{"paper":{"title":"Scarred eigenstates for arithmetic toral point scatterers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.NT","nlin.CD"],"primary_cat":"math-ph","authors_text":"Lior Rosenzweig, P\\\"ar Kurlberg","submitted_at":"2015-08-12T16:22:58Z","abstract_excerpt":"We investigate eigenfunctions of the Laplacian perturbed by a delta potential on the standard tori $\\mathbb{R}^d/2 \\pi\\mathbb{Z}^d$ in dimensions $d=2,3$. Despite quantum ergodicity holding for the set of \"new\" eigenfunctions we show that there is scarring in the momentum representation for $d=2,3$, as well as in the position representation for $d=2$ (i.e., the eigenfunctions fail to equidistribute in phase space along an infinite subsequence of new eigenvalues.) For $d=3$, scarred eigenstates are quite rare, but for $d=2$ scarring in the momentum representation is very common --- with $N_{2}("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02978","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"}