Work

Families of isospectral and isoscattering quantum graphs

Year: 2025

Type: article

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 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.

Source: Physical Review Research

DOI: 10.1103/6yk9-17y3

Authors: Pavel Kurasov, Omer Farooq, Michał Ławniczak, Szymon Bauch, Mats-Erik Pistol, Matthew de Courcy-Ireland, Leszek Sirko

Institutions: Stockholm University, Institute of Physics, Polish Academy of Sciences, Lund University, Nordic Institute for Theoretical Physics

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

OpenAlex ID: W4410348485

FWCI: 6.801

Cites: 53

Cited by: 4

Related to: 10