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Published online by Cambridge University Press: 28 February 2011
Coherent excitations of localized states, represented by a selfsimilar Cayley tree, produce a gap in the density of states, which is deeper as the number of generations increases.
The model can suitably describe systems in which an optimized concentration of “defects” allows self similarity of the state-tree and coherent coupling between clusters of localized states.
A renormalization of the state-tree leads to a hierarchy of the energy eigenvalues.