On the Kotani-Last Conjecture for the Dirac Operator

Nyah Davis; íris Emilsdóttir; Long Li; Hangqi Liang

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arXiv · 2509.19072

On the Kotani-Last Conjecture for the Dirac Operator

Nyah Davis·íris Emilsdóttir·Long Li·Hangqi Liang

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Abstract

We prove a dichotomy of almost periodicity for reflectionless one-dimensional Dirac operators whose spectra satisfy certain geometric conditions, extending work of Volberg--Yuditskii. We also construct a weakly mixing Dirac operator with a non-constant continuous potential whose spectrum is purely absolutely continuous, adapting Avila's argument for continuous Schr\"odinger operators. In particular, we disprove the Kotani--Last conjecture in the setting of one-dimensional Dirac operators.

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Nyah Davis, íris Emilsdóttir, Long Li, Hangqi Liang. 2025-09-23. On the Kotani-Last Conjecture for the Dirac Operator. https://arxiv.org/abs/2509.19072

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