Transport properties of a Luttinger liquid in the presence of several time-dependent impurities

摘要

We study the transport properties of a Luttinger liquid in the presence ofseveral time-dependent weak point-like impurities. Our starting point is thebosonized form of the Luttinger liquid Hamiltonian with a potential introducedby the impurities. We find the correction to the total current due to thebackscattering of the electrons by the impurities in first order ofperturbation theory for a general time-dependent impurity potential. We thenapply this result to a single time-dependent impurity, and show that itreproduces the result obtained by Feldman and Gefen in Ref. [7], in particularthat the current enhancement occurs only for strong repulsive electron-electroninteractions. For the case of two impurities oscillating with the samefrequency, we find a novel effect, namely, that the dc-component of thebackscattering current is positive {it even for weak repulsive interactions},due to the presence of the interference term induced by spatial correlations inthe Luttinger liquid. We show that the impurity frequencies at which theenhancement takes place form a band-like structure. In the case of severalimpurities, the bands become broader, because of interference effects.