Dynamical Localization and Transport properties of Quantum Walks on the hexagonal lattice

IF 1.1 3区数学 Q3 MATHEMATICS, APPLIED

Mathematical Physics, Analysis and Geometry Pub Date : 2025-10-08 DOI:10.1007/s11040-025-09531-1

Andreas Schaefer

引用次数: 0

Abstract

We study coined Random Quantum Walks on the hexagonal lattice, where the strength of disorder is monitored by the coin matrix. Each lattice site is equipped with an i.i.d. random variable that is uniformly distributed on the torus and acts as a random phase in every step of the QW. We show exponential decay of the fractional moments of the Green function in the regime of strong disorder, that is whenever the coin matrix is sufficiently close to the fully localized case, using a fractional moment criterion and a finite volume method. In the decorrelated case, we deduce dynamical localization. Moreover, we adapt a topological index to our model and thereby obtain transport for some coin matrices.

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六边形晶格上量子行走的动力学局域化和输运性质

我们研究了六边形晶格上的随机量子行走，其中无序强度由硬币矩阵监控。每个点阵位置都配备了一个i.i.d随机变量，该随机变量均匀分布在环面上，在量子阱的每一步中都充当随机相位。我们用分数矩准则和有限体积方法证明了在强无序状态下，即当硬币矩阵足够接近完全局域情况时，Green函数的分数矩的指数衰减。在去相关的情况下，我们推导出动态局部化。此外，我们在模型中引入了一个拓扑指标，从而得到了一些硬币矩阵的输运。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Physics, Analysis and Geometry 数学-物理：数学物理

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.