Anderson Localization for radial tree-like random quantum graphs

Details Anderson Localization for radial tree-like random quantum graphs Anderson Localization for radial tree-like random quantum graphs

2006-11-10

arxiv.org/abs/math-ph/0611022v2

Physics

Mathematical Physics

64 pages, 5 figures, typos corrected

Scientific paper

We prove that certain random models associated with radial, tree-like, rooted quantum graphs exhibit Anderson localization at all energies. The two main examples are the random length model (RLM) and the random Kirchhoff model (RKM). In the RLM, the lengths of each generation of edges form a family of independent, identically distributed random variables (iid). For the RKM, the iid random variables are associated with each generation of vertices and moderate the current flow through the vertex. We consider extensions to various families of decorated graphs and prove stability of localization with respect to decoration. In particular, we prove Anderson localization for the random necklace model.

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