On the Rate of Quantum Ergodicity on hyperbolic Surfaces and Billiards
Abstract
The rate of quantum ergodicity is studied for three strongly chaotic (Anosov) systems. The quantal eigenfunctions on a compact Riemannian surface of genus g=2 and of two triangular billiards on a surface of constant negative curvature are investigated. One of the triangular billiards belongs to the class of arithmetic systems. There are no peculiarities observed in the arithmetic system concerning the rate of quantum ergodicity. This contrasts to the peculiar behaviour with respect to the statistical properties of the quantal levels. It is demonstrated that the rate of quantum ergodicity in the three considered systems fits well with the known upper and lower bounds. Furthermore, Sarnak's conjecture about quantum unique ergodicity for hyperbolic surfaces is confirmed numerically in these three systems.
Keywords
Cite
@article{arxiv.chao-dyn/9707016,
title = {On the Rate of Quantum Ergodicity on hyperbolic Surfaces and Billiards},
author = {R. Aurich and M. Taglieber},
journal= {arXiv preprint arXiv:chao-dyn/9707016},
year = {2009}
}
Comments
19 pages, Latex, This file contains no figures. A postscript file with all figures is available at http://www.physik.uni-ulm.de/theo/qc/ (Delay is expected to 23.7.97 since our Web master is on vacation.)