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- François Germinet, Abel Klein
- 2001

We investigate the Anderson metal-insulator transition for random Schrödinger operators. We define the strong insulator region to be the part of the spectrum where the random operator exhibits strong dynamical localization in the Hilbert-Schmidt norm. We introduce a local transport exponent β(E), and set the metallic transport region to be the part of the… (More)

- Franç Ois Germinet, Abel Klein, Jeffrey H Schenker
- 2004

We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynam-ical localization at the edges of each disordered-broadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and… (More)

- Abel Klein, Andrew Koines
- 2001

We study localization of classical waves in random media in the general framework introduced in Part I of this work [KK]. This framework allows for two random coefficents, encompasses acoustic waves with random position dependent compressibility and mass density, elastic waves with random position dependent Lamé moduli and mass density, and electromagnetic… (More)

- Franç Ois, Germinet And, Abel Klein
- 2005

We study the region of complete localization in a class of random operators which includes random Schrödinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding model. We establish new characterizations or criteria for this region of complete localization, given either by the decay of… (More)

- Abel Klein, Andrew Koines
- 2001

We i n troduce a general framework for studying the localization of classical waves in inhomogeneous media, which encompasses acoustic waves with position dependent compressibility and mass density, elastic waves with position dependent Lam e moduli and mass density, and electromagnetic waves with position dependent magnetic permeabil-ity and dielectric… (More)

- Jean-Marc Bouclet, Franç Ois Germinet, Abel Klein, Jeffrey H Schenker
- 2004

We justify the linear response theory for an ergodic Schrödinger operator with magnetic field within the non-interacting particle approximation , and derive a Kubo formula for the electric conductivity tensor. To achieve that, we construct suitable normed spaces of measurable covariant operators where the Liouville equation can be solved uniquely. If the… (More)

- Abel Klein
- 2002

A discussion of the method of multiscale analysis in the study of lo-calization of random operators based on lectures given at Random Schrödinger operators: methods, results, and perspectives, ´

- Franç Ois Germinet, Peter D Hislop, Abel Klein
- 2006

We prove exponential and dynamical localization at low energies for the Schrödinger operator with an attractive Poisson random potential in any dimension. We also conclude that the eigenvalues in that spectral region of localization have finite multiplicity.

- François Germinet, Peter Hislop, Abel Klein
- 2005

We prove exponential localization for the Schrödinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson densities. In addition, we obtain dynamical localization and finite multiplicity of the eigenvalues. Résumé On démontre… (More)