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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2502.18402 |
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| _version_ | 1866908429745913856 |
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| author | Yuste, Santos Bravo Baumgaertner, A. Abad, E. |
| author_facet | Yuste, Santos Bravo Baumgaertner, A. Abad, E. |
| contents | We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring walkers cannot exceed a threshold value $Δ$ and therefore call them ``tethered walkers'' (they behave as if bounded by strings which tighten fully when reaching the maximum length $Δ$). For finite $Δ$, we study the diffusional relaxation to the equilibrium state and characterize the latter [the long-time relaxation is exponential with a characteristic time that scales as $(NΔ)^2/D$]. In particular, our approximate approach for the $N$-particle probability distribution yields the one-particle distribution function of the central and edge particles [the first two positional moments are given as power expansions in $Δ/\sqrt{4Dt}$]. For $N=2$, we find an exact solution (both in the continuum case and on-lattice) and use it to test our approximations for one-particle distributions, positional moments, and correlations. For finite $Δ$ and arbitrary $N$, edge particles move with an effective long-time diffusivity $D/N$, in sharp contrast with the $1/\ln(N)$-behavior observed when $Δ=\infty$. Finally, we compute the probability distribution of the equilibrium system length and the associated entropy. We find that the force required to change this length by a given amount is linear in this quantity, the (entropic) spring constant being $6k_BT/(NΔ^2)$. In this respect, the system behaves like an ideal polymer. Our main analytical results are confirmed by Monte Carlo simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Single file dynamics of tethered random walkers Yuste, Santos Bravo Baumgaertner, A. Abad, E. Statistical Mechanics We consider the single-file dynamics of $N$ identical random walkers moving with diffusivity $D$ in one dimension (walkers bounce off each other when attempting to overtake). Additionally, we require that the separation between neighboring walkers cannot exceed a threshold value $Δ$ and therefore call them ``tethered walkers'' (they behave as if bounded by strings which tighten fully when reaching the maximum length $Δ$). For finite $Δ$, we study the diffusional relaxation to the equilibrium state and characterize the latter [the long-time relaxation is exponential with a characteristic time that scales as $(NΔ)^2/D$]. In particular, our approximate approach for the $N$-particle probability distribution yields the one-particle distribution function of the central and edge particles [the first two positional moments are given as power expansions in $Δ/\sqrt{4Dt}$]. For $N=2$, we find an exact solution (both in the continuum case and on-lattice) and use it to test our approximations for one-particle distributions, positional moments, and correlations. For finite $Δ$ and arbitrary $N$, edge particles move with an effective long-time diffusivity $D/N$, in sharp contrast with the $1/\ln(N)$-behavior observed when $Δ=\infty$. Finally, we compute the probability distribution of the equilibrium system length and the associated entropy. We find that the force required to change this length by a given amount is linear in this quantity, the (entropic) spring constant being $6k_BT/(NΔ^2)$. In this respect, the system behaves like an ideal polymer. Our main analytical results are confirmed by Monte Carlo simulations. |
| title | Single file dynamics of tethered random walkers |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2502.18402 |