Anderson localization for the unitary almost Mathieu operator
IF 1.6
2区 数学
Q2 MATHEMATICS, APPLIED
引用次数: 0
Abstract
We prove Anderson localization for all Diophantine frequencies and all non-resonant phases for a model that arises from a 2D quantum walk model subject to an external magnetic field, also known as the unitary almost Mathieu operator. Our work provides the first localization results for all Diophantine frequencies in quasi-periodic quantum walk and CMV matrix setting. We also obtain sharp asymptotics of the localized eigenfunctions.几乎是马修单元算子的安德森局部化
我们证明了一个二维量子行走模型在外部磁场作用下的所有二相频率和所有非共振相的安德森定位，该模型也被称为单元近似马修算子。我们的研究首次提供了准周期量子行走和 CMV 矩阵背景下所有 Diophantine 频率的定位结果。我们还获得了本地化特征函数的尖锐渐近线。
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来源期刊
Nonlinearity
物理-物理：数学物理
CiteScore
3.00
自引率
5.90%
发文量
170
审稿时长
12 months
期刊介绍：
Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest.
Subject coverage:
The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal.
Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena.
Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.
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