Related papers: The regular tree Anderson model at low disorder
We prove a result of delocalization for the Anderson model on the regular tree (Bethe lattice). When the disorder is weak, it is known that large parts of the spectrum are a.s. purely absolutely continuous, and that the dynamical transport…
We prove the almost sure existence of absolutely continuous spectrum at low disorder for the Anderson model on the simplest example of a product of a regular tree with a finite graph. This graph contains loops of unbounded size.
We give a new proof of a version of Klein's theorem on the existence of absolutely continuous spectrum for the Anderson model on the Bethe Lattice at weak disorder.
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 determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to…
For Anderson localization on the Cayley tree, we study the statistics of various observables as a function of the disorder strength $W$ and the number $N$ of generations. We first consider the Landauer transmission $T_N$. In the localized…
We consider the Anderson localization problem on the infinite regular tree. Within the localized phase, we derive a rigorous lower bound on the free energy function recently introduced by Aizenman and Warzel. Using a finite volume…
We prove persistence of absolutely continuous spectrum for the Anderson model on a general class of tree-like graphs.
We study analytically and numerically the Anderson model in one dimension with "stealthy" disorder, defined as having a power spectrum that vanishes in a continuous band of wave numbers. Motivated by recent studies on the optical…
We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams…
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 show how certain properties of the Anderson model on a tree are related to the solutions of a non-linear integral equation. Whether the wave function is extended or localized, for example, corresponds to whether or not the equation has a…
The Anderson localization problem in one and two dimensions is solved analytically via the calculation of the generalized Lyapunov exponents. This is achieved by making use of signal theory. The phase diagram can be analyzed in this way. In…
Our recently established criterion for the formation of extended states on tree graphs in the presence of disorder is shown to have the surprising implication that for bounded random potentials, as in the Anderson model, there is no…
We extend Edmonds' Branching Theorem to locally finite infinite digraphs. As examples of Oxley or Aharoni and Thomassen show, this cannot be done using ordinary arborescences, whose underlying graphs are trees. Instead we introduce the…
We provide an analytic theory of Anderson localization on a lattice with a weak short-range correlated disordered potential. Contrary to the general belief we demonstrate that even next-neighbor statistical correlations in the potential can…
We consider the Laplacian on a rooted metric tree graph with branching number $ K \geq 2 $ and random edge lengths given by independent and identically distributed bounded variables. Our main result is the stability of the absolutely…
We discuss the conditions under which an anomaly occurs in conductance and localization length of Anderson model on a lattice. Using the ladder hamiltonian and analytical calculation of average conductance we find the set of resonance…
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 provide a simplified version of the geometric method given by Froese, Hasler and Spitzer and use it to prove the existence of absolutely continuous spectrum for a Cayley tree of arbitrary degree k.