{"paper":{"title":"Spectral gap and the exponential localization in general one-particle systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Tomotaka Kuwahara","submitted_at":"2014-04-28T15:43:05Z","abstract_excerpt":"We investigate the relationship between the spectral gap delta E_0 and the localization length xi in general one-particle systems. A relationship for many-body systems between the spectral gap and the exponential clustering has been derived from the Lieb-Robinson bound, which reduces to the inequality xi le const. times delta E_0^{-1} for one-particle systems. This inequality, however, turned out not to be optimal qualitatively. As a refined upper bound, we here prove the inequality xi le const. times delta E_0^{-1/2} in general one-particle systems. Our proof is not based on the Lieb-Robinson"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7026","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"}