed persistence in 1-D gas diffusion. Analytical approximations and numerical simulations have indicated that for an initially random array of spins undergoing diffusion, the probability p(t) that the average spin magnetization in a given region has not changed sign (i.e., ``persists'') up to time t follows a power law t^{-\theta}, where \theta\ depends on the dimensionality of the system. Using laser-polarized ^{129}Xe gas, we prepared an initial ``quasirandom'' 1D array of spin magnetization and then monitored the ensemble's evolution due to diffusion using real-time NMR imaging. Our measurements are consistent with analytical and numerical predictions of \theta \approx 0.12.