We show for a large class of random Schrödinger operators H ο on and on that dynamical
localization holds, ie that, with probability one, for a suitable energy interval I and for qa …

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 …

The object of the present study is the integrated density of states of a quantum particle in
multi-dimensional Euclidean space which is characterized by a Schrödinger operator with a …

Random Schrödinger operators are models for the quantum mechanical description of
disordered media. The main aim of the analysis of such models is the understanding of the …

arXiv:0708.2292v1 [math-ph] 16 Aug 2007 Page 1 arXiv:0708.2292v1 [math-ph] 16 Aug 2007
MULTISCALE ANALYSIS AND LOCALIZATION OF RANDOM OPERATORS ABEL KLEIN …

These notes correspond to a series of Lectures delivered in July 2001 at the Summer School
Geometry, Topology and Quantum Field Theory, that was organized at Villa de Leyva, in …

We prove quantization of the Hall conductance for continuous ergodic Landau Hamiltonians
under a condition on the decay of the Fermi projections. This condition and continuity of the …

We give finite volume criteria for localization of quantum or classical waves in continuous
random media. We provide explicit conditions, depending on the parameters of the model …

A detailed mathematical proof is given that the energy spectrum of a non-relativistic quantum
particle in multi-dimensional Euclidean space under the influence of suitable random …

Electronic properties of amorphous or non-crystalline disordered solids are often modelled
by one-particle Schrödinger operators with random potentials which are ergodic with respect …