{"paper":{"title":"Invariant Gibbs measure for a Schrodinger equation with exponential nonlinearity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.AP","authors_text":"Tristan Robert","submitted_at":"2021-04-29T13:57:00Z","abstract_excerpt":"We investigate the invariance of the Gibbs measure for the fractional Schrodinger equation of exponential type (expNLS) $i\\partial_t u + (-\\Delta)^{\\frac{\\alpha}2} u = 2\\gamma\\beta e^{\\beta|u|^2}u$ on $d$-dimensional compact Riemannian manifolds $\\mathcal{M}$, for a dispersion parameter $\\alpha>d$, some coupling constant $\\beta>0$, and $\\gamma\\neq 0$. (i) We first study the construction of the Gibbs measure for (expNLS). We prove that in the defocusing case $\\gamma>0$, the measure is well-defined in the whole regime $\\alpha>d$ and $\\beta>0$ (Theorem 1.1 (i)), while in the focusing case $\\gamma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.14348","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/2104.14348/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"}