Diffusion with two resetting points
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929257569058816 |
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| author | Julián-Salgado, Pedro Dagdug, Leonardo Boyer, Denis |
| author_facet | Julián-Salgado, Pedro Dagdug, Leonardo Boyer, Denis |
| contents | We study the problem of a target search by a Brownian particle subject to stochastic resetting to a pair of sites. The mean search time is minimized by an optimal resetting rate which does not vary smoothly, in contrast with the well-known single site case, but exhibits a discontinuous transition as the position of one resetting site is varied while keeping the initial position of the particle fixed, or vice-versa. The discontinuity vanishes at a "liquid-gas" critical point in position space. This critical point exists provided that the relative weight $m$ of the further site is comprised in the interval $[2.9028...,8.5603...]$. When the initial position follows the resetting point distribution, a discontinuous transition also exists for the optimal rate as the distance between the resetting points is varied, provided that $m$ exceeds the critical value $m_c=6.6008...$ This setup can be mapped onto an intermittent search problem with switching diffusion coefficients and represents a minimal model for the study of distributed resetting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_11897 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Diffusion with two resetting points Julián-Salgado, Pedro Dagdug, Leonardo Boyer, Denis Statistical Mechanics Populations and Evolution We study the problem of a target search by a Brownian particle subject to stochastic resetting to a pair of sites. The mean search time is minimized by an optimal resetting rate which does not vary smoothly, in contrast with the well-known single site case, but exhibits a discontinuous transition as the position of one resetting site is varied while keeping the initial position of the particle fixed, or vice-versa. The discontinuity vanishes at a "liquid-gas" critical point in position space. This critical point exists provided that the relative weight $m$ of the further site is comprised in the interval $[2.9028...,8.5603...]$. When the initial position follows the resetting point distribution, a discontinuous transition also exists for the optimal rate as the distance between the resetting points is varied, provided that $m$ exceeds the critical value $m_c=6.6008...$ This setup can be mapped onto an intermittent search problem with switching diffusion coefficients and represents a minimal model for the study of distributed resetting. |
| title | Diffusion with two resetting points |
| topic | Statistical Mechanics Populations and Evolution |
| url | https://arxiv.org/abs/2311.11897 |