{"paper":{"title":"Spacing gain and absorption in a simple $\\mathcal{PT}$-symmetric model: spectral singularities and ladders of eigenvalues and resonances","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","math.SP","physics.optics"],"primary_cat":"math-ph","authors_text":"D.A. Zezyulin, D.I. Borisov","submitted_at":"2019-08-18T06:46:35Z","abstract_excerpt":"We consider a parity-time ($\\mathcal{PT}$-) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Schr\\\"odiner operator with localized complex $\\mathcal{PT}$-symmetric potential. Properties of the latter Hamiltonian are considered subject to the change of the gain-to-loss distance. Resonances, spectral singularities and eigenvalues are analyzed in detail and discussed in the context of the associated laser-absorber modes and $\\mathcal{PT}$-symmetry breaking phase transition. Increasing gain-to-loss distance creates"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06383","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.06383/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}