Single-file diffusion in spatially inhomogeneous systems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908533559132160 |
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| author | Sorkin, Benjamin Dean, David S. |
| author_facet | Sorkin, Benjamin Dean, David S. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10500 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Single-file diffusion in spatially inhomogeneous systems Sorkin, Benjamin Dean, David S. Statistical Mechanics 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. |
| title | Single-file diffusion in spatially inhomogeneous systems |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2306.10500 |