Home // International Journal On Advances in Systems and Measurements, volume 5, numbers 1 and 2, 2012 // View article

Reflectionless and Equiscattering Quantum Graphs and Their Applications

Authors:
Taksu Cheon

Keywords: quantum graph; singular vertex; quantum wire; inverse scattering;quantum filter

Abstract:
The inverse scattering problem of a quantum star graph is shown to be solvable as a diagonalization problem of Hermitian unitary matrix when the connection condition is given by scale invariant Fulop-Tsutsui form. This enables the construction of quantum graphs with desired properties. The quantum vertices with uniform and reflectionless scatterings are examined, and their finite graph approximations are constructed. It is shown that a controllable spectral filter can be constructed from a certain reflectionless graph with the application of external potential on a line.

Pages: 34 to 44

Copyright: Copyright (c) to authors, 2012. Used with permission.

Publication date: June 30, 2012

Published in: journal

ISSN: 1942-261x