Wave localization in number-theoretic landscapes
Wave localization in number-theoretic landscapes
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DOI：
10.1103/physrevb.106.224203
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发表时间：
2022-08
影响因子：
3.7
通讯作者：
L. D. Negro;Yilin Zhu;Yuyao Chen;M. Prado;F. A. Pinheiro
中科院分区：
文献类型：
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作者：
L. D. Negro;Yilin Zhu;Yuyao Chen;M. Prado;F. A. Pinheiro
我们研究了非周期结构中的波的局部化，这些结构体现了某些算术函数的多尺度复杂性，这些算术函数在数论中具有核心作用。特别地，我们研究了紧束缚薛定谔方程模型的本征谱和波局部化性质，其中在位势按照Liouville函数λ（n），Müobius函数μ（n）和模素数的二次剩余的Legendre序列分布。我们采用多重分形去趋势涨落分析（MDFA），并建立在这些系统中的能量谱的多重分形标度特性。此外，通过系统地分析空间本征模和它们的能级间距分布，我们发现在整个能谱中没有能级排斥和宽带局域化。我们的研究引入了确定性非周期系统，其本征模都强烈地局限于现实的有限一维系统，并为新型量子和经典器件提供了机会，这些器件对工程散斑势和增强的光-物质相互作用中的冷原子实验特别重要。
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 Schr¨odinger equation models with on-site potentials distributed according to the Liouville function λ ( n ), the M¨obius 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.