On quantum ergodicity for linear maps of the torus

Pär Kurlberg*, Zeév Rudnick

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 √N.

Original languageEnglish
Pages (from-to)201-227
Number of pages27
JournalCommunications in Mathematical Physics
Volume222
Issue number1
DOIs
StatePublished - Aug 2001

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