Multiplicative Jensen's formula and quantitative global theory of one-frequency Schr\"odinger operators
Dynamical Systems
2023-08-21 v2 Mathematical Physics
math.MP
Spectral Theory
Abstract
We introduce the concept of dual Lyapunov exponents, leading to a multiplicative version of the classical Jensen's formula for one-frequency analytic Schr\"odinger cocycles. This formula, in particular, gives a new proof and a quantitative version of the fundamentals of Avila's global theory \cite{avila}, fully explaining the behavior of complexified Lyapunov exponent through the dynamics of the dual cocycle. In particular, concepts of (sub/super) critical regimes and acceleration are all explained (in a quantitative way) through the duality approach. This leads to a number of powerful spectral and physics applications
Keywords
Cite
@article{arxiv.2306.16387,
title = {Multiplicative Jensen's formula and quantitative global theory of one-frequency Schr\"odinger operators},
author = {Lingrui Ge and Svetlana Jitomirskaya and Jiangong You and Qi Zhou},
journal= {arXiv preprint arXiv:2306.16387},
year = {2023}
}
Comments
45 pages, introduction updated