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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2310.08477 |
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| _version_ | 1866909147390279680 |
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| author | Dorignac, Jérôme Geniet, Fred Pitard, Estelle |
| author_facet | Dorignac, Jérôme Geniet, Fred Pitard, Estelle |
| contents | We address the question of the time needed by $N$ particles, initially located on the first sites of a finite 1D lattice of size $L$, to exit that lattice when they move according to a TASEP transport model. Using analytical calculations and numerical simulations, we show that when $N \ll L$, the mean exit time of the particles is asymptotically given by $T_N(L) \sim L+β_N \sqrt{L}$ for large lattices. Building upon exact results obtained for 2 particles, we devise an approximate continuous space and time description of the random motion of the particles that provides an analytical recursive relation for the coefficients $β_N$. The results are shown to be in very good agreement with numerical results. This approach sheds some light on the exit dynamics of $N$ particles in the regime where $N$ is finite while the lattice size $L\rightarrow \infty$. This complements previous asymptotic results obtained by Johansson in \cite{Johansson2000} in the limit where both $N$ and $L$ tend to infinity while keeping the particle density $N/L$ finite. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08477 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | TASEP Exit Times Dorignac, Jérôme Geniet, Fred Pitard, Estelle Disordered Systems and Neural Networks We address the question of the time needed by $N$ particles, initially located on the first sites of a finite 1D lattice of size $L$, to exit that lattice when they move according to a TASEP transport model. Using analytical calculations and numerical simulations, we show that when $N \ll L$, the mean exit time of the particles is asymptotically given by $T_N(L) \sim L+β_N \sqrt{L}$ for large lattices. Building upon exact results obtained for 2 particles, we devise an approximate continuous space and time description of the random motion of the particles that provides an analytical recursive relation for the coefficients $β_N$. The results are shown to be in very good agreement with numerical results. This approach sheds some light on the exit dynamics of $N$ particles in the regime where $N$ is finite while the lattice size $L\rightarrow \infty$. This complements previous asymptotic results obtained by Johansson in \cite{Johansson2000} in the limit where both $N$ and $L$ tend to infinity while keeping the particle density $N/L$ finite. |
| title | TASEP Exit Times |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2310.08477 |