Universal fluctuations of single-particle diffusivity in a quenched environment

Takuma Akimoto, Eli Barkai, Keiji Saito

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22 Scopus citations


Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. We consider finite systems with quenched disorder in order to investigate the effects of sample disorder fluctuations and confinement on single-particle diffusivity. While the system is ergodic in a single disorder realization, the time-averaged mean square displacement depends crucially on the disorder; i.e., the system is ergodic but non-self-averaging. Moreover, we show that the disorder average of the time-averaged mean square displacement decreases with the system size. We find a universal distribution for diffusivity in the sense that the shape of the distribution does not depend on the dimension. Quantifying the degree of the non-self-averaging effect, we show that fluctuations of single-particle diffusivity far exceed the corresponding annealed theory and also find confinement effects. The relevance for experimental situations is also discussed.

Original languageEnglish
Article number180602
Pages (from-to)180602
JournalPhysical Review Letters
Issue number18
StatePublished - 28 Oct 2016

Bibliographical note

Funding Information:
T. A. and K. S. were supported by JSPS KAKENHI Grants No. 26800204 and No. JP25103003, respectively. E. B. acknowledges the Israel Science Foundation.

Publisher Copyright:
© 2016 American Physical Society.


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