{"paper":{"title":"The Landau Hamiltonian with $\\delta$-potentials supported on curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.FA","math.MP"],"primary_cat":"math.SP","authors_text":"Jussi Behrndt, Markus Holzmann, Pavel Exner, Vladimir Lotoreichik","submitted_at":"2018-12-21T14:30:05Z","abstract_excerpt":"The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian $A_\\alpha =(i \\nabla + A)^2 + \\alpha\\delta$ in $L^2(R^2)$ with a $\\delta$-potential supported on a finite $C^{1,1}$-smooth curve $\\Sigma$ are studied. Here $A = \\frac{1}{2} B (-x_2, x_1)^\\top$ is the vector potential, $B>0$ is the strength of the homogeneous magnetic field, and $\\alpha\\in L^\\infty(\\Sigma)$ is a position-dependent real coefficient modeling the strength of the singular interaction on the curve $\\Sigma$. After a general discussion of the qualitative spectral properties of $A_\\alpha$ and its resolv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.09145","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"}