Non-self-averaging of the concentration: Trapping by sinks in the fluctuation regime.

We consider the nonstationary diffusion of particles in a medium with static random traps-sinks. We address the problem of self-averaging of the particle concentration (or survival probability) in the fluctuation regime in the long-time limit. We demonstrate that the concentration of surviving particles and their trapping rate are strongly non-self-averaging quantities. Their reciprocal standard deviations grow with time as the stretched exponentials ≈ exp const d , 1 t d / d + 2 . In higher dimensions d , no tendency to restore self-averaging is revealed. Exponential non-self-averaging is preserved for d = ∞. The 1D solution and the leading exponential terms in higher dimensions are exact. The strong non-self-averaging of the concentration signifies the poor reproducibility of single measurements in different samples, both in experiments and simulations. • Survival probability of particles is strongly non-self-averaging in presence of sinks. • Its reciprocal fluctuations grow with time as a stretched exponential. • In high dimensions strong non-self-averaging is retained. • The leading exponential terms of the solutions are exact. • Reaction rate or trapping intensity is also strongly non-self-averaging. [ABSTRACT FROM AUTHOR]