The interacting disordered electron problem is reviewed with emphasis on the quantum
phase transitions that occur in a model system and on the field-theoretic methods used to …

An elementary proof is given of localization for linear operators H= Ho+ λV, with Ho
translation invariant, or periodic, and V (·) a random potential, in energy regimes which for …

Our geometric concepts evolved first through the discovery of Non-Euclidean geometry. The
discovery of quantum mechanics in the form of the noncommuting coordinates on the phase …

The work presents a short proof of localization under the conditions of either strong disorder
(λ> λ 0) or extreme energies for a wide class of self adjoint operators with random matrix …

We prove that for Diophantine ω and almost every θ, the almost Mathieu operator,(Hω, λ,
θΨ)(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 …

We prove exponential localization in the Anderson model under very weak assumptions on
the potential distribution. In one dimension we allow any measure which is not concentrated …

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 …

A new proof of localization in the Anderson tight binding model Page 1 Commun. Math. Phys.
124, 285-299 (1989) Communications in MaUlemaUc © Springer-Verlag 1989 A New Proof of …