Related papers: On the local eigenvalue spacings for certain Ander…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
We consider several local versions of the doubling condition and Poincar\'e inequalities on metric spaces. Our first result is that in proper connected spaces, the weakest local assumptions self-improve to semilocal ones, i.e. holding…
The purpose of the present work is to establish decorrelation estimates for the locally renormalized eigenvalues of the discrete Anderson model near two distinct energies inside the localization region. In dimension one, we prove these…
We study the localization properties of non-interacting waves propagating in a speckle-like potential superposed on a one-dimensional lattice. Using a decimation/renormalization procedure, we estimate the localization length for a…
We establish the phenomenon of Anderson localisation for a quantum two-particle system on a d-dimensional lattice with short-range interaction and in presence of an IID external potential with sufficiently regular marginal distribution.
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…
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear $\sigma$-model…
We present a new perturbation theory for quantum mechanical energy eigenstates when the potential equals the sum of two localized, but not necessarily weak potentials $V_{1}(\vec{r})$ and $V_{2}(\vec{r})$, with the distance $L$ between the…
We analyse a two-particle quantum system in $\R^d$ with interaction and in presence of a random external potential field with a continuous argument (an Anderson model in a continuous space). Our aim is to establish the so-called Wegner-type…
The eigenvalue spacing of a uniformly chosen random finite unipotent matrix in its permutation action on lines is studied. We obtain bounds for the mean number of eigenvalues lying in a fixed arc of the unit circle and offer an approach…
We obtain a new bound on the location of eigenvalues for a non-self-adjoint Schr\"odinger operator with complex-valued potentials by obtaining a weighted $L^2$ estimate for the resolvent of the Laplacian.
Eigenfunctions of 1d disordered Hamiltonian with constant imaginary vector potential are investigated. Even within the domain of complex eigenvalues the wave functions are shown to be strongly localized. However, this localization is of a…
This paper addresses the so-called inverse problem which consists in searching for (possibly multiple) parent target Hamiltonian(s), given a single quantum state as input. Starting from $\Psi_0$, an eigenstate of a given local Hamiltonian…
We extend the bootstrap multiscale analysis developed by Germinet and Klein to the multi-particle continuous Anderson Hamiltonian, obtaining Anderson localization with finite multiplicity of eigenvalues, decay of eigenfunction correlations,…
We consider the discrete Anderson model and prove enhanced Wegner and Minami estimates where the interval length is replaced by the IDS computed on the interval. We use these estimates to improve on the description of finite volume…
We examine perturbations of eigenvalues and resonances for a class of multi-channel quantum mechanical model-Hamiltonians describing a particle interacting with a localized spin in dimension $d=1,2,3$. We consider unperturbed Hamiltonians…
We give conditions for boundedness of Hausdorff operators on real Hardy spaces $H^1$ over homogeneous spaces of locally compact groups with local doubling property. The special case of the hyperbolic plane is considered.
We establish new quantitative estimates for localized finite differences of solutions to the Poisson problem for the fractional Laplace operator with homogeneous Dirichlet conditions of solid type settled in bounded domains satisfying the…
In this paper we review results of Anderson localization for different random families of operators which enter in the framework of random quasi-one-dimensional models. We first recall what is Anderson localization from both physical and…
We prove Anderson localization at the internal band-edges for periodic magnetic Schr{\"o}dinger operators perturbed by random vector potentials of Anderson-type. This is achieved by combining new results on the Lifshitz tails behavior of…