On quantum graph filters with flat passbands

TL;DR

This paper characterizes quantum graph vertices that act as controllable band-pass filters with flat passbands, where the bandwidth is adjustable via auxiliary edge potentials, advancing understanding of quantum graph scattering.

Contribution

It provides a new characterization of vertex couplings enabling flat passband transmission, highlighting the effectiveness of the $ST$-form boundary conditions for quantum graph scattering analysis.

Findings

Vertices with specific couplings act as controllable band-pass filters.

Bandwidth of the passband is directly controlled by auxiliary edge potentials.

The $ST$-form boundary conditions are effective for scattering studies in quantum graphs.

Abstract

We examine transmission through a quantum graph vertex to which auxiliary edges with constant potentials are attached. We find a characterization of vertex couplings for which the transmission probability from a given "input" line to a given "output" line shows a flat passband. The bandwidth is controlled directly by the potential on the auxiliary edges. Vertices with such couplings can thus serve as controllable band-pass filters. The paper extends earlier works on the topic. The result also demonstrates the effectivity of the $ST$-form of boundary conditions for a study of scattering in quantum graph vertices.