利用Rellich函数分析\(\mathbb Z^d\)上Lipschitz单调拟周期Schrödinger算子的局部化

IF 2.2 1区物理与天体物理 Q1 PHYSICS, MATHEMATICAL

Communications in Mathematical Physics Pub Date : 2025-04-04 DOI:10.1007/s00220-025-05288-4

Hongyi Cao, Yunfeng Shi, Zhifei Zhang

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引用次数: 0

摘要

在多尺度分析的基础上，基于Rellich函数分析，建立了\(\mathbb Z^d\)上一类具有有界或无界Lipschitz单调势的拟周期Schrödinger算子的Anderson局部化和指数动态局部化。我们通过一种新颖的Schur补论证证明了在每个尺度下，共振Rellich函数一致地继承了势的Lipschitz单调性。

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Localization for Lipschitz Monotone Quasi-periodic Schrödinger Operators on \(\mathbb Z^d\) via Rellich Functions Analysis

We establish the Anderson localization and exponential dynamical localization for a class of quasi-periodic Schrödinger operators on \(\mathbb Z^d\) 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.

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来源期刊

Communications in Mathematical Physics 物理-物理：数学物理

CiteScore

4.70

自引率

8.30%

发文量

226

审稿时长

3-6 weeks

期刊介绍： The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.