Anderson localization for radial tree-like random quantum graphs

Anderson localization for radial tree-like random quantum graphs (0)

by P Hislop, O Post

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Stollmann: Eigenfunction expansion for Schrödinger operators on metric graphs (Preprint arXiv:0801.1376

by Daniel Lenz, Carsten Schubert, Peter Stollmann

"... Abstract. We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices. ..."

Abstract - Cited by 7 (4 self) - Add to MetaCart

Abstract. We construct an expansion in generalized eigenfunctions for Schrödinger operators on metric graphs. We require rather minimal assumptions concerning the graph structure and the boundary conditions at the vertices.

Localization on quantum graphs with random vertex couplings

by Frédéric Klopp, Konstantin Pankrashkin - J. Statist. Phys

"... 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 ..."

Abstract - Cited by 6 (0 self) - Add to MetaCart

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.