Quantum Unique Ergodicity for Maps on the Torus

On Quantum Unique Ergodicity for Linear Maps of the Torus

The problem of “quantum ergodicity” addresses the limiting distribution of eigenfunctions of classically chaotic systems. I survey recent progress on this question in the case of quantum maps of the torus. This example leads to analogues of traditional problems in number theory, such as the classical conjecture of Gauss and Artin that any (reasonable) integer is a primitive root for infinitely ...

Quantum Unique Ergodicity for Parabolic Maps

We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of quantum observables converge to the classical phase-space average with respect to Liouville measure of the corresponding classical observable. The possible existence of any exceptional subsequences of eigenstates is an i...

On Quantum Ergodicity for Linear Maps of the Torus

v 2 2 6 M ay 2 00 4 Proof of the Rudnick - Kurlberg Rate

In this paper we give a proof of the Hecke quantum unique ergodic-ity rate conjecture for the Berry-Hannay model. A model of quantum mechanics on the 2-dimensional torus. In the paper " Quantization of linear maps on the torus-Fresnel diffrac-tion by a periodic grating " , published in 1980 (see [BH]), the physicists M.V. Berry and J. Hannay explore a model for quantum mechanics on the 2-dimens...

A pr 2 00 4 Proof of the Rudnick - Kurlberg Rate

In this paper we give a proof of the Hecke quantum unique ergodic-ity rate conjecture for the Berry-Hannay model. A model of quantum mechanics on the 2-dimensional torus. In the paper " Quantization of linear maps on the torus-Fresnel diffrac-tion by a periodic grating " , published in 1980 (see [BH]), the physicists M.V. Berry and J. Hannay explore a model for quantum mechanics on the 2-dimens...