Gibbs-like measure for spectrum of a class of one-dimensional Schrödinger operator with Sturm potentials

Shen Fan, Qing-Hui Liu, Zhi-Ying Wen

Let $\alpha \in (0,1)$ be an irrational, and $[0;a_1,a_2,...]$ the continued fraction expansion of $\alpha$. Let $H_{\alpha ,V}$ be the one-dimensional Schrödinger operator with Sturm potential of f…