{"paper":{"title":"On the bound states of magnetic Laplacians on wedges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"A. P\\'erez-Obiol, P. Exner, V. Lotoreichik","submitted_at":"2017-03-10T13:08:13Z","abstract_excerpt":"This paper is mainly inspired by the conjecture about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture $\\phi\\in (0,\\pi)$. So far, a proof was only obtained for apertures $\\phi\\lesssim 0.511\\pi$. The conviction in the validity of this conjecture for apertures $\\phi\\gtrsim 0.511\\pi$ mainly relied on numerical computations. In this paper we succeed to prove the existence of bound states for any aperture $\\phi \\lesssim 0.583\\pi$ using a variational argument with suitably chosen test functions. Employing some more involved test functions and combining a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.03667","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}