Work

Inverse scattering problem for quantum graph vertices

Year: 2011

Type: article

Abstract: We demonstrate how the inverse scattering problem of a quantum star graph can be solved by means of diagonalization of the Hermitian unitary matrix when the vertex coupling is of the scale-invariant (or F\"ul\"op-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.

Source: Physical Review A

DOI: 10.1103/physreva.83.062715

Authors: Taksu Cheon, Pavel Exner, Ondřej Turek

Institutions: Kochi University of Technology, Czech Academy of Sciences, Nuclear Physics Institute, Czech Technical University in Prague

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: Ministry of Education, Culture, Sports, Science and Technology, Grantová Agentura České Republiky, Japan Society for the Promotion of Science

Awards: Mathematical physics of exotic quantum holonomy, Guided Quantum Dynamics, G4394890256, G789053023