{"paper":{"title":"Gauge Equivalence and the Inverse Spectral Problem for the Magnetic Schr\\\"odinger Operator on the Torus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Gregory Eskin, Jim Ralston","submitted_at":"2013-12-14T06:32:14Z","abstract_excerpt":"We study the inverse spectral problem for the Schr\\\"odinger operator $H$ on the two-dimensional torus with even magnetic field $B(x)$ and even electric potential $V(x)$. V.Guillemin [11] proved that the spectrum of $H$ determines $B(x)$ and $V(x)$. A simple proof of Guillemin's results was given by the authors in [3]. In the present paper we consider gauge equivalent classes of magnetic potentials and give conditions which imply that the gauge equivalence class and the spectrum of $H$ determine the magnetic field and the electric potential. We also show that generically the spectrum and the ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4008","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"}