The article surveys the main topics, techniques, and results of the theory of periodic
operators arising in mathematical physics and other areas. Close attention is paid to …

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 …

This review is an extended version of my mini course at the Etats de la recherche:
Operateurs de Schroedinger aleatoires at the Universite Paris 13 in June 2002, a summer …

Disorder is one of the predominant topics in science today. The present text is devoted to the
mathematical studyofsome particular cases ofdisordered systems. It deals with waves in …

We introduce an enhanced multiscale analysis that yields subexponentially decaying
probabilities for bad events. For quantum and classical waves in random media, we obtain …

7.1 Introduction A photonic crystal, or photonic band gap (PBG) optical material, is an
artificially created periodic low-loss dielectric medium in which electromagnetic waves of …

A technically convenient signature of localization, exhibited by discrete operators with
random potentials, is exponential decay of the fractional moments of the Green function …

We study localization effects of disorder on the spectral and dynamical properties of
Schrödinger operators with random potentials. The new results include exponentially …

We prove that the integrated density of states (IDS) of random Schrödinger operators with
Anderson-type potentials on L 2 (R d) for d≥ 1 is locally Hölder continuous at all energies …

We survey some aspects of the theory of the integrated density of states (IDS) of random
Schrödinger operators. The first part motivates the problem and introduces the relevant …