Related papers: Simplicity of eigenvalues in the Anderson model
We show almost sure simplicity of eigenvalues for several models of Anderson-type random Schr\"odinger operators, extending methods introduced by Simon for the discrete Anderson model. These methods work throughout the spectrum and are not…
We derive a field-theoretical representation for the moments of the eigenstates in the generalized Anderson model. The representation is exact and can be used for the Anderson model with generic non-random hopping elements in any…
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 continuous Anderson Hamiltonians with non-degenerate single site probability distribution of bounded support, without any regularity condition on the single site probability distribution. We prove the existence of a strong form of…
We introduce a new approach for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model at high disorder. In contrast to the usual strategy, we do not study finite…
We show absence of energy levels repulsion for the eigenvalues of random Schr\"odinger operators in the continuum. We prove that, in the localization region at the bottom of the spectrum, the properly rescaled eigenvalues of a continuum…
We present an eigensystem multiscale analysis for proving localization (pure point spectrum with exponentially decaying eigenfunctions, dynamical localization) for the Anderson model in an energy interval. In particular, it yields…
We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.
We develop a local moment approach to static properties of the symmetric Anderson model in the presence of a magnetic field, focussing in particular on the strong coupling Kondo regime. The approach is innately simple and physically…
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 with no atoms. As an application, we derive new results about…
We establish exponential localization for a multi-particle Anderson model in a Euclidean space of an arbitrary dimension, in presence of a non-trivial short-range interaction and an alloy-type random external potential. Specifically, we…
We prove that, for a general class of random operators, the family of the unfolded eigenvalues in the localization region is asymptotically ergodic in the sense of N. Minami (see [Mi:11]). N. Minami conjectured this to be the case for…
In this work we consider the Anderson model on the $d$-dimensional lattice with the single site potential having singular distribution, mainly $\alpha$-H\"older continuous ones and show that the eigenvalue statistics is Poisson in the…
We study a particular class of families of multi-dimensional lattice Schr\"o\-dinger operators with deterministic (including quasi-periodic) potentials generated by the "hull" given by an orthogonal series over the Haar wavelet basis on the…
For the weakly interacting one-dimensional multi-particle Anderson model in the continuum space of configurations, we prove the spectral exponential and the strong dynamical localization. The results require the interaction amplitude to be…
We prove that a large class of hierarchical Anderson models with spectral dimension ${\rm d}\leq 2$ has only pure point spectrum.
In this paper, we give estimates for both upper and lower bounds of eigenvalues of a simple matrix. The estimates are shaper than the known results.
We study localization properties of the eigenstates and wave transport in one-dimensional system consisting of a set of barriers/wells of fixed thickness and random heights. The inherent peculiarity of the system resulting in the enhanced…
We give a widely self-contained introduction to the mathematical theory of the Anderson model. After defining the Anderson model and determining its almost sure spectrum, we prove localization properties of the model. Here we discuss…
The detection of the top eigenvalue and its corresponding eigenvector in ensembles of random matrices has significant applications across various fields. An existing method, based on the linear stability of a complementary set of cavity…