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Bibliographic Details
Main Author: Schwartz, Nir
Format: Preprint
Published: 2021
Subjects:
Online Access:https://arxiv.org/abs/2103.06633
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author Schwartz, Nir
author_facet Schwartz, Nir
contents 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 $-Δ_g$ on compact hyperbolic surfaces from [arXiv:1705.05019], relying on the fractal uncertainty principle in [arXiv:1612.09040].
format Preprint
id arxiv_https___arxiv_org_abs_2103_06633
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle The full delocalization of eigenstates for the quantized cat map
Schwartz, Nir
Analysis of PDEs
Mathematical Physics
Spectral Theory
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 $-Δ_g$ on compact hyperbolic surfaces from [arXiv:1705.05019], relying on the fractal uncertainty principle in [arXiv:1612.09040].
title The full delocalization of eigenstates for the quantized cat map
topic Analysis of PDEs
Mathematical Physics
Spectral Theory
url https://arxiv.org/abs/2103.06633