On the Kotani-Last Conjecture for the Dirac Operator
Spectral Theory
2025-09-24 v1 Dynamical Systems
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.
Cite
@article{arxiv.2509.19072,
title = {On the Kotani-Last Conjecture for the Dirac Operator},
author = {Nyah Davis and íris Emilsdóttir and Long Li and Hangqi Liang},
journal= {arXiv preprint arXiv:2509.19072},
year = {2025}
}
Comments
23 pages