{"paper":{"title":"Long-wavelength amplification of an NLS conserved-charge violation in a one-dimensional Gross-Pitaevskii-Poisson field","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Rin Takada","submitted_at":"2026-03-29T21:59:24Z","abstract_excerpt":"Can weak self-gravity be treated as a small, generic perturbation of the integrable one-dimensional cubic nonlinear Schr\\\"odinger equation? We test this question by following the first nontrivial local NLS charge, $Q_3$. In the Gross-Pitaevskii-Poisson model it obeys the exact identity $\\dot Q_3=\\kappa F_3$, where $F_3$ is the instantaneous gravitational force on the charge. We quantify the initial violation through the normalized mean-square displacement of $Q_3$. Its curvature coefficient, $A_3={\\rm Var}(F_3)/{\\rm Var}(Q_3)$, measures the root-mean-square initial speed of the charge in units"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.27887","kind":"arxiv","version":2},"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/2603.27887/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"}