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| Main Author: | |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.02027 |
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| _version_ | 1866908748494143488 |
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| author | Cuesta, Javier Echevarría |
| author_facet | Cuesta, Javier Echevarría |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02027 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Emergence of quantum dynamics from chaos: The case of prequantum cat maps Cuesta, Javier Echevarría Dynamical Systems Mathematical Physics Spectral Theory 81Q50, 81S10 (Primary) 37C30, 37D20 (Secondary) 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. |
| title | Emergence of quantum dynamics from chaos: The case of prequantum cat maps |
| topic | Dynamical Systems Mathematical Physics Spectral Theory 81Q50, 81S10 (Primary) 37C30, 37D20 (Secondary) |
| url | https://arxiv.org/abs/2209.02027 |