Families of isospectral and isoscattering quantum graphs

• URL: http://arxiv.org/abs/2505.16621v1
• Date: Thu, 22 May 2025 12:54:52 GMT
• Title: Families of isospectral and isoscattering quantum graphs
• Authors: Pavel Kurasov, Omer Farooq, Michał Ławniczak, Szymon Bauch, Mats-Erik Pistol, Matthew de Courcy-Ireland, Leszek Sirko,
• Abstract summary: A concept of germ graphs and the M-function formalism are employed to construct large families of isospectral and isoscattering graphs.<n>We demonstrate that the introduced formalism can also be extended to graphs with dissipation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: A concept of germ graphs and the M-function formalism are employed to construct large families of isospectral and isoscattering graphs. This approach represents a complete departure from the original approach pioneered by Sunada, where isospectral graphs are obtained as quotients of a certain large symmetric graph. Using the M-function formalism and the symmetries of the graph itself we construct isospectral and isoscattering pairs. In our novel approach isospectral pairs do not need to be embedded into a larger symmetric graph as in Sunada's approach. We demonstrate that the introduced formalism can also be extended to graphs with dissipation. The theoretical predictions are validated experimentally using microwave networks emulating open quantum graphs with dissipation.

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