{"paper":{"title":"Scattering in $\\cal PT$ and $\\cal RT$ Symmetric Multimode Waveguides: Generalized Conservation Laws and Spontaneous Symmetry Breaking beyond One Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"physics.optics","authors_text":"Demetrios N. Christodoulides, Konstantinos G. Makris, Liang Feng, Li Ge","submitted_at":"2015-10-27T03:23:18Z","abstract_excerpt":"We extend the generalize conservation law of light propagating in a one-dimensional $\\cal PT$-symmetric system, i.e., $|T-1|=\\sqrt{R_LR_R}$ for the transmittance $T$ and the reflectance $R_{L,R}$ from the left and right, to a multimode waveguide with either $\\cal PT$ or $\\cal RT$ symmetry, in which higher dimensional investigations are necessary. These conservation laws exist not only in a matrix form for the transmission and reflection matrices; they also exist in a scalar form for real-valued quantities by defining generalized transmittance and reflectance. We then discuss, for the first tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07760","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"}