{"paper":{"title":"Small scale quantum ergodicity in cat maps. I","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.DS","math.MP","math.SP"],"primary_cat":"math-ph","authors_text":"Xiaolong Han","submitted_at":"2018-10-29T04:21:08Z","abstract_excerpt":"In this series, we investigate quantum ergodicity at small scales for linear hyperbolic maps of the torus (\"cat maps\"). In Part I of the series, we prove quantum ergodicity at various scales. Let $N=1/h$, in which $h$ is the Planck constant. First, for all integers $N\\in\\mathbb{N}$, we show quantum ergodicity at logarithmical scales $|\\log h|^{-\\alpha}$ for some $\\alpha>0$. Second, we show quantum ergodicity at polynomial scales $h^\\alpha$ for some $\\alpha>0$, in two special cases: $N\\in S(\\mathbb{N})$ of a full density subset $S(\\mathbb{N})$ of integers and Hecke eigenbasis for all integers."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11949","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"}