Exponential dynamical localization for the almost Mathieu operator

TL;DR

This paper proves that for the supercritical almost Mathieu operator with Diophantine frequency, the exponential moments of the position operator remain bounded, indicating a form of dynamical localization.

Contribution

It establishes exponential dynamical localization for the supercritical almost Mathieu operator with Diophantine frequency, a significant result in spectral theory.

Findings

Exponential moments of the position operator are bounded.

Dynamical localization is proven for the supercritical case.

Results apply to Diophantine frequency conditions.

Abstract

We prove that the exponential moments of the position operator stay bounded for the supercritical almost Mathieu operator with Diophantine frequency.