Universal Fluctuations of Single-Particle Diffusivity in a Quenched Environment.
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.
Graduate School of Science and Technology, Keio University, Yokohama 223-8522, Japan.
Takuma
T
Akimoto
Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel.
Eli
E
Barkai
Department of Physics, Keio University, Yokohama 223-8522, Japan.
Keiji
K
Saito