Entropy of semiclassical measures of the Walsh-quantized baker's map
Mathematical Physics
2016-08-16 v3 Dynamical Systems
math.MP
Chaotic Dynamics
Abstract
We study the baker's map and its Walsh quantization, as a toy model of a quantized chaotic system. We focus on localization properties of eigenstates, in the semiclassical regime. Simple counterexamples show that quantum unique ergodicity fails for this model. We obtain, however, lower bounds on the entropies associated with semiclassical measures, as well as on the Wehrl entropies of eigenstates. The central tool of the proofs is an "entropic uncertainty principle".
Keywords
Cite
@article{arxiv.math-ph/0512052,
title = {Entropy of semiclassical measures of the Walsh-quantized baker's map},
author = {Nalini Anantharaman and Stéphane Nonnenmacher},
journal= {arXiv preprint arXiv:math-ph/0512052},
year = {2016}
}
Comments
34 pages, 4 Postscript figures