{"paper":{"title":"Comparison of two different integration methods for the (1+1)-Dimensional Schr\\\"odinger-Poisson Equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.quant-gas","physics.comp-ph"],"primary_cat":"gr-qc","authors_text":"Javier Madro\\~nero, Nico Schwersenz, Sandro Wimberger, Tim Zimmermann, Victor Loaiza","submitted_at":"2024-05-08T09:46:25Z","abstract_excerpt":"We compare two different numerical methods to integrate in time spatially delocalized initial densities using the Schr\\\"odinger-Poisson equation system as the evolution law. The basic equation is a nonlinear Schr\\\"odinger equation with an auto-gravitating potential created by the wave function density itself. The latter is determined as a solution of Poisson's equation modelling, e.g., non-relativistic gravity. For reasons of complexity, we treat a one-dimensional version of the problem whose numerical integration is still challenging because of the extreme long-range forces (being constant in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04924","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/2405.04924/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"}