Sharp Phase transitions for the almost Mathieu operator
Spectral Theory
2017-10-18 v1 Mathematical Physics
Dynamical Systems
math.MP
Abstract
It is known that the spectral type of the almost Mathieu operator depends in a fundamental way on both the strength of the coupling constant and the arithmetic properties of the frequency. We study the competition between those factors and locate the point where the phase transition from singular continuous spectrum to pure point spectrum takes place, which solves Jitomirskaya's conjecture in \cite{Ji95,J07}. Together with \cite{Aab}, we give the sharp description of phase transitions for the almost Mathieu operator.
Keywords
Cite
@article{arxiv.1512.03124,
title = {Sharp Phase transitions for the almost Mathieu operator},
author = {Artur Avila and Jiangong You and Qi Zhou},
journal= {arXiv preprint arXiv:1512.03124},
year = {2017}
}