Related papers: Anderson Localization for Long-Range operators wit…

We consider a random Schr\"odinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, $Q_r$, and a random transversally periodic potential, $\kappa Q_t$, with coupling constant…

We prove exponential spectral localization in a two-particle lattice Anderson model, with a short-range interaction and external random i.i.d. potential, at sufficiently low energies. The proof is based on the multi-particle multi-scale…

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…

This paper revisits the proof of Anderson localization for multi-particle systems. We introduce a multi-particle version of the eigensystem multi-scale analysis by Elgart and Klein, which had previously been used for single-particle…

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…

We prove spectral and dynamical localization for a one-dimensional Dirac operator to which is added an ergodic random potential, with a discussion on the different types of potential. We use scattering properties to prove the positivity of…

In this paper, we prove the large deviation estimates and Anderson localization for CMV matrices on $\ell^2(\mathbb{Z}_+)$ with Verblunsky coefficients defined dynamically by the hyperbolic toral automorphism. Part of positivity results on…

We study spectral properties of partial differential operators modelling composite materials with highly contrasting constituents, comprised of soft spherical inclusions with random radii dispersed in a stiff matrix. Such operators have…

We use trace class scattering theory to exclude the possibility of absolutely continuous spectrum in a large class of self-adjoint operators with an underlying hierarchical structure and provide applications to certain random hierarchical…

We establish strong dynamical localization for a class of multi-particle Anderson models in a Euclidean space with an alloy-type random potential and a sub-exponentially decaying interaction of infinite range. For the first time in the…

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 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 study the region of complete localization in a class of random operators which includes random Schr\"odinger operators with Anderson-type potentials and classical wave operators in random media, as well as the Anderson tight-binding…

At low temperature, a quasi-one-dimensional ensemble of atoms with attractive interaction forms a bright soliton. When exposed to a weak and smooth external potential, the shape of the soliton is hardly modified, but its center-of-mass…

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.

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…

For the almost Mathieu operator $(H_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+2\lambda \cos2\pi(\theta+n\alpha)u_n$, Avila and Jitomirskaya guess that for a.e. $\theta$, $H_{\lambda,\alpha,\theta}$ satisfies Anderson localization if $…

We consider random Schr\"{o}dinger operators on $\ell^2(\mathbb{Z}^d)$ when the distribution of single site potentials is $\alpha$-H\"{o}lder continuous ($0<\alpha\leq 1$). In localized regime we study the distribution of eigenfunctions…

Proofs of localization for random Schr\"odinger operators with sufficiently regular distribution of the potential can take advantage of the fractional moment method introduced by Aizenman-Molchanov, or use the classical Wegner estimate as…

Anderson localization is a quantum phenomenon in which disorder localizes electronic wavefunctions. In this work, we propose a new approach to study Anderson localization based on the density matrix formalism. Drawing an analogy to the…