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Families of isospectral and isoscattering quantum graphs

Kurasov, Pavel LU ; Farooq, Omer ; Ławniczak, Michał ; Bauch, Szymon ; Pistol, Mats Erik LU ; De Courcy-Ireland, Matthew and Sirko, Leszek (2025) In Physical Review Research 7(2).
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... (More)

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.

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author
; ; ; ; ; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review Research
volume
7
issue
2
article number
L022071
publisher
American Physical Society
external identifiers
  • scopus:105023157160
ISSN
2643-1564
DOI
10.1103/6yk9-17y3
language
English
LU publication?
yes
id
4cfd2852-0e71-4bb8-b143-cdabf65d7122
date added to LUP
2026-02-03 14:58:46
date last changed
2026-02-09 08:41:52
@article{4cfd2852-0e71-4bb8-b143-cdabf65d7122,
  abstract     = {{<p>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.</p>}},
  author       = {{Kurasov, Pavel and Farooq, Omer and Ławniczak, Michał and Bauch, Szymon and Pistol, Mats Erik and De Courcy-Ireland, Matthew and Sirko, Leszek}},
  issn         = {{2643-1564}},
  language     = {{eng}},
  number       = {{2}},
  publisher    = {{American Physical Society}},
  series       = {{Physical Review Research}},
  title        = {{Families of isospectral and isoscattering quantum graphs}},
  url          = {{http://dx.doi.org/10.1103/6yk9-17y3}},
  doi          = {{10.1103/6yk9-17y3}},
  volume       = {{7}},
  year         = {{2025}},
}