{"paper":{"title":"Asymptotics of eigenvalues of the operator describing Aharonov-Bohm effect combined with homogeneous magneticfield coupled with a strong $\\delta$-interaction on a loop","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"G.Honnouvo, M.N. Hounkonnou","submitted_at":"2003-10-25T17:16:52Z","abstract_excerpt":"We investigate the two-dimensional magnetic operator\n $H_{c_0,B,\\beta} = {(-i\\nabla -A)}^{2}-\\beta\\delta(.-\\Gamma),$ where $\\Gamma$ is a smooth loop. The vector potential has the form $A=c_0\\bigg(\\frac{-y}{{x^2+y^2}}; \\frac{x}{{x^2+y^2}} \\bigg)+ \\frac{B}{2}\\bigg(-y; x\\bigg) $; $B>0,$ $c_0\\in]0;1[$. The asymptotics of negative eigenvalues of $H_{c_0,B,\\beta}$ for $\\beta \\longrightarrow +\\infty$ is found. We also prove that for large enough positive value of $\\beta$ the system exhibits persistent currents."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0310055","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":""},"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"}