{"paper":{"title":"Instability of resonances under Stark perturbations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Arne Jensen, Kenji Yajima","submitted_at":"2018-04-16T11:45:45Z","abstract_excerpt":"Let $H^{\\varepsilon}=-\\frac{d^2}{dx^2}+\\varepsilon x +V$, $\\varepsilon\\geq0$, on $L^2(\\mathbf{R})$. Let $V=\\sum_{k=1}^Nc_k|\\psi_k\\rangle\\langle\\psi_k|$ be a rank $N$ operator, where the $\\psi_k\\in L^2(\\mathbf{R})$ are real, compactly supported, and even. Resonances are defined using analytic scattering theory. The main result is that if $\\zeta_n$, ${\\rm Im}\\zeta_n<0$, are resonances of $H^{\\varepsilon_n}$ for a sequence $\\varepsilon_n\\downarrow0$ as $n\\to\\infty$ and $\\zeta_n\\to\\zeta_0$ as $n\\to\\infty$, ${\\rm Im}\\zeta_0<0$, then $\\zeta_0$ is \\emph{not} a resonance of $H^0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.05620","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"}