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arXiv · 2306.10500

Single-file diffusion in spatially inhomogeneous systems

Benjamin Sorkin·David S. Dean
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Abstract

We study the effect of spatially-varying potential and diffusivity on the dispersion of a tracer particle in single-file diffusion. Non-interacting particles in such a system exhibit normal diffusion at late times, which is characterised by an effective diffusion constant $D_\mathrm{eff}$. Here we demonstrate the physically appealing result that the dispersion of single-file tracers in this system has the same long-time behavior as that for Brownian particles in a spatially-homogeneous system with constant diffusivity $D_\mathrm{eff}$. Our results are based on a late-time analysis of the Fokker-Planck equation, motivated by the mathematical theory of homogenization. The findings are confirmed by numerical simulations for both annealed and quenched initial conditions.

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Benjamin Sorkin, David S. Dean. 2023-06-18. Single-file diffusion in spatially inhomogeneous systems. https://doi.org/10.1103/physreve.108.054125

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