Localization for Lipschitz monotone quasi-periodic Schrödinger operators on ℤ^d via Rellich functions analysis

2024/07/02 by Hongyi Cao, Yunfeng Shi, Cao, Hongyi +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2407.01970

openalex publication_date 2024/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schrödinger operators on ℤ^d with bounded or unbounded Lipschitz monotone potentials via multi-scale analysis based on Rellich function analysis in the perturbative regime. We show that at each scale, the resonant Rellich function uniformly inherits the Lipschitz monotonicity property of the potential via a novel Schur complement argument.

Related

• All couplings localization for quasiperiodic operators with Lipschitz monotone potentials
• Anderson localized states for the quasi-periodic nonlinear Schrödinger equation on \mathbb Z^d
• Convergence of perturbation series for unbounded monotone quasiperiodic operators
• On the spectrum of quasi-periodic Schrödinger operators on ℤ^d with C²-cosine type potentials
• Localization for quasiperiodic operators with unbounded monotone potentials