Recovering quantum graphs from their Bloch spectrum

Ralf Rueckriemen

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arXiv · 1101.6002

Recovering quantum graphs from their Bloch spectrum

Ralf Rueckriemen

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Abstract

We define the Bloch spectrum of a quantum graph to be the collection of the spectra of a family of Schrodinger operators parametrized by the cohomology of the quantum graph. We show that the Bloch spectrum determines the Albanese torus, the block structure and the planarity of the graph. It determines a geometric dual of a planar graph. This enables us to show that the Bloch spectrum completely determines planar 3-connected quantum graphs.

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BibTeX RIS

Ralf Rueckriemen. 2011-01-31. Recovering quantum graphs from their Bloch spectrum. https://arxiv.org/abs/1101.6002

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