{"paper":{"title":"On eigenvalue asymptotics for strong delta-interactions supported by surfaces with boundaries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP","quant-ph"],"primary_cat":"math-ph","authors_text":"Ch. K\\\"uhn, J. Dittrich, K. Pankrashkin, P. Exner","submitted_at":"2015-06-22T13:06:06Z","abstract_excerpt":"Let $S\\subset\\mathbb{R}^3$ be a $C^4$-smooth relatively compact orientable surface with a sufficiently regular boundary. For $\\beta\\in\\mathbb{R}_+$, let $E_j(\\beta)$ denote the $j$th negative eigenvalue of the operator associated with the quadratic form \\[ H^1(\\mathbb{R}^3)\\ni u\\mapsto \\iiint_{\\mathbb{R}^3} |\\nabla u|^2dx -\\beta \\iint_S |u|^2d\\sigma, \\] where $\\sigma$ is the two-dimensional Hausdorff measure on $S$. We show that for each fixed $j$ one has the asymptotic expansion \\[ E_j(\\beta)=-\\dfrac{\\beta^2}{4}+\\mu^D_j+ o(1) \\;\\text{ as }\\; \\beta\\to+\\infty\\,, \\] where $\\mu_j^D$ is the $j$th "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06583","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"}