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Localization on quantum graphs with random vertex couplings. (English) Zbl 1144.82061
Summary: We consider Schrödinger operators on a class of periodic quantum graphs with randomly distributed Kirchhoff coupling constants at all vertices. We obtain necessary 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.

82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics
82C44 Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics
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