{"paper":{"title":"Spatio-temporal fluctuations in the passive and active Riesz gas on the circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.soft","math-ph","math.MP","math.PR"],"primary_cat":"cond-mat.stat-mech","authors_text":"Gregory Schehr, Leo Touzo, Pierre Le Doussal","submitted_at":"2024-11-02T20:26:33Z","abstract_excerpt":"We consider a periodic Riesz gas consisting of $N$ classical particles on a circle, interacting via a two-body repulsive potential which behaves locally as a power law of the distance, $\\sim g/|x|^s$ for $s>-1$. Long range (LR) interactions correspond to $s<1$, short range (SR) interactions to $s>1$, while the cases $s=0$ and $s=2$ describe the well-known log-gas and the Calogero-Moser (CM) model respectively. We study the fluctuations of the positions around the equally spaced crystal configuration, both for Brownian and run-and-tumble particles (RTP). Focusing on the regime of weak noise, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.01355","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.01355/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}