Localization on quantum graphs with random vertex couplings

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 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.

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Cited by in corpus (7)

• Unitary dimension reduction for a class of self-adjoint extensions with applications to graph-like structures
• Continuity of the integrated density of states on random length metric graphs
• Localization on quantum graphs with random edge lengths
• Decorrelation estimates for some continuous and discrete random schrödinger operators in dimension one and applications to spectral statistics
• Some abstract Wegner estimates with applications
• Anderson Localization for a Multi-Particle Quantum Graph
• Spectral localization for quantum Hamiltonians with weak random delta interaction