%0 Unpublished work
%T TASEP Exit Times
%+ Laboratoire Charles Coulomb (L2C)
%A Dorignac, Jérôme
%A Geniet, Fred
%A Pitard, Estelle
%Z 10 pages, 4 figures
%8 2023-11-10
%D 2023
%Z 2310.08477
%Z Physics [physics]Preprints, Working Papers, ...
%X 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 $T_N(L) \sim L+\beta_N \sqrt{L}$ 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 $\beta_N$. 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.
%G English
%2 https://hal.science/hal-04279672/document
%2 https://hal.science/hal-04279672/file/2310.08477.pdf
%L hal-04279672
%U https://hal.science/hal-04279672
%~ CNRS
%~ L2C
%~ UNIV-MONTPELLIER
%~ UM-2015-2021
%~ UM-EPE