Absolutely Continuous Spectrum of a Polyharmonic Operator with a Limit Periodic Potential in Dimension Two

Abstract

We consider a polyharmonic operator $H=(-\Delta {)}^l+V(x)$ in dimension two with $l\ge 6$, $l$ being an integer, and a limit-periodic potential $V(x)$. We prove that the spectrum contains a semiaxis of absolutely continuous spectrum.

33 pages, 8 figures