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

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  • Pronin, K.A.

Abstract

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 ≈expconstd,1td/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.

Suggested Citation

  • Pronin, K.A., 2022. "Non-self-averaging of the concentration: Trapping by sinks in the fluctuation regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    • Handle: RePEc:eee:phsmap:v:596:y:2022:i:c:s0378437122001819
    DOI: 10.1016/j.physa.2022.127180
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