Single-file Diffusion of Atomic and Colloidal Systems: Asymptotic Laws
- 9 May 2003
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 90 (18), 180602
- https://doi.org/10.1103/physrevlett.90.180602
Abstract
We present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a particle at position after time , when the particle was located at at , follows a Gaussian distribution in the long-time limit, with variance for overdamped systems and with variance for classical systems. The asymptotic behavior of the mean-squared displacement, , is shown to be independent of the nature of interactions for homogeneous systems in the fluid state. Moreover, the long-time behavior of self-diffusion is determined by short-time and large-scale collective density fluctuations.
Keywords
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