The Creation of Spectral Gaps by Graph Decoration

Jeffrey H. Schenker; Michael Aizenman

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arXiv · math-ph/0008013

The Creation of Spectral Gaps by Graph Decoration

Jeffrey H. Schenker·Michael Aizenman

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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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Jeffrey H. Schenker, Michael Aizenman. 2000-08-04. The Creation of Spectral Gaps by Graph Decoration. https://arxiv.org/abs/math-ph/0008013

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