We consider the spectral and dynamical properties of quantum systems of n particles on the
lattice Z^ d, of arbitrary dimension, with a Hamiltonian which in addition to the kinetic term …

Abstract We study continuous Anderson Hamiltonians with non-degenerate single site
probability distribution of bounded support, without any regularity condition on the single site …

We provide a complete and self-contained proof of spectral and dynamical localization for
the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent …

We generalize Minami's estimate for the Anderson model and its extensions to n
eigenvalues, allowing for n arbitrary intervals and arbitrary single-site probability measures …

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 …

We prove a unique continuation principle for spectral projections of Schrödinger operators.
We consider a Schrödinger operator H=− Δ+ V on\rm L^ 2 (R^ d) L 2 (R d), and let H Λ …

We justify the linear response theory for an ergodic Schrödinger operator with magnetic field
within the noninteracting particle approximation, and derive a Kubo formula for the electric …

We study various statistics related to the eigenvalues and eigenfunctions of random
Hamiltonians in the localized regime. Consider a random Hamiltonian at an energy E in the …

We study many-body localization properties of the disordered XXZ spin chain in the Ising
phase. Disorder is introduced via a random magnetic field in the z-direction. We prove a …

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 …