{"paper":{"title":"Decay estimates for Schr\\\"{o}dinger's equation with magnetic potentials in three dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Hyun-Kyoung Kwon, Marius Beceanu","submitted_at":"2024-11-18T18:03:11Z","abstract_excerpt":"In this paper we prove that Schr\\\"{o}dinger's equation with a Hamiltonian of the form $H=-\\Delta+i(A \\nabla + \\nabla A) + V$, which includes a magnetic potential $A$, has the same dispersive and solution decay properties as the free Schr\\\"{o}dinger equation. In particular, we prove $L^1 \\to L^\\infty$ decay and some related estimates for the wave equation.\n  The potentials $A$ and $V$ are short-range and $A$ has four derivatives, but they can be arbitrarily large. All results hold in three space dimensions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.11787","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/2411.11787/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"}