Inverse scattering problem for quantum graph vertices
Quantum Physics
2011-09-22 v1 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
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.
Cite
@article{arxiv.1104.1048,
title = {Inverse scattering problem for quantum graph vertices},
author = {Taksu Cheon and Pavel Exner and Ondrej Turek},
journal= {arXiv preprint arXiv:1104.1048},
year = {2011}
}
Comments
ReVTeX, 4 pages, four figures