Identification of the absent spectral gaps in a class of generalized Kronig-Penney Hamiltonians

Abstract

We study the spectral gaps of the generalized Kronig-Penney Hamiltonians which possesses two point interactions in the basic period cell. We suppose that each interaction is given by a rotation. We determine whether or not the jth spectral gap of the Hamiltonian is absent for a given $j \in \mathbb{N}$.