Related papers: Wegner estimate and Anderson localization for rand…
We prove exponential and dynamical localization at low energies for the Schr\"odinger operator with an attractive Poisson random potential in any dimension. We also conclude that the eigenvalues in that spectral region of localization have…
We present a simple construction of a random Schr\"odinger operator subject to a magnetic field with a regularity as low as $0^-$-H\"older and a Gaussian white noise electric potential on a two-dimensional bounded box. This construction is…
The phenomenon of Anderson localization is studied for a class of one-particle Schr\"odinger operators with random Zeeman interactions. These operators arise as follows: Static spins are placed randomly on the sites of a simple cubic…
An approximate analytic solution for the ground electron state are found to the Schroedinger equation for a combination of a uniform magnetic field and single attractive delta-potential. Effect of the magnetic field on this bound localized…
We prove that at large disorder, with large probability and for a set of Diophantine frequencies of large measure, Anderson localization in $\Bbb Z^d$ is {\it stable} under localized time-quasi-periodic perturbations by proving that the…
We consider alloy type random Schr\"odinger operators on a cubic lattice whose randomness is generated by the sign-indefinite single-site potential. We derive Anderson localization for this class of models in the Lifshitz tails regime, i.e.…
We prove a Wegner estimate for alloy type models merely assuming that the single site potential is lower bounded by a characteristic function of a thick set, that is a particular set of positive measure. The proof is based on two…
We study localization properties for a class of one-dimensional, matrix-valued, continuous, random Schr\"odinger operators, acting on $L^2(\R)\otimes \C^N$, for arbitrary $N\geq 1$. We prove that, under suitable assumptions on the…
We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding…
We consider the Anderson model on the multi-dimensional cubic lattice and prove a positive lower bound on the density of states under certain conditions. For example, if the random variables are independently and identically distributed and…
We consider $N\times N$ Hermitian random matrices with independent identically distributed entries (Wigner matrices). The matrices are normalized so that the average spacing between consecutive eigenvalues is of order $1/N$. Under suitable…
We prove a Wegner estimate for a large class of multiparticle Anderson Hamiltonians on the lattice. These estimates will allow us to prove Anderson localization for such systems. A detailed proof of localization will be given in a…
In this paper we solve a long standing open problem for Random Schr\"odinger operators on $L^2(\mathbb{R}^d)$ with i.i.d single site random potentials. We allow a large class of free operators, including magnetic potential, however our…
We prove an optimal one-volume Wegner estimate for interacting systems of $N$ quantum particles moving in the presence of random potentials. The proof is based on the scale-free unique continuation principle recently developed for the…
We study effects of a bounded and compactly supported perturbation on multi-dimensional continuum random Schr\"odinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schr\"odinger…
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 provided by F\"urstenberg's theorem. That is, a…
We study the Schroedinger operator with a constant magnetic field in the exterior of a two-dimensional compact domain. Functions in the domain of the operator are subject to a boundary condition of the third type (Robin condition). In…
We evaluate the localization length of the wave (or Schroedinger) equation in the presence of a disordered speckle potential. This is relevant for experiments on cold atoms in optical speckle potentials. We focus on the limit of large…
We establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…
We study spectral properties of a system of two quantum particles on an integer lattice with a bounded short-range two-body interaction, in an external random potential field $V(x,\omega)$ with independent, identically distributed values.…