Dynamical phase transition in the first-passage probability of a Brownian motion
Résumé
We study theoretically, experimentally and numerically the probability distribution $F(t_f|x_0,L)$ of the first passage times $t_f$ needed by a freely diffusing Brownian particle to reach a target at a distance $L$ from the initial position $x_0$, taken from a normalized distribution $(1/\sigma)\, g(x_0/\sigma)$ of finite width $\sigma$. We show the existence of a critical value $b_c$ of the parameter $b=L/\sigma$, which determines the shape of $F(t_f|x_0,L)$. For $b>b_c$ the distribution $F(t_f|x_0,L)$ has a maximum and a minimum whereas for $b
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Physique [physics]Claudine Le Vaou : Connectez-vous pour contacter le contributeur
https://hal.science/hal-03301450
Soumis le : mardi 27 juillet 2021-15:04:36
Dernière modification le : mardi 27 juin 2023-03:11:00
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Identifiants
- HAL Id : hal-03301450 , version 1
- ARXIV : 2102.07232
- DOI : 10.1103/PhysRevE.104.L012102
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Benjamin Besga, Felix Faisant, Artyom Petrosyan, Sergio Ciliberto, Satya N. Majumdar, et al.. Dynamical phase transition in the first-passage probability of a Brownian motion. Physical Review E , 2021, 104 (1), ⟨10.1103/PhysRevE.104.L012102⟩. ⟨hal-03301450⟩
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