{"paper":{"title":"On the semi-classical analysis of Schr\\\"odinger operators with purely imaginary electric potentials in a bounded domain","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Rapha\\\"el Henry","submitted_at":"2014-05-23T19:16:37Z","abstract_excerpt":"In this paper, we describe the leftmost eigenvalue of the non-selfadjoint operator $\\mathcal{A}_h = -h^2\\Delta+iV(x)$ with Dirichlet boundary conditions on a smooth bounded domain $\\Omega\\subset\\mathbb{R}^n\\,$, as $h\\rightarrow0\\,$. $V$ is assumed to be a Morse function without critical point at the boundary of $\\Omega\\,$. More precisely, we compare $\\inf\\Re\\sigma(\\mathcal{A}_h)$ with the minimum of the spectrum's real part for some model operator. In the case where $V$ has no critical point, the spectrum is determined by the boundary points where $\\nabla V$ is orthogonal, and the model operat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6183","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"}