Absolutely continuous spectrum for limit-periodic Schrödinger operators
arXiv:1304.2805
Abstract
We show that a large class of limit-periodic Schrödinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one. The proof proceeds through the non-perturbative construction of limit-periodic extended states. An essential step is a new estimate of the probability (in quasi-momentum) that the Floquet Bloch operators have only simple eigenvalues.