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arXiv · 2211.05465

Distinguishing co-spectral quantum graphs by scattering

Delio Mugnolo·Vyacheslav Pivovarchik
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Abstract

We propose a simple method for resolution of co-spectrality of Schr\"odinger operators on metric graphs. Our approach consists of attaching a lead to them and comparing the $S$-functions of the corresponding scattering problems on these (non-compact) graphs. We show that in several cases -- including general graphs on at most 6 vertices, general trees on at most 9 vertices, and general fuzzy balls -- eigenvalues and scattering data are together sufficient to distinguish co-spectral metric graphs.

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Delio Mugnolo, Vyacheslav Pivovarchik. 2022-11-10. Distinguishing co-spectral quantum graphs by scattering. https://doi.org/10.1088/1751-8121%2Facbb44

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