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arXiv · 2103.06633

The full delocalization of eigenstates for the quantized cat map

Nir Schwartz
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Abstract

We consider the quantum cat map - a toy model of a quantized chaotic system. We show that its eigenstates are fully delocalized on $\mathbb{T}^2$ in the semiclassical limit (or equivalently that each semiclassical measure is fully supported on $\mathbb{T}^2$). We adapt the proof of a similar result proved for the eigenstates of $-\Delta_g$ on compact hyperbolic surfaces from [arXiv:1705.05019], relying on the fractal uncertainty principle in [arXiv:1612.09040].

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Nir Schwartz. 2021-03-11. The full delocalization of eigenstates for the quantized cat map. https://doi.org/10.2140/paa.2024.6.1017

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