Scattering from isospectral quantum graphs

Abstract

Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles distributions are therefore identical. The scattering matrices are studied using a recently developed isospectral theory. At the same time, the scattering approach offers a new insight on the mentioned isospectral construction.

References in corpus (3)

• The Isospectral Fruits of Representation Theory: Quantum Graphs and Drums
• The inverse scattering problem for metric graphs and the traveling salesman problem
• Nodal domains on isospectral quantum graphs: the resolution of isospectrality ?

Cited by in corpus (10)

• Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
• Chaos in Dirac electron optics: Emergence of a relativistic quantum chimera
• Green's function approach for quantum graphs: an overview
• Non-abelian Quantum Statistics on Graphs
• Isospectral graphs with identical nodal counts
• Resonances and poles in isoscattering microwave networks and graphs
• On the Effective Size of a Non-Weyl Graph
• Families of isospectral and isoscattering quantum graphs
• Discovering hidden layers in quantum graphs
• Note on the role of symmetry in scattering from isospectral graphs and drums