{"paper":{"title":"A Scattering Result Around a Non-Localised Equilibria for the Quintic Hartree Equation for Random Fields","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Cyril Mal\\'ez\\'e","submitted_at":"2023-09-19T10:24:28Z","abstract_excerpt":"We consider a quintic Hartree equation for a random field, which describes the temporal evolution of a infinitely many fermions, considering a three body interaction. We show a scattering result around a non-localised equilibria of the equation, for high dimensions $d\\geq 4$. The Hartree equation for random variables was introduced by Anne-Sophie de Suzzoni but only for a two body interaction, that leads to a cubic Hartree equation for random variables. Scattering results for the cubic Hartree equation have been shown by Charles Collot and Anne-Sophie de Suzzoni, and we extend those results to"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.10500","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/2309.10500/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"}