Bethe-Sommerfeld Conjecture and Absolutely Continuous Spectrum of Multi-Dimensional Quasi-Periodic Schrödinger Operators

Yulia Karpeshina, Leonid Parnovski, Roman Shterenberg

We consider Schrödinger operators $H=-\Delta +V(\mathbf{x})$ in ${\mathbb{R}}^d$, $d\ge 2$, with quasi-periodic potentials $V(\mathbf{x})$. We prove that the absolutely continuous spect…