Dynamic enhancement of conductance in fractional quantum Hall constriction

A disparity in the charge of quasi-particle excitations across a tunnel junction can trigger Andreev-like processes, creating an effect similar to that of a step-up transformer. We study such a junction in its strong coupling limit in the context of quantum Hall states. Specifically, for filling fractions $\nu =1$ and $1\mathrm{/}3$, we show the DC gain in the transformer action is bounded by 3/2, irrespective of the interedge interaction range, while the AC gain is bounded by $\sqrt{3}$ and is sensitive to the range of the interaction. This setup presents a unique possibility of frequency-tunable resonances and anti-resonances across the QPC.