Related papers: Ergodicity and dynamical localization for Delone-A…
Despite all the analogies with "usual random" models, tight binding operators for quasicrystals exhibit a feature which clearly distinguishes them from the former: the integrated density of states may be discontinuous. This phenomenon is…
We study spectral properties of ergodic random Schr\"odinger operators on $L^2 (\RR^d)$. The density of states is shown to exist for a certain class of alloy type potentials with single site potentials of changing sign. The Wegner estimate…
We provide an ergodic theorem for certain Banach-space valued functions on structures over $\ZZ^d$, which allow for existence of frequencies of finite patterns. As an application we obtain existence of the integrated density of states for…
We give a detailed survey of results obtained in the most recent half decade which led to a deeper understanding of the random displacement model, a model of a random Schr\"odinger operator which describes the quantum mechanics of an…
In a tight binding framework, we analyze the characteristics of electronic states in strongly disordered materials (hopping sites are placed randomly with no local order) with tunneling matrix elements decaying exponentially in the atomic…
In the present note we show dynamical localization for an Anderson model with missing sites in a discrete setting at the bottom of the spectrum in arbitrary dimension $d$. In this model, the random potential is defined on a relatively dense…
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…
The density of states of Dirac fermions with a random mass on a two-dimensional lattice is considered. We give the explicit asymptotic form of the single-electron density of states as a function of both energy and (average) Dirac mass, in…
We investigate the behavior of ultracold bosons in optical lattices with a disorder potential generated via a secondary species frozen in random configurations. The statistics of disorder is associated with the physical state in which the…
We investigate the integrated density of states of the Schr\"odinger operator in the Euclidean plane with a perpendicular constant magnetic field and a random potential. For a Poisson random potential with a non-negative algebraically…
This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum…
We continue the investigations of Kirsch, Metzger and the second-named author [J. Stat. Phys. 143, 1035--1054 (2011)] on spectral properties of a certain type of random block operators. In particular, we establish an alternative version of…
Motivated by current interest in disordered systems of interacting electrons, the effectiveness of the geometrically averaged density of states, $\rho_g(\omega)$, as an order parameter for the Anderson transition is examined. In the context…
We characterize the soft modes of the dynamical matrix at the depinning transition, and compare it with the properties of the Anderson model (and long--range generalizations). The density of states at the edge of the spectrum displays a…
We prove that the random Schrodinger operators on $\mathbb{R}^3$ with independent, identically distributed random variables and single-site potentials given by $\delta$-functions on $\mathbb{Z}^3$, exhibit both dynamical localization and…
We study spectra and localization properties of Euclidean random matrices. The problem is approximately mapped onto that of a matrix defined on a random graph. We introduce a powerful method to find the density of states and the…
We present a new large-deviation approach to investigate the critical properties of the Anderson model on the Bethe lattice close to the localization transition in the thermodynamic limit. Our method allows us to study accurately the…
We prove that, for a density of disorder $\rho$ small enough, a certain class of discrete random Schr\"odinger operators on $\Z^d$ with diluted potentials exhibits a Lifschitz behaviour from the bottom of the spectrum up to energies at a…
The presence and character of local integrals of motion -- quasi-local operators that commute with the Hamiltonian -- encode valuable information about the dynamics of a quantum system. In particular, strongly disordered many-body systems…
We consider the discrete Laplace operator $\Delta^{(N)}$ on Erd\H{o}s--R\'{e}nyi random graphs with $N$ vertices and edge probability $p/N$. We are interested in the limiting spectral properties of $\Delta^{(N)}$ as $N\to\infty$ in the…