The full delocalization of eigenstates for the quantized cat map

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].

41 pages, 3 figures

References in corpus (1)

• Semiclassical measures for higher dimensional quantum cat maps

Cited by in corpus (3)

• Semiclassical measures for higher dimensional quantum cat maps
• Macroscopic limits of chaotic eigenfunctions
• Fractal uncertainty principle for discrete Cantor sets with random alphabets