Single-file diffusion in spatially inhomogeneous systems

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.

arXiv comment14 pages, 5 figures

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Cited by in corpus (5)

• Occupation time of a system of Brownian particles on the line with steplike initial condition
• Fast Brownian cluster dynamics
• The effective diffusion constant of stochastic processes with spatially periodic noise
• Uphill drift in the absence of current in single-file diffusion
• Unexpected Effects of Disorder on Current Fluctuations in the Symmetric Simple Exclusion Process