{"paper":{"title":"Lyapunov exponent of the random Schr\\\"{o}dinger operator with short-range correlated noise potential","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 Godin","submitted_at":"2011-04-15T20:18:53Z","abstract_excerpt":"We study the influence of disorder on propagation of waves in one-dimensional structures. Transmission properties of the process governed by the Schr\\\"{o}dinger equation with the white noise potential can be expressed through the Lyapunov exponent $\\gamma$ which we determine explicitly as a function of the noise intensity \\sigma and the frequency \\omega. We find uniform two-parameter asymptotic expressions for $\\gamma$ which allow us to evaluate $\\gamma$ for different relations between \\sigma and \\omega. The value of the Lyapunov exponent is also obtained in the case of a short-range correlate"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3150","kind":"arxiv","version":3},"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"}