{"paper":{"title":"Designing lasing and perfectly absorbing potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"physics.optics","authors_text":"Boris Vainberg, Evgeny Lakshtanov, Vladimir V. Konotop","submitted_at":"2018-12-13T16:15:40Z","abstract_excerpt":"Existence of a spectral singularity (SS) in the spectrum of {a Schr\\\"{o}dinger operator with} a non-Hermitian potential requires exact matching of parameters of the potential. We provide a necessary and sufficient condition for a potential to have a SS at a given wavelength. It is shown that potentials with SSs at prescribed wavelengths can be obtained by a simple and effective procedure. In particular, the developed approach allows one to obtain potentials with several SSs and with SSs of the second order, as well as potentials obeying a given symmetry, say, $\\PT-$symmetric potentials. Also, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.05499","kind":"arxiv","version":2},"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"}