Half-delocalization for semiclassical measures of split higher-dimensional quantum cat maps

Vincent Ferrari-Dominguez

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arXiv · 2610.28026

Half-delocalization for semiclassical measures of split higher-dimensional quantum cat maps

Vincent Ferrari-Dominguez

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Abstract

We study quantum cat maps on multidimensional tori and prove an optimal lower bound for the Kolmogorov-Sinai entropy of their semiclassical measures under the hypothesis that the dynamics splits over the rationals. This is the first instance of such a bound for a dynamical system with multiple positive Lyapunov exponents. The proof is based on a new notion of conditional quantum dynamical entropy and a careful study of the multiple Ehrenfest time adapted to the dynamics.

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Vincent Ferrari-Dominguez. 2026-10-20. Half-delocalization for semiclassical measures of split higher-dimensional quantum cat maps. https://arxiv.org/abs/2610.28026

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