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<p>We study the Kohmoto model including Sturmian Hamiltonians and the associated Kohmoto butterfly. We prove spectral estimates for the operators using Farey numbers. In addition, we determine the impurities at rational rotations leading to the spectral defects in the Kohmoto butterfly. Our results are similar to the ones obtained for the almost-Mathieu operator and the associated Hofstadter butterfly.</p>

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Spectral Regularity and Defects for the Kohmoto Model

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年5月10日

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  • Siegfried Beckus,
  • Jean Bellissard,
  • Yannik Thomas

摘要

We study the Kohmoto model including Sturmian Hamiltonians and the associated Kohmoto butterfly. We prove spectral estimates for the operators using Farey numbers. In addition, we determine the impurities at rational rotations leading to the spectral defects in the Kohmoto butterfly. Our results are similar to the ones obtained for the almost-Mathieu operator and the associated Hofstadter butterfly.