Proof of the Kurlberg-Rudnick Rate Conjecture

TL;DR

This paper proves the Hecke quantum unique ergodicity conjecture for the Berry-Hannay model, a quantum mechanics model on a 2D torus, confirming long-standing theoretical predictions in quantum chaos.

Contribution

It provides the first proof of the Kurlberg-Rudnick Rate Conjecture for quantum ergodicity on the torus, advancing understanding of quantum chaos and ergodic properties.

Findings

Proof of the Hecke quantum unique ergodicity conjecture

Validation of the Kurlberg-Rudnick Rate Conjecture

Confirmation of quantum ergodic behavior on the torus

Abstract

In this paper we present a proof of the {\it Hecke quantum unique ergodicity conjecture} for the Berry-Hannay model, a model of quantum mechanics on a two dimensional torus. This conjecture was stated in Z. Rudnick's lectures at MSRI, Berkeley, 1999 and ECM, Barcelona, 2000.