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

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.