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Anderson localization of long-range quasi-periodic operators via Dynamical Rigidity

Zhenfu Wang, Jiangong You, Qi Zhou

Abstract

We establish Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies, the proof is based on a novel dynamical rigidity argument.

Anderson localization of long-range quasi-periodic operators via Dynamical Rigidity

Abstract

We establish Anderson localization for long-range quasi-periodic operators with large trigonometric potentials and Diophantine frequencies, the proof is based on a novel dynamical rigidity argument.
Paper Structure (3 sections, 6 theorems, 12 equations)

This paper contains 3 sections, 6 theorems, 12 equations.

Table of Contents

  1. Introduction
  2. Aubry duality and dynamical rigidity
  3. Proof of Theorem \ref{['main']}

Key Result

Theorem 1.1

Let $\alpha \in DC$We say that $\alpha\in DC$, if there exists $\gamma>0,\tau>d-1$, such that $\inf_{j\in{\mathbb Z}}|\langle k,\alpha\rangle-j|\geq\frac{\gamma}{|k|^\tau},\forall k\in{\mathbb Z}^d\backslash \{0\}.$ and $v$ be a trigonometric polynomial. Assume that $|w_k| \leq Ce^{-c|k|}$ for some

Theorems & Definitions (9)

  • Theorem 1.1
  • Proposition 2.1
  • proof
  • Theorem 3.1
  • Theorem 3.2: WXYZ
  • Theorem 3.3: WXYZ
  • Proposition 3.1
  • proof
  • proof : Proof of Theorem \ref{['main']}