Spectral filtering in quantum Y-junction

TL;DR

This paper investigates the scattering properties of quantum Y-junctions with degree 2 and 3, introducing a new boundary condition representation to design spectral branch-filters.

Contribution

It presents a novel boundary condition framework for singular vertices, enabling the design of quantum spectral filters in Y-junctions.

Findings

Effective representation of vertex boundary conditions.

Ability to design quantum spectral branch-filters.

Enhanced understanding of scattering in quantum junctions.

Abstract

We examine scattering properties of singular vertex of degree $n=2$ and $n=3$, taking advantage of a new form of representing the vertex boundary condition, which has been devised to approximate a singular vertex with finite potentials. We show that proper identification of $\delta$ and $\delta'$ components in the connection condition between outgoing lines enables the designing of quantum spectral branch-filters.