Related papers: Anderson Localization for Radial Tree Graphs With …
Anderson localization has been observed in various types of waves, such as matter waves, optical waves and acoustic waves. Here we reveal that the effect of Anderson localization can be also induced in metallic nonlinear nanoparticle arrays…
Topic of the thesis is a theoretical description of the ultracold atomic gases in one- and two-dimensional optical lattices in the presence of the disorder leading to the Anderson localization. The disorder is created by interaction of the…
In this paper we present a class of Anderson type operators with independent, non-stationary (non-decaying) random potentials supported on a subset of positive density in the odd-dimensional lattice and prove the existence of pure…
We consider unitary analogs of $1-$dimensional Anderson models on $l^2(\Z)$ defined by the product $U_\omega=D_\omega S$ where $S$ is a deterministic unitary and $D_\omega$ is a diagonal matrix of i.i.d. random phases. The operator $S$ is…
We prove long time Anderson localization for nonlinear random Schroedinger equation in $\ell^2$ by making a Birkoff normal form type transform to creat an energy barrier where there is essentially no mode propagation. One of the new…
We study Anderson localization in quasi--one--dimensional disordered wires within the framework of the replica $\sigma$--model. Applying a semiclassical approach (geodesic action plus Gaussian fluctuations) recently introduced within the…
We consider discrete one-dimensional Schr\"odinger operators with random potentials obtained via a block code applied to an i.i.d. sequence of random variables. It is shown that, almost surely, these operators exhibit spectral and dynamical…
We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport…
This paper considers the family of Schr\"odinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the…
This paper is devoted to the study of the random displacement model on $\R^d$. We prove that, in the weak displacement regime, Anderson and dynamical localization holds near the bottom of the spectrum under a generic assumption on the…
We consider Schr\"odinger operators on $L^2(R^d)$ with a random potential concentrated near the surface $R^{d_1}\times\{0\}\subset R^d $. We prove that the integrated density of states of such operators exhibits Lifshits tails near the…
The Schr\"odinger operator on a metric tree is a family of ordinary differential operators on its edges complemented by certain matching conditions at the vertices. The regular trees are highly symmetric. This allows one to construct an…
We study the spectral theory of a class of piecewise centrosymmetric Jacobi operators defined on an associated family of substitution graphs. Given a finite centrosymmetric matrix viewed as a weight matrix on a finite directed path graph…
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…
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 analyse the eigenvectors of the adjacency matrix of a random inhomogeneous graph constructed from a specified degree sequence. We assume that the empirical degree sequence has bounded mean and variance. We show that near the edges of the…
We study the Laplacian on family preserving metric graphs. These are graphs that have a certain symmetry that, as we show, allows for a decomposition into a direct sum of one-dimensional operators whose properties are explicitly related to…
The arithmetic version of Anderson localization (AL), i.e., AL with explicit arithmetic description on both the localization frequency and the localization phase, was first given by Jitomirskaya \cite{J} for the almost Mathieu operators…
In this article we study the problem of localization of eigenvalues for the non-homogeneous hierarchical Anderson model. More specifically, given the hierarchical Anderson model with spectral dimension $0<d<1$ with a random potential acting…
This work investigates the local convergence behavior of Anderson acceleration in solving nonlinear systems. We establish local R-linear convergence results for Anderson acceleration with general depth $m$ under the assumptions that the…