论文标题
在数字理论景观中浪潮本地化
Wave localization in number-theoretic landscapes
论文作者
论文摘要
我们研究了波浪中波的定位，这些结构表现出某些算术函数的特征多尺度复杂性，在数字理论中具有中心作用。特别是，我们研究了根据liouville函数$λ（n）$，möbius函数$μ（n）$以及Quadratic残基Modulo a modulo a prime（QRS）的legendre序列（Qrs），具有分布的现场电位的紧密结合Schrödinger方程模型的特征和波浪定位性能。我们采用多纹状体下降波动分析（MDFA），并在这些系统中建立了能量光谱的多重尺度缩放特性。此外，通过系统地分析空间特征模及其水平间距分布，我们表明了整个能量光谱中宽带定位的水平排斥不存在。我们的研究介绍了确定性的基本系统，其本征模均在现实的有限的一维系统中局部定位，并为新颖的量子和经典设备提供了对工程斑点潜力中冷原子实验特别重要的新型量子和经典设备的机会，并提供了机会。
We investigate the localization of waves in aperiodic structures that manifest the characteristic multiscale complexity of certain arithmetic functions with a central role in number theory. In particular, we study the eigenspectra and wave localization properties of tight-binding Schrödinger equation models with on-site potentials distributed according to the Liouville function $λ(n)$, the Möbius function $μ(n)$, and the Legendre sequence of quadratic residues modulo a prime (QRs). We employ Multifractal Detrended Fluctuation Analysis (MDFA) and establish the multifractal scaling properties of the energy spectra in these systems. Moreover, by systematically analyzing the spatial eigenmodes and their level spacing distributions, we show the absence of level repulsion with broadband localization across the entire energy spectra. Our study introduces deterministic aperiodic systems whose eigenmodes are all strongly localized in realistic finite one-dimensional systems and provides opportunities for novel quantum and classical devices of particular importance to cold-atom experiments in engineered speckle potentials and enhanced light-matter interactions.
