On quantum ergodicity for linear maps of the torus
2001 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, Vol. 222, no 1, 201-227 p.Article in journal (Refereed) Published
We prove a strong version of quantum ergodicity for linear hyperbolic maps of the torus (cat maps). We show that there is a density one sequence of integers so that as N tends to infinity along this sequence., all eigenfunctions of the quantum propagator at inverse Planck constant N are uniformly distributed. A key step in the argument is to show that for a hyperbolic matrix in the modular group. there is a density one sequence of integers N for which its order (or period) modulo N is somewhat larger than rootN.
Place, publisher, year, edition, pages
2001. Vol. 222, no 1, 201-227 p.
IdentifiersURN: urn:nbn:se:kth:diva-20927ISI: 000170888900008OAI: oai:DiVA.org:kth-20927DiVA: diva2:339624
QC 201005252010-08-102010-08-10Bibliographically approved