Localization on quantum graphs with random edge lengths
arXiv:0810.1006 · doi:10.1007/s11005-009-0293-8
Abstract
The spectral properties of the Laplacian on a class of quantum graphs with random metric structure are studied. Namely, we consider quantum graphs spanned by the simple $\ZZ^d$-lattice with -type boundary conditions at the vertices, and we assume that the edge lengths are randomly independently identically distributed. Under the assumption that the coupling constant at the vertices does not vanish, we show that the operator exhibits the Anderson localization at the bottom of the spectrum almost surely. We also study the case of other 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
- Transport properties of anyons in random topological environments
- Anderson Localization for a Multi-Particle Quantum Graph
- Some abstract Wegner estimates with applications
- Localization for quantum graphs with a random potential
- Random Schrödinger Operators on discrete structures