PreprintCC BY-NC-SA 4.0arXiv
Half-delocalization for semiclassical measures of split higher-dimensional quantum cat maps
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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BibTeX
@misc{ferraridominguez2026halfdelocalization,
title = {{Half-delocalization for semiclassical measures of split higher-dimensional quantum cat maps}},
author = {Vincent Ferrari-Dominguez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.28026},
eprint = {2610.28026},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.28026},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Half-delocalization for semiclassical measures of split higher-dimensional quantum cat maps
AU - Vincent Ferrari-Dominguez
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.28026
UR - https://arxiv.org/abs/2610.28026
AB - 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.
ER -