Related papers: Anderson Localization for Radial Tree Graphs With …
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 consider a two dimensional magnetic Schroedinger operator on a square lattice with a spatially stationary random magnetic field. We prove Anderson localization near the spectral edges. We use a new approach to establish a Wegner estimate…
We consider disordered Hamiltonians given by the Laplace operator subject to arbitrary random self-adjoint singular perturbations supported on random discrete subsets of the real line. Under minimal assumptions on the type of disorder, we…
We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the…
The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lattice with $\delta$-type boundary conditions at the vertices,…
We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional…
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…
In this paper, we use Cartan estimate for meromorphic functions to prove Anderson localization for a class of long-range operators with singular potenials.
In this paper, we prove Anderson localization for a hierarchical Anderson-Bernoulli model on lattice with arbitrary dimension, where the potential is characterized by a geometric hierarchical structure combined with fluctuations induced by…
We consider a random Schr\"odinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, $Q_r$, and a random transversally periodic potential, $\kappa Q_t$, with coupling constant…
We prove non-perturbative Anderson localization for quasi-periodic Jacobi block matrix operators assuming non-vanishing of all Lyapunov exponents. The base dynamics on tori $\mathbb{T}^b$ is assumed to be a Diophantine rotation. Results on…
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…
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 investigate the distribution of the resonances near spectral thresholds of Laplace operators on regular tree graphs with $k$-fold branching, $k \geq 1$, perturbed by nonself-adjoint exponentially decaying potentials. We establish results…
A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale…
In this paper, we establish Anderson localization for a class of Jacobi matrices associated with skew shifts on $\mathbb{T}^{d}$, $d\geq3$.
Anderson localization is studied for two-dimensional Dirac fermions in the presence of strong random scattering. Averaging with respect to the latter leads to a graphical representation of the correlation function with entangled random…
We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on $\ZZ^d$. We establish geometric…
We prove localization and probabilistic bounds on the minimum level spacing for the Anderson tight-binding model on the lattice in any dimension, with single-site potential having a discrete distribution taking N values, with N large.
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…