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Localization on Quantum Graphs with Random Edge Lengths |
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| Authors: | Frédéric Klopp Konstantin Pankrashkin |
| Affiliation: | 1. Laboratoire Analyse, Géométrie et Applications, CNRS UMR 7539, Institut Galilée, Université Paris-Nord, 99 av. Jean-Baptiste Clément, 93430, Villetaneuse, France 2. Institut Universitaire de France, 103 bd. Saint-Michel, 75005, Paris, France 3. Institut für Mathematik, Humboldt-Universit?t, Rudower Chaussee 25, 12489, Berlin, Germany 4. Laboratoire de mathématiques, CNRS UMR 8628, Unversité Paris-Sud, Batiment 425, 91405, Orsay, France |
| 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 ${mathbb Z^d}$ -lattice with δ-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 near the spectral edges situated outside a certain forbidden set. |
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