Distinguishing co-spectral quantum graphs by scattering

Abstract

We propose a simple method for resolution of co-spectrality of Schrödinger 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.

References in corpus (2)

• Isospectral graphs via spectral bracketing
• Cospectral quantum graphs

Cited by in corpus (1)

• Families of isospectral and isoscattering quantum graphs