The Creation of Spectral Gaps by Graph Decoration |
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| Authors: | Schenker Jeffrey H. Aizenman Michael |
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| Affiliation: | (1) Department of Mathematics, Princeton University, Princeton, NJ, 08544, U.S.A.;(2) Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08544, U.S.A. |
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| Abstract: | We present a mechanism for the creation of gaps in the spectra of self-adjoint operators defined over a Hilbert space of functions on a graph, which is based on the process of graph decoration. The resulting Hamiltonians can be viewed as associated with discrete models exhibiting a repeated local structure and a certain bottleneck in the hopping amplitudes. |
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| Keywords: | spectral gaps graph Laplacians graph decoration |
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