标题： 在准晶体中寻找光谱间隙 显示英文标题

标题： Finding spectral gaps in quasicrystals

摘要： 我们提出一种算法，用于可靠且系统地证明具有准晶体序的哈密顿量中谱隙的存在性，该算法基于有限区域上的数值计算。 我们将该算法应用于证明平面的Ammann-Beenker镶嵌上的Hofstadter模型在某些能量下存在谱隙，并且我们能够证明在之前数值结果不明确的地方存在谱隙。 我们的算法适用于具有有限局部复杂性的更一般的系统，并最终找到所有谱隙，绕过了关于一般哈密顿量谱隙可计算性的早期不可能定理。 显示英文摘要

摘要： We present an algorithm for reliably and systematically proving the existence of spectral gaps in Hamiltonians with quasicrystalline order, based on numerical calculations on finite domains. We apply this algorithm to prove that the Hofstadter model on the Ammann-Beenker tiling of the plane has spectral gaps at certain energies, and we are able to prove the existence of a spectral gap where previous numerical results were inconclusive. Our algorithm is applicable to more general systems with finite local complexity and eventually finds all gaps, circumventing an earlier no-go theorem regarding the computability of spectral gaps for general Hamiltonians.