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arXiv · 2607.06361

Complete hierarchical structure of the spectral bands in the Kohmoto model

Ram Band·Siegfried Beckus·Raphael Loewy
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Abstract

We study the Kohmoto model, a family of discrete Schr\"odinger operators with Sturmian potentials depending on a frequency and a coupling constant. We prove that, for all non-vanishing coupling constants, all spectral bands admit a hierarchical structure. This structure offers a variety of applications, including a detailed description of the Kohmoto butterfly and a central step towards the resolution of the dry ten Martini problem for Sturmian Hamiltonians, which we carry out in a subsequent work.

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Ram Band, Siegfried Beckus, Raphael Loewy. 2026-07-07. Complete hierarchical structure of the spectral bands in the Kohmoto model. https://arxiv.org/abs/2607.06361

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