{"paper":{"title":"Eigenvalue estimates for a three-dimensional magnetic Schr\\\"odinger operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.SP","authors_text":"Bernard Helffer, Yuri A. Kordyukov","submitted_at":"2012-03-19T02:36:43Z","abstract_excerpt":"We consider a magnetic Schr\\\"odinger operator $H^h=(-ih\\nabla-\\vec{A})^2$ with the Dirichlet boundary conditions in an open set $\\Omega \\subset {\\mathbb R}^3$, where $h>0$ is a small parameter. We suppose that the minimal value $b_0$ of the module $|\\vec{B}|$ of the vector magnetic field $\\vec{B}$ is strictly positive, and there exists a unique minimum point of $|\\vec{B}|$, which is non-degenerate. The main result of the paper is upper estimates for the low-lying eigenvalues of the operator $H^h$ in the semiclassical limit. We also prove the existence of an arbitrary large number of spectral g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.4021","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"}