{"paper":{"title":"$\\mathcal{PT}$-symmetric strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Francisco M. Fern\\'andez, German Gutierrez, Javier Garcia, Paolo Amore","submitted_at":"2013-06-06T14:29:43Z","abstract_excerpt":"We study both analytically and numerically the spectrum of inhomogeneous strings with $\\mathcal{PT}$-symmetric density. We discuss an exactly solvable model of $\\mathcal{PT}$-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules $Z(p) \\equiv \\sum_{n=1}^\\infty 1/E_n^p$, with $p=1,2,\\dots$ and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1419","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"}