Peculiarity of Symmetric Ring Systems with Double Y-Junctions and the magnetic effects

TL;DR

This paper analyzes quantum dynamics in symmetric ring systems with double Y-junctions, revealing inevitable localized states and resonant perfect transmission, and explores the effects of magnetic disturbances on these phenomena.

Contribution

It introduces a mathematical formulation of symmetric ring systems with Y-junctions using scattering matrices and uncovers their unique localization and transmission properties.

Findings

Localized states exist inevitably in symmetric ring systems.

Resonant perfect transmission occurs at specific wavenumbers.

Magnetic disturbances influence the quantum dynamics in these systems.

Abstract

We discuss quantum dynamics in the ring systems with double Y-junctions in which two arms have same length. The node of a Y-junction can be parametrized by U(3). Considering mathematically permitted junction conditions seriously, we formulate such systems by scattering matrices. We show that the symmetric ring systems, which consist of two nodes with the same parameters under the reflection symmetry, have remarkable aspects that there exist localized states inevitably, and resonant perfect transmission occurs when the wavenumber of an incoming wave coincides with that of the localized states, for any parameters of the nodes except for the extremal cases in which the absolute values of components of scattering matrices take $1$. We also investigate the magnetic disturbance to the symmetric ring systems.