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The
full delocalization of eigenstates for the quantized cat
map
Nir Schwartz |
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Vol. 6 (2024), No. 4, 1017–1053
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Abstract |
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We consider the quantum cat map — a toy model of a quantized chaotic system. We show that its eigenstates are fully delocalized on in the semiclassical limit (or equivalently that each semiclassical measure is fully supported on ). We adapt the proof of a similar result proved for the eigenstates of on compact hyperbolic surfaces by Dyatlov and Jin (Acta Math. 220:2 (2018), 297–339), relying on the fractal uncertainty principle of Bourgain and Dyatlov (Ann. of Math. 187:3 (2018), 825–867). |
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Keywords
quantum chaos, quantum map, fractal uncertainty principle
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Mathematical Subject Classification
Primary: 37D20, 37Dxx, 81Q20, 81Q50, 81S07
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Milestones
Received: 20 October 2021
Revised: 4 October 2024
Accepted: 5 November 2024
Published: 26 December 2024
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Authors |
| Nir Schwartz | |
| Université Paris-Saclay CNRS, Laboratoire de Mathématiques d’Orsay Orsay France |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). |
