First-passage and extreme value statistics for overdamped Brownian motion in a linear potential
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912432250683392 |
|---|---|
| author | Huang, Feng Chen, Hanshuang |
| author_facet | Huang, Feng Chen, Hanshuang |
| contents | We investigate the first-passage properties and extreme-value statistics of an overdamped Brownian particle confined by an external linear potential $V(x)=μ|x-x_0|$, where $μ>0$ is the strength of the potential and $x_0>0$ is the position of the lowest point of the potential, which coincides with the starting position of the particle. The Brownian motion terminates whenever the particle passes through the origin at a random time $t_f$. Our study reveals that the mean first-passage time $\langle t_f \rangle$ exhibits a nonmonotonic behavior with respect to $μ$, with a unique minimum occurring at an optimal value of $μ\simeq 1.24468D/x_0$, where $D$ is the diffusion constant of the Brownian particle. Moreover, we examine the distribution $P(M|x_0)$ of the maximum displacement $M$ during the first-passage process, as well as the statistics of the time $t_m$ at which $M$ is reached. Intriguingly, there exists another optimal $μ\simeq 1.24011 D/x_0$ that minimizes the mean time $\langle t_m \rangle$. All our analytical findings are corroborated through numerical simulations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | First-passage and extreme value statistics for overdamped Brownian motion in a linear potential Huang, Feng Chen, Hanshuang Statistical Mechanics We investigate the first-passage properties and extreme-value statistics of an overdamped Brownian particle confined by an external linear potential $V(x)=μ|x-x_0|$, where $μ>0$ is the strength of the potential and $x_0>0$ is the position of the lowest point of the potential, which coincides with the starting position of the particle. The Brownian motion terminates whenever the particle passes through the origin at a random time $t_f$. Our study reveals that the mean first-passage time $\langle t_f \rangle$ exhibits a nonmonotonic behavior with respect to $μ$, with a unique minimum occurring at an optimal value of $μ\simeq 1.24468D/x_0$, where $D$ is the diffusion constant of the Brownian particle. Moreover, we examine the distribution $P(M|x_0)$ of the maximum displacement $M$ during the first-passage process, as well as the statistics of the time $t_m$ at which $M$ is reached. Intriguingly, there exists another optimal $μ\simeq 1.24011 D/x_0$ that minimizes the mean time $\langle t_m \rangle$. All our analytical findings are corroborated through numerical simulations. |
| title | First-passage and extreme value statistics for overdamped Brownian motion in a linear potential |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2506.13112 |