相关论文: Regularity of the density of states for random Dir…

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…

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…

We study the existence of uniformly bounded extension and trace operators for $W^{1,p}$-functions on randomly perforated domains, where the geometry is assumed to be stationary ergodic. Such extension and trace operators are important for…

It is shown that gauge field-dependent fermion Dirac operators from lattice QCD form an ergodic operator family in the probabilistic sense, provided the gauge field is an ergodic random field. As a consequence, the integrated density of…

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 establish spectral and dynamical localization for several Anderson models on metric and discrete radial trees. The localization results are obtained on compact intervals contained in the complement of discrete sets of exceptional…

We discuss various approaches to localization results for one-dimensional random Schr\"odinger operators, both discrete and continuum. We focus in particular on the approach based on F\"urstenberg's Theorem and the Kunz-Souillard method.…

We prove dynamical and spectral localization at all energies for the discrete generalized Anderson model via the Kunz-Souillard approach to localization. This is an extension of the original Kunz-Souillard approach to localization for…

We introduce a generalization of local density of states which is "windowed" with respect to position and energy, called the windowed local density of states (wLDOS). This definition generalizes the usual LDOS in the sense that the usual…

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…

Metaplectic Wigner distributions were recently investigated as natural generalizations of the classical Wigner distribution, and provide a wide class of time-frequency representations that exploits the structure of the symplectic group.…

We consider a Schroedinger operator with random potential distributed according to a Poisson process. We show that expectations of matrix elements of the resolvent as well as the density of states can be approximated to arbitrary precision…

The Wigner function for one and two-mode quantum systems is explicitely expressed in terms of the marginal distribution for the generic linearly transformed quadratures. Then, also the density operator of those systems is written in terms…

We prove a strictly positive, locally uniform lower bound on the density of states (DOS) of continuum random Schr\"odinger operators on the entire spectrum, i.e. we show that the DOS does not have a zero within the spectrum. This follows…

We consider Schr\"{o}dinger operators on $L^{2}({\mathbb R}^{d})\otimes L^{2}({\mathbb R}^{\ell})$ of the form $ H_{\omega}~=~H_{\perp}\otimes I_{\parallel} + I_{\perp} \otimes {H_\parallel} + V_{\omega}$, where $H_{\perp}$ and…

We establish large sets of Anderson localized states for the quasi-periodic nonlinear wave equation on $\mathbb Z^d$, thus extending nonlinear Anderson localization from the random \cite{BW08} to a deterministic setting.

We show regularity properties of local densities of solutions of stochastic differential equations (SDEs) with the Fourier analytic approach. With this simple method, statements that were previously derived with approaches using Malliavin…

In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…

We prove that a random group in the triangular density model has, for density larger than 1/3, fixed point properties for actions on $L^p$-spaces (affine isometric, and more generally $(2-2\epsilon)^{1/2p}$-uniformly Lipschitz) with $p$…

This paper provides a general framework for Stein's density method for multivariate continuous distributions. The approach associates to any probability density function a canonical operator and Stein class, as well as an infinite…