{"paper":{"title":"Fluctuations of random matrix products and 1D Dirac equation with random mass","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"Christophe Texier, Kabir Ramola","submitted_at":"2014-02-27T15:46:36Z","abstract_excerpt":"We study the fluctuations of certain random matrix products $\\Pi_N=M_N\\cdots M_2M_1$ of $\\mathrm{SL}(2,\\mathbb{R})$, describing localisation properties of the one-dimensional Dirac equation with random mass. In the continuum limit, i.e. when matrices $M_n$'s are close to the identity matrix, we obtain convenient integral representations for the variance $\\Gamma_2=\\lim_{N\\to\\infty}\\mathrm{Var}(\\ln||\\Pi_N||)/N$. The case studied exhibits a saturation of the variance at low energy $\\varepsilon$ along with a vanishing Lyapunov exponent $\\Gamma_1=\\lim_{N\\to\\infty}\\ln||\\Pi_N||/N$, leading to the beh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.6943","kind":"arxiv","version":2},"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"}