Dynamical fluctuations in the Riesz gas
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866909997951090688 |
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| author | Dandekar, Rahul Krapivsky, P. L. Mallick, Kirone |
| author_facet | Dandekar, Rahul Krapivsky, P. L. Mallick, Kirone |
| contents | We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the $|x-y|^{-s}$ Riesz potential, causing the over-damped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for $0 < s < 1$, the standard deviations of both quantities grow as $t^{\frac{s}{2(1+s)}}$. When $s>1$, the interactions are effectively short-ranged, and the universal sub-diffusive $t^\frac{1}{4}$ growth emerges with only amplitude depending on the exponent. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05583 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Dynamical fluctuations in the Riesz gas Dandekar, Rahul Krapivsky, P. L. Mallick, Kirone Statistical Mechanics We consider an infinite system of particles on a line performing identical Brownian motions and interacting through the $|x-y|^{-s}$ Riesz potential, causing the over-damped motion of particles. We investigate fluctuations of the integrated current and the position of a tagged particle. We show that for $0 < s < 1$, the standard deviations of both quantities grow as $t^{\frac{s}{2(1+s)}}$. When $s>1$, the interactions are effectively short-ranged, and the universal sub-diffusive $t^\frac{1}{4}$ growth emerges with only amplitude depending on the exponent. We also show that the two-time correlations of the tagged-particle position have the same form as for fractional Brownian motion. |
| title | Dynamical fluctuations in the Riesz gas |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2212.05583 |