Spectral filtering in quantum Y-junction

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.