{"paper":{"title":"Localization for random perturbations of periodic Schroedinger operators with regular Floquet eigenvalues","license":"","headline":"","cross_cats":["math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Ivan Veselic'","submitted_at":"2005-10-17T11:25:41Z","abstract_excerpt":"We prove a localization theorem for continuous ergodic Schr\\\"odinger operators $ H_\\omega := H_0 + V_\\omega $, where the random potential $ V_\\omega $ is a nonnegative Anderson-type perturbation of the periodic operator $ H_0$. We consider a lower spectral band edge of $ \\sigma (H_0) $, say $ E= 0 $, at a gap which is preserved by the perturbation $ V_\\omega $. Assuming that all Floquet eigenvalues of $ H_0$, which reach the spectral edge 0 as a minimum, have there a positive definite Hessian, we conclude that there exists an interval $ I $ containing 0 such that $ H_\\omega $ has only pure poi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0510063","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"}