{"paper":{"title":"Level Crossings in a PT-symmetric Double Well","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP","quant-ph"],"primary_cat":"math-ph","authors_text":"Riccardo Giachetti, Vincenzo Grecchi","submitted_at":"2015-06-04T16:18:22Z","abstract_excerpt":"We consider a \\textit{PT}-symmetric cubic oscillator with an imaginary double well. We prove the existence of an infinite number of level crossings with a definite selection rule. Decreasing the positive parameter $\\hbar$ from large values, at a value $\\hbar_n$ we find the crossing of the pair of levels $(E_{2n+1}(\\hbar),E_{2n}(\\hbar))$ becoming the pair of levels $(E_n^+(\\hbar),E_n^-(\\hbar))$. For large parameters, a level is a holomorphic function $E_m(\\hbar)$ with different semiclassical behaviors, $E_j^\\pm(\\hbar),$ along different paths. The corresponding $m$-nodes delocalized state $\\psi_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.01637","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"}