Tuning the strength of emergent correlations in a Brownian gas via batch resetting
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910012657369088 |
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| author | de Mauro, Gabriele Majumdar, Satya N. Schehr, Gregory |
| author_facet | de Mauro, Gabriele Majumdar, Satya N. Schehr, Gregory |
| contents | We study a gas of $N$ diffusing particles on the line subject to batch resetting: at rate $r$, a uniformly random subset of $m$ particles is reset to the origin. Despite the absence of interactions, the dynamics generates a nonequilibrium stationary state (NESS) with long-range correlations. We obtain exact results, both for the NESS and for the time dependence of the correlations, which are valid for arbitrary $m$ and $N$. By varying $m$, the system interpolates between an uncorrelated regime ($m=1$) and the fully synchronous resetting case ($m=N$). For all $1<m<N$, correlations exhibit a non-monotonic time dependence due to the emergence of an intrinsic decorrelation mechanism. In the stationary state, the correlation strength can be tuned by varying $m$, and it displays a transition at a critical value $N_c=6$. Our predictions extend straightforwardly to any spatial dimension $d$ and the critical value $N_c=6$ remains the same in all dimensions. Our predictions are testable in existing experimental setups on optically trapped colloidal particles. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_20077 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Tuning the strength of emergent correlations in a Brownian gas via batch resetting de Mauro, Gabriele Majumdar, Satya N. Schehr, Gregory Statistical Mechanics We study a gas of $N$ diffusing particles on the line subject to batch resetting: at rate $r$, a uniformly random subset of $m$ particles is reset to the origin. Despite the absence of interactions, the dynamics generates a nonequilibrium stationary state (NESS) with long-range correlations. We obtain exact results, both for the NESS and for the time dependence of the correlations, which are valid for arbitrary $m$ and $N$. By varying $m$, the system interpolates between an uncorrelated regime ($m=1$) and the fully synchronous resetting case ($m=N$). For all $1<m<N$, correlations exhibit a non-monotonic time dependence due to the emergence of an intrinsic decorrelation mechanism. In the stationary state, the correlation strength can be tuned by varying $m$, and it displays a transition at a critical value $N_c=6$. Our predictions extend straightforwardly to any spatial dimension $d$ and the critical value $N_c=6$ remains the same in all dimensions. Our predictions are testable in existing experimental setups on optically trapped colloidal particles. |
| title | Tuning the strength of emergent correlations in a Brownian gas via batch resetting |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2601.20077 |