Related papers: Simplicity of eigenvalues in the Anderson model

As a supplement of our previous work, we consider the localized region of the random Schroedinger operators on $l^2({\bf Z}^d)$ and study the point process composed of their eigenvalues and corresponding localization centers. For the…

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…

We consider the Anderson model at large disorder on $\mathbb{Z}^2$ where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These…

We develop a new approach for the Anderson localization problem. The implementation of this method yields strong numerical evidence leading to a (surprising to many) conjecture: The two dimensional discrete random Schroedinger operator with…

We show that any simple holomorphic disc admits the annulus property, i.e., each interior point is surrounded by an arbitrary small annulus consisting entirely of injective points. As an application we show that interior singularities of…

We establish the complete spectral exponential, and the strong Hilbert-Schmidt dynamical localization for the one-dimensional multi-particle Anderson tight-binding model and for weakly interacting particles system. In other words, we show…

In 1990, Klein, Lacroix, and Speis proved (spectral) Anderson localisation for the Anderson model on the strip of width $W \geqslant 1$, allowing for singular distribution of the potential. Their proof employs multi-scale analysis, in…

We consider the notion of equilibration for an isolated quantum system exhibiting Anderson localization. The system is assumed to be in a pure state, i.e., described by a wave-function undergoing unitary dynamics. We focus on the simplest…

We investigate the scaling properties of eigenstates of a one-dimensional (1D) Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this…

We survey the known results about simple permutations. In particular, we present a number of recent enumerative and structural results pertaining to simple permutations, and show how simple permutations play an important role in the study…

We show that the spacing between eigenvalues of the discrete 1D Hamiltonian with arbitrary potentials which are bounded, and with Dirichlet or Neumann Boundary Conditions is bounded away from zero. We prove an explicit lower bound, given by…

We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.

Anderson localization is ubiquitous in wavy systems with strong static and uncorrelated disorder. The delicate destructive interference underlying Anderson localization is usually washed out in the presence of temporal fluctuations or…

We prove delocalization for the Anderson model on an infinite regular tree (or Cayley graph or Bethe lattice) at low disorder. This extends earlier results of Klein and Aizenman--Warzel by filling in the previously missing parts of the…

Wave localization occurs in all types of vibrating systems, in acoustics, mechanics, optics, or quantum physics. It arises either in systems of irregular geometry (weak localization) or in disordered systems (Anderson localization). We…

Anderson localization is a famous wave phenomenon that describes the absence of diffusion of waves in a disordered medium. Here we generalize the landscape theory of Anderson localization to general elliptic operators and complex boundary…

Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions…

We discuss the techniques and results of the multi-particle Anderson localization theory for disordered quantum systems with nontrivial interaction. After a detailed presentation of the approach developed earlier by Aizenman and Warzel, we…

In this paper, we prove that every invertible $2$-local or local automorphism of a simple generalized Witt algebra over any field of characteristic $0$ is an automorphism. In particular, every $2$-local or local automorphism of Witt…

We show analytically that the apparent non-analyticity discovered recently in the inverse participation ratio (IPR) of the eigenstates in Anderson's model of localization is also present in a simple two-site model, along with a concurrent…