Related papers: Resonant delocalization on the Bethe strip
We consider perturbations of quasi-periodic Schr\"odinger operators on the integer lattice with analytic sampling functions by decaying potentials and seek decay conditions under which various spectral properties are preserved. In the…
This paper studies the delocalized regime of an ultrametric random operator whose independent entries have variances decaying in a suitable hierarchical metric on $\mathbb{N}$. When the decay-rate of the off-diagonal variances is…
We resolve an existing question concerning the location of the mobility edge for operators with a hopping term and a random potential on the Bethe lattice. The model has been among the earliest studied for Anderson localization, and it…
We investigate spectral properties of a discrete random displacement model, a Schr\"odinger operator on $\ell^2(\Z^d)$ with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of…
We consider Schr\"odinger operators with periodic electric and magnetic potentials on periodic discrete graphs. The spectrum of such operators consists of an absolutely continuous (a.c.) part (a union of a finite number of non-degenerate…
We study localisation effects of strong disorder on the spectral and dynamical properties of (matrix and scalar) Schroedinger operators with non-monotone random potentials, on the d-dimensional lattice. Our results include dynamical…
We consider Schr\"odinger operators $H=-\Delta+V({\mathbf x})$ in ${\mathbb R}^d$, $d\geq2$, with quasi-periodic potentials $V({\mathbf x})$. We prove that the absolutely continuous spectrum of a generic $H$ contains a semi-axis…
We prove spectral and dynamical localization on a cubic-lattice quantum graph with a random potential. We use multiscale analysis and show how to obtain the necessary estimates in analogy to the well-studied case of random Schroedinger…
For random operators it is conjectured that spectral properties of an infinite-volume operator are related to the distribution of spectral gaps of finite-volume approximations. In particular, localization and pure point spectrum in infinite…
We consider Schr\"odinger operators in $\ell^2(\mathbb{Z})$ whose potentials are given by the sum of an ergodic term and a random term of Anderson type. Under the assumption that the ergodic term is generated by a homeomorphism of a…
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 study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic…
We show that one-dimensional Schr{\"o}dinger operators whose potentials arise by randomly concatenating words from an underlying set exhibit exponential dynamical localization (EDL) on any compact set which trivially intersects a finite set…
The theory of random sets is demonstrated to prove useful for the theory of random operators. A random operator is here defined by requiring the graph to be a random set. It is proved that the spectrum and the set of eigenvalues of random…
A tree-strip of finite cone type is the product of a tree of finite cone type with a finite set. We consider random Schr\"odinger operators on these tree strips, similar to the Anderson model. We prove that for small disorder the spectrum…
We consider normalized Laplacians and their perturbations by periodic potentials (Schr\"odinger operators) on periodic discrete graphs. The spectrum of the operators consists of an absolutely continuous part (a union of a finite number of…
It is conjectured that the eigenvalues of random Schrodinger operators at the localization transition in dimensions d>=2 behave like the eigenvalues of the Gaussian Orthogonal Ensemble (GOE). We show that there are sequences of n by m boxes…
We prove a quantum-ergodicity theorem on large graphs, for eigenfunctions of Schr\"odinger operators in a very general setting. We consider a sequence of finite graphs endowed with discrete Schr\"odinger operators, assumed to have a local…
We consider multi-dimensional Schr\"odinger operators with a weak random perturbation distributed in the cells of some periodic lattice. In every cell the perturbation is described by the translate of a fixed abstract operator depending on…
We consider a natural class of extensions of the Anderson model on $\mathbb Z^d$, called random block Schr\"odinger operators (RBSOs), defined on the $d$-dimensional torus $(\mathbb Z/L\mathbb Z)^d$. These operators take the form…