{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"c12de272d3b751bb186cf65f7eec081d16b0f0f81bf13192b92224db13e5baab","created":"2026-10-03T07:18:06Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"a89ccd7329102589b1ea87dd47da48ac840a9098bd338ccf084fe4d82e5050f5","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":[],"external_id":"mathph.quantum-chaos.que-negative-curvature","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"On a curved surface where every classical orbit is chaotic, every high-frequency standing wave should spread evenly over the surface. This is proven only for special surfaces with number-theoretic symmetry.","posed_since":"1994","precise":"Compact Riemannian surface $M$ of variable negative curvature, eigenfunctions $-\\operatorname{Lap} \\phi_{j} = \\lambda_{j} \\phi_{j}$ with $||\\phi_{j}||_{2} = 1$. Prove or disprove that $|\\phi_{j}|^{2} \\,\\mathrm{dvol} \\to \\mathrm{dvol}/\\operatorname{vol}(M)$ weakly for the whole sequence (Rudnick-Sarnak conjecture). Answer: yes or no with proof.","problem_ref":null,"references":"","settled_by":"A proof for all negatively curved surfaces, or a counterexample sequence of eigenfunctions with a non-uniform limit.","status_note":"Proven for Hecke eigenfunctions on arithmetic surfaces (Lindenstrauss, 2006; Soundararajan, 2010); density-one subsequences equidistribute by quantum ergodicity; for all negatively curved surfaces every semiclassical limit has full support (Dyatlov and Jin, 2018; Dyatlov, Jin and Nonnenmacher, 2022); Hassell's 2010 failure of QUE is for stadium billiards, which are not negatively curved surfaces.","title":"Quantum unique ergodicity on negatively curved surfaces","topic_ref":"ea13ab5f74a1c82c80da965948277a56b113b5df57a11f41c996b317accddd90"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"55634efd725e0a9d0c39db14956ff7ecd10f0b717feb9c4131b2171bc0a155d5","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"d237f6ac1f750f6505507d09d0560b807220aef06f0a29887c09250fe5e5a475","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"CPrgqDHKWvvlZOhEH4tHseymXB-a1D2422pfQvBHjGhTcV74PSsvWHT5Q9ciIWrwjbPxScaeE8gqqNi4FA8qCg"},"schema":"pubphys.envelope/1"},"record_hash":"55634efd725e0a9d0c39db14956ff7ecd10f0b717feb9c4131b2171bc0a155d5","leaf_index":1650}