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arXiv · 1003.5061

Entropy of quantum limits for symplectic linear maps of the multidimensional torus

Gabriel Riviere
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Abstract

In the case of a linear symplectic map A of the 2d-torus, semiclassical measures are A-invariant probability measures associated to sequences of high energy quantum states. Our main result is an explicit lower bound on the entropy of any semiclassical measure of a given quantizable matrix A in Sp(2d,Z). In particular, our result implies that if A has an eigenvalue outside the unit circle, then a semiclassical measure cannot be carried by a closed orbit of A.

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Gabriel Riviere. 2010-03-26. Entropy of quantum limits for symplectic linear maps of the multidimensional torus. https://doi.org/10.1093/imrn%2Frnq155

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