English

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.

Keywords

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}
}
R2 v1 2026-06-21T09:32:32.078Z