{"paper":{"title":"Difference between level statistics, ergodicity and localization transitions on the Bethe lattice","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","quant-ph"],"primary_cat":"cond-mat.dis-nn","authors_text":"A. C. Ribeiro-Teixeira, G. Biroli, M. Tarzia","submitted_at":"2012-11-30T18:38:11Z","abstract_excerpt":"We show that non-interacting disordered electrons on a Bethe lattice display a new intermediate phase which is delocalized but non-ergodic, i.e. it is characterized by Poisson instead of GOE statistics. The physical signature of this phase is a very heterogenous transport that proceeds over a few disorder dependent paths only. We show that the transition to the usual ergodic delocalized phase, which takes place for a disorder strength smaller than the one leading to the localization transition, is related to the freezing-glass transition of directed polymers in random media. The numerical stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.7334","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"}