2000 character limit reached
On the Kotani-Last Conjecture for the Dirac Operator (2509.19072v1)
Published 23 Sep 2025 in math.SP and math.DS
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.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.
