Localization on quantum graphs with random vertex couplings
Mathematical Physics
2009-11-13 v1 math.MP
Abstract
We consider Schr\"odinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. These conditions hold in the strong disorder limit and at the spectral edges.
Cite
@article{arxiv.0710.3065,
title = {Localization on quantum graphs with random vertex couplings},
author = {Frédéric Klopp and Konstantin Pankrashkin},
journal= {arXiv preprint arXiv:0710.3065},
year = {2009}
}