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arXiv · 2209.02027

Emergence of quantum dynamics from chaos: The case of prequantum cat maps

Javier Echevarría Cuesta
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Abstract

Faure and Tsujii recently proposed a new quantization theory for symplectic Anosov diffeomorphisms. It combines prequantization with the study of the Pollicott--Ruelle resonances of an associated transfer operator. We apply this framework to the hyperbolic symplectic automorphisms of the $2n$-dimensional torus, the so-called cat maps. Our main result gives an explicit relation between the resonances of the prequantum transfer operator and the eigenvalues of the standard quantum cat maps, generalizing the case $n=1$ previously treated by Faure.

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BibTeXRIS

Javier Echevarría Cuesta. 2022-09-05. Emergence of quantum dynamics from chaos: The case of prequantum cat maps. https://doi.org/10.3934/dcds.2026016

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