Absolutely continuous spectrum for a random potential on a tree with strong transverse correlations and large weighted loops

Abstract

We consider random Schrödinger operators on tree graphs and prove absolutely continuous spectrum at small disorder for two models. The first model is the usual binary tree with certain strongly correlated random potentials. These potentials are of interest since for complete correlation they exhibit localization at all disorders. In the second model we change the tree graph by adding all possible edges to the graph inside each sphere, with weights proportional to the number of points in the sphere.

25 pages, 4 figures

References in corpus (4)

• Absolutely Continuous Spectra of Quantum Tree Graphs with Weak Disorder
• The Canopy Graph and Level Statistics for Random Operators on Trees
• Singular Continuous Spectrum for the Laplacian on Certain Sparse Trees
• Localization for the Anderson Model on Trees with Finite Dimensions

Cited by in corpus (6)

• Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel
• Absolutely Continuous Spectrum for random Schroedinger operators on the Fibonacci and similar tree-strips
• Absolutely Continuous Spectrum for Random Schroedinger Operators on Tree-Strips of finite cone type
• On the AC spectrum of one-dimensional random Schroedinger operators with matrix-valued potentials
• A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
• Absolutely Continuous Spectrum for the Anderson Model on Some Tree-like Graphs