{"paper":{"title":"Commensurability effects in one-dimensional Anderson localization: anomalies in eigenfunction statistics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.dis-nn","authors_text":"V.E.Kravtsov, V.I.Yudson","submitted_at":"2010-11-05T18:53:36Z","abstract_excerpt":"The one-dimensional (1d) Anderson model (AM) has statistical anomalies at any rational point $f=2a/\\lambda_{E}$, where $a$ is the lattice constant and $\\lambda_{E}$ is the de Broglie wavelength. We develop a regular approach to anomalous statistics of normalized eigenfunctions $\\psi(r)$ at such commensurability points. The approach is based on an exact integral transfer-matrix equation for a generating function $\\Phi_{r}(u, \\phi)$ ($u$ and $\\phi$ have a meaning of the squared amplitude and phase of eigenfunctions, $r$ is the position of the observation point). The descender of the generating f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1480","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"}