Fluctuations of Mean-Square Displacement in Presence of Traps: Non-Self-Averaging versus Ensemble Averaging

Abstract

We consider nonstationary diffusion in a medium with random traps-sinks. We study the self-averaging of the mean-square displacement (MSD) of the ensemble of N particles in the fluctuational long-time limit. We demonstrate that MSD of survivors is self-averaging with respect to the number of engaged particles N and is strongly non-self-averaging with respect to time t . To measure MSD of survivors with required accuracy at the required time of observation t 0 , the initial number of particles N 0 must be exponentially large in t 0 . Any N 0 , whatever large, will be insufficient at long enough time. In the formulation, when all particles, both survivors and trapped ones, contribute to MSD, we find self-averaging in N and non-strong non-self-averaging over t .