Localization on quantum graphs with random edge lengths

Details Localization on quantum graphs with random edge lengths Localization on quantum graphs with random edge lengths

2008-10-06

arxiv.org/abs/0810.1006v2

Physics

Mathematical Physics

Scientific paper

10.1007/s11005-009-0293-8

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 $\delta$-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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