Backscattering off a point impurity: Current enhancement and conductance greater than $e^2/h$ per channel

It is well known that while forward scattering has no effect on the conductance of one-dimensional systems, backscattering off a static impurity suppresses the current. We study the effect of a time-dependent point impurity on the conductance of a one-channel quantum wire. At strong repulsive interaction (Luttinger liquid parameter $g<\mathrm{}1/2),$ backscattering renders the linear conductance greater than its value $e^2/h$ in the absence of the impurity. A possible experimental realization of our model is a constricted quantum wire or a constricted Hall bar at fractional filling factors $\nu =1/(2n+1)\mathrm{}$ with a time-dependent voltage at the constriction.