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The Creation of Spectral Gaps by Graph Decoration

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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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Authors and Affiliations

  1. Department of Mathematics, Princeton University, Princeton, NJ, 08544, U.S.A.

    Jeffrey H. Schenker

  2. Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08544, U.S.A.

    Michael Aizenman

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  1. Jeffrey H. Schenker
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  2. Michael Aizenman
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Schenker, J.H., Aizenman, M. The Creation of Spectral Gaps by Graph Decoration. Letters in Mathematical Physics 53, 253–262 (2000). https://doi.org/10.1023/A:1011032212489

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  • DOI: https://doi.org/10.1023/A:1011032212489

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