Speaker: Christian Sadel, Pontificia Universidad Católica de Chile

Title: One-Channel Operators, a General Radial Transfer Matrix Approach and Absolutely Continuous Spectrum

Date: 07/18/2018

Time: 11:00 AM - 12:00 PM

Place: C304 Wells Hall

First I will introduce one-channel operators and their spectral theory analyses through transfer matrices solving the eigenvalue equation.
Then, inspired from the specific form of these transfer matrices, we will define sets of transfer matrices for any discrete Hermitian operator with locally finite hopping by considering quasi-spherical partitions.
A generalization of some spectral averaging formula for Jacobi operators is given and criteria for the existence and pureness of absolutely continuous spectrum are derived.
As applications we will mention certain cases of random operators with absolutely continuous spectrum (Anderson model on anti trees and partial anti-trees; random decaying shell-matrix potential).