Frédéric Klopp

Localization for random quantum graphs (joint with K. Pankrashkin)

Abstract : we consider Schrödinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. Using the technique of self-adjoint extensions and finite volume localization criteria for discrete random Schrödinger operators, we obtain conditions for localization on quantum graphs in terms of finite volume criteria for some energy-dependent discrete Hamiltonians. This is then applied to large coupling and band edge localization.