{"paper":{"title":"A magnetic version of the Smilansky-Solomyak model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SP","authors_text":"Diana Barseghyan, Pavel Exner","submitted_at":"2017-08-24T12:32:22Z","abstract_excerpt":"We analyze spectral properties of two mutually related families of magnetic Schr\\\"{o}dinger operators, $H_{\\mathrm{Sm}}(A)=(i \\nabla +A)^2+\\omega^2 y^2+\\lambda y \\delta(x)$ and $H(A)=(i \\nabla +A)^2+\\omega^2 y^2+ \\lambda y^2 V(x y)$ in $L^2(R^2)$, with the parameters $\\omega>0$ and $\\lambda<0$, where $A$ is a vector potential corresponding to a homogeneous magnetic field perpendicular to the plane and $V$ is a regular nonnegative and compactly supported potential. We show that the spectral properties of the operators depend crucially on the one-dimensional Schr\\\"{o}dinger operators $L= -\\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07375","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"}