The distinctive electronic properties of quasicrystals stem from their long-range structural
order, with invariance under rotations and under discrete scale change, but without …

This is a comprehensive review of the uses of potential theory in studying the spectral theory
of orthogonal polynomials. Much of the article focuses on the Stahl-Totik theory of regular …

We prove that for Diophantine ω and almost every θ, the almost Mathieu operator,(H ω, λ, θ
Ψ)(n)= Ψ (n+ 1)+ Ψ (n-1)+ λ cos 2π (ω n+ θ) Ψ (n), exhibits localization for λ> 2 and purely …

This book provides an introduction to the mathematical theory of disorder effects on quantum
spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics …

In this survey we discuss spectral and quantum dynamical properties of discrete one-
dimensional Schrödinger operators whose potentials are obtained by real-valued sampling …

It is known that the spectral type of the almost Mathieu operator (AMO) depends in a
fundamental way on both the strength of the coupling constant and the arithmetic properties …

In this paper we consider various regularity results for discrete quasi-periodic Schrödinger
equations-ψn+ 1-ψn-1+ V (θ+ nω) ψn= Eψn with analytic potential V. We prove that on …

We show that for almost every frequency α∈ ℝ\ℚ, for every C^ω potential v: ℝ/ℤ→ ℝ, and for
almost every energy E the corresponding quasiperiodic Schrödinger cocycle is either …

Using the resolvent operator, we develop an algorithm for computing smoothed
approximations of spectral measures associated with self-adjoint operators. The algorithm …

We obtain approximate solutions defining the mobility edge separating localized and
extended states for several classes of generic one-dimensional quasiperiodic models. We …