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We prove Anderson localization at the internal band-edges for periodic magnetic Schr{o}dinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of the integrated density of states for random magnetic Schr{o}dinger operators, thereby providing the initial length-scale estimate, and a Wegner estimate, for such models.
Weyl points are degenerate points on the spectral bands at which energy bands intersect conically. They are the origins of many novel physical phenomena and have attracted much attention recently. In this paper, we investigate the existence of such p
We study the Bloch variety of discrete Schrodinger operators associated with a complex periodic potential and a general finite-range interaction, showing that the Bloch variety is irreducible for a wide class of lattice geometries in arbitrary dimens
We develop a general technique for finding self-adjoint extensions of a symmetric operator that respect a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrodinger operators with singul
Motivated by the long-time transport properties of quantum waves in weakly disordered media, the present work puts random Schrodinger operators into a new spectral perspective. Based on a stationary random version of a Floquet type fibration, we redu
We prove that the local eigenvalue statistics at energy $E$ in the localization regime for Schrodinger operators with random point interactions on $mathbb{R}^d$, for $d=1,2,3$, is a Poisson point process with the intensity measure given by the densit