{"paper":{"title":"The effect of disorder on the wave propagation in one-dimensional periodic optical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Boris Vainberg, Stanislav Molchanov, Yuri A. Godin","submitted_at":"2011-10-18T22:05:17Z","abstract_excerpt":"The influence of disorder on the transmission through periodic waveguides is studied. Using a canonical form of the transfer matrix we investigate dependence of the Lyapunov exponent $\\gamma$ on the frequency $\\nu$ and magnitude of the disorder $\\sigma$. It is shown that in the bulk of the bands $\\gamma \\sim \\sigma^2$, while near the band edges it has the order $\\gamma \\sim \\sigma^{2/3}$. This dependence is illustrated by numerical simulations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4132","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"}