Impurity induced coherent current oscillations in one-dimensional conductors

We study theoretically the electronic transport through a single impurity in a repulsive Luttinger liquid (LL), and find that above a threshold voltage related to a strength of the impurity potential the DC current $\bar I$ is accompanied by coherent oscillations with frequency $f = \bar I/e$. There is an analogy with Josephson junctions: the well-known regime of power-law I-V curves in the LL corresponds to damping of the Josephson current below the critical one, while the oscillatory regime in the LL can be compared with the Josephson oscillations above the critical current.