{"paper":{"title":"Coupled Oscillator Systems Having Partial PT Symmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Alireza Beygi, Carl M. Bender, S. P. Klevansky","submitted_at":"2015-03-19T11:54:53Z","abstract_excerpt":"This paper examines chains of $N$ coupled harmonic oscillators. In isolation, the $j$th oscillator ($1\\leq j\\leq N$) has the natural frequency $\\omega_j$ and is described by the Hamiltonian $\\frac{1}{2}p_j^2+\\frac{1}{2}\\omega_j^2x_j^2$. The oscillators are coupled adjacently with coupling constants that are purely imaginary; the coupling of the $j$th oscillator to the $(j+1)$st oscillator has the bilinear form $i\\gamma x_jx_{j+1}$ ($\\gamma$ real). The complex Hamiltonians for these systems exhibit {\\it partial} $\\mathcal{PT}$ symmetry; that is, they are invariant under $i\\to-i$ (time reversal)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05725","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"}