论文标题
在准晶体中查找光谱差距
Finding spectral gaps in quasicrystals
论文作者
论文摘要
我们基于对有限域的数值计算，提出了一种用于可靠，系统地证明具有准稳定顺序的频谱差距的算法。我们应用该算法来证明平面Ammann-Beenker瓷砖上的Hofstadter模型在某些能量处具有光谱差距，并且我们能够证明存在频谱差距，而以前的数值结果不确定。我们的算法适用于具有有限局部复杂性的更通用的系统，并最终发现了所有差距，从而规避了关于一般性汉密尔顿一般频谱差距的可计算性的较早的NO-GON定理。
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.
