Threshold resonance and controlled filtering in quantum star graphs

We design two simple quantum devices applicable as an adjustable quantum spectral filter and as a flux controller. Their function is based upon the threshold resonance in a F\"ul\"op-Tsutsui type star graph with an external potential added on one of the lines. Adjustment of the potential strength directly controls the quantum flow from the input to the output line. This is the first example to date in which the quantum flow control is achieved by addition of an external field not on the channel itself, but on other lines connected to the channel at a vertex.