https://doi.org/10.1140/epjb/s10051-022-00350-9
Regular Article - Statistical and Nonlinear Physics
Ensemble averaging versus non-self-averaging: survival probability in the presence of traps-sinks
Institute of Biochemical Physics, Russian Academy of Sciences, Kosygin Street 4, 119 334, Moscow, Russia
Received:
16
October
2021
Accepted:
6
May
2022
Published online:
25
May
2022
We consider nonstationary diffusion in a medium with static random traps-sinks. We address the problem of self-averaging of the survival probability (or concentration) of the ensemble of 
particles in the fluctuation regime in the long-time limit. We demonstrate that the relative standard deviation of the survival probability decreases with the number of engaged particles as 
and increases with time as a stretched exponential 
. Therefore, the survival probability is self-averaging in parameter and is strongly non-self-averaging over time 
. To measure the concentration with the required accuracy at the required time of observation 
, the initial number of particles 
must be exponentially large in . At later times 
the relative fluctuations continue to diverge exponentially beyond the required accuracy. In the limit of high dimensions, there is no tendency to restore self-averaging over time in the ensemble of particles. The solution in 1D is exact. In higher dimensions, the leading exponential term of the solution is exact.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022
