Universal Dynamics of a Passive Particle Driven by Brownian Motion
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909437313155072 |
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| author | Basu, Urna Krapivsky, P. L. Majumdar, Satya N. |
| author_facet | Basu, Urna Krapivsky, P. L. Majumdar, Satya N. |
| contents | We investigate the overdamped dynamics of a `passive' particle driven by nonreciprocal interaction with a `driver' Brownian particle. When the interaction between them is short-ranged, the long-time behavior of the driven particle is remarkably universal -- the mean-squared displacement (MSD) and the typical position of the driven particle exhibits the same qualitative behaviors independent of the specific form of the potential. In particular, the MSD grows as $t^{1/2}$ in one dimension and $\log t$ in two spatial dimensions. We compute the exact scaling functions for the position distribution in $d=1$ and $d=2$. These functions are universal when the interaction is short-ranged. For long-ranged interactions, the MSD of the driven particle grows as $t^ϕ$ with exponent $ϕ$ depending on the tail of the potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_16436 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal Dynamics of a Passive Particle Driven by Brownian Motion Basu, Urna Krapivsky, P. L. Majumdar, Satya N. Statistical Mechanics We investigate the overdamped dynamics of a `passive' particle driven by nonreciprocal interaction with a `driver' Brownian particle. When the interaction between them is short-ranged, the long-time behavior of the driven particle is remarkably universal -- the mean-squared displacement (MSD) and the typical position of the driven particle exhibits the same qualitative behaviors independent of the specific form of the potential. In particular, the MSD grows as $t^{1/2}$ in one dimension and $\log t$ in two spatial dimensions. We compute the exact scaling functions for the position distribution in $d=1$ and $d=2$. These functions are universal when the interaction is short-ranged. For long-ranged interactions, the MSD of the driven particle grows as $t^ϕ$ with exponent $ϕ$ depending on the tail of the potential. |
| title | Universal Dynamics of a Passive Particle Driven by Brownian Motion |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2407.16436 |