%0 Journal Article
%T Entropy of quantum limits for symplectic linear maps of the multidimensional torus
%A Gabriel Riviere
%J Mathematics
%D 2010
%I arXiv
%R 10.1093/imrn/rnq155
%X 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.
%U http://arxiv.org/abs/1003.5061v1