Entropy of semiclassical measures of the Walsh-quantized baker's map

Details Entropy of semiclassical measures of the Walsh-quantized baker's map Entropy of semiclassical measures of the Walsh-quantized baker's map

2005-12-15

arxiv.org/abs/math-ph/0512052v3

Annales Henri Poincar\'{e} 8 (23/02/2007) 37-74

Physics

Mathematical Physics

34 pages, 4 Postscript figures

Scientific paper

10.1007/s00023-006-0299-z

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".

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