Inverse scattering problem for quantum graph vertices
Taksu Cheon, Pavel Exner, Ondrej Turek
TL;DR
This paper presents a method to solve the inverse scattering problem for quantum star graphs with scale-invariant vertex coupling, enabling tailored construction of quantum graphs with specific properties.
Contribution
It introduces a diagonalization approach for Hermitian unitary matrices to solve the inverse scattering problem for scale-invariant quantum graph vertices.
Findings
Method works for vertices with equal transmission probabilities
Allows construction of quantum graphs with desired scattering properties
Provides a systematic approach for quantum graph design
Abstract
We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of Hermitian unitary matrix when the vertex coupling is of the scale invariant (or F\"ul\H{o}p-Tsutsui) form. This enables the construction of quantum graphs with desired properties in a tailor-made fashion. The procedure is illustrated on the example of quantum vertices with equal transmission probabilities.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.