{"paper":{"title":"Confluent Crum-Darboux transformations in Dirac Hamiltonians with $PT$-symmetric Bragg gratings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI","physics.optics","quant-ph"],"primary_cat":"hep-th","authors_text":"Francisco Correa, Vit Jakubsky","submitted_at":"2016-12-19T20:48:11Z","abstract_excerpt":"We consider optical systems where propagation of light can be described by a Dirac-like equation with $PT$-symmetric Hamiltonian. In order to construct exactly solvable configurations, we extend the confluent Crum-Darboux transformation for the one-dimensional Dirac equation. The properties of the associated intertwining operators are discussed and the explicit form for higher-order transformations is presented. We utilize the results to derive a multi-parametric class of exactly solvable systems where the balanced gain and loss represented by the $PT$-symmetric refractive index can imply loca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.06349","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"}