{"paper":{"title":"Dynamical Localization for the Random Dimer Model","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"F. Germinet, S. De Bi\\`evre","submitted_at":"1999-07-07T08:32:18Z","abstract_excerpt":"We study the one-dimensional random dimer model, with Hamiltonian $H_\\omega=\\Delta + V_\\omega$, where for all $x\\in\\Z, V_\\omega(2x)=V_\\omega(2x+1)$ and where the $V_\\omega(2x)$ are i.i.d. Bernoulli random variables taking the values $\\pm V, V>0$. We show that, for all values of $V$ and with probability one in $\\omega$, the spectrum of $H$ is pure point. If $V\\leq1$ and $V\\neq 1/\\sqrt{2}$, the Lyapounov exponent vanishes only at the two critical energies given by $E=\\pm V$. For the particular value $V=1/\\sqrt{2}$, respectively $V=\\sqrt{2}$, we show the existence of additional critical energies "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/9907006","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"}