Scarred eigenstates for quantum cat maps of minimal periods

@inproceedings{Faure2008ScarredEF,
title={Scarred eigenstates for quantum cat maps of minimal periods},
author={Fr{\'e}d{\'e}ric Faure and St{\'e}phane Nonnenmacher and Stephan De Bievre},
year={2008}
}

In this paper we construct a sequence of eigenfunctions of the “quantum Arnold’s cat map” that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a semiclassical limit measure that is the sum of 1/2 the normalized Lebesgue measure on the torus plus 1/2 the normalized Dirac measure concentrated on any a priori given periodic orbit of the dynamics. It is known (the Schnirelman theorem) that “most” sequences of… CONTINUE READING