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Related Experiment Video

Updated: Jan 11, 2026

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

Published on: August 2, 2019

Isoscattering non-isospectral quantum graphs.

Omer Farooq¹, Michał Ławniczak¹, Pavel Kurasov²

¹Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668, Warszawa, Poland.

Scientific Reports

|November 12, 2025

Summary

This summary is machine-generated.

Researchers explored isoscattering, non-isospectral quantum graphs, which have identical lengths but different structures. Experimental verification using microwave networks confirmed theoretical predictions for these complex systems.

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Area of Science:

Quantum mechanics
Graph theory
Mathematical physics

Background:

Isoscattering quantum graphs with identical total length but different topologies are challenging to identify and analyze.
Failure to recognize these graphs can lead to misinterpretations of spectral data.

Purpose of the Study:

To investigate the properties of isoscattering, non-isospectral quantum graphs.
To propose a method for experimentally identifying and analyzing these graphs.
To address the challenges in spectral interpretation caused by these graph types.

Main Methods:

Utilizing the Titchmarsh-Weyl M-function formalism.
Developing parameter-dependent non-isoscattering and non-isospectral graphs.
Transitioning graph parameters to zero to achieve isoscattering states.
Experimental verification using microwave networks.

Main Results:

Demonstrated the transformation of parameter-dependent graphs into isoscattering, non-isospectral pairs.
Confirmed theoretical predictions through experimental microwave network analysis.
Provided a method for constructing and studying isoscattering, non-isospectral quantum graphs.

Conclusions:

Isoscattering, non-isospectral quantum graphs can be experimentally identified and analyzed.
The proposed method offers a viable approach to understanding spectral properties in complex quantum systems.
This research highlights the importance of considering graph topology in spectral analysis.