Transient effects in the backscattered current of a Luttinger liquid

We study the backscattered current in a Luttinger liquid in the presence of a point like weak impurity switched on at finite time, taking into account finite-temperature effects. We show how the well-known results for a static impurity are distorted. We derive a dimensionless parameter $\tau_{R}$ as function of the electron-electron interaction and the temperature, such that for $\tau_{R} < 1$ ($> 1$) the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter $K$ through time measurements in transport experiments at fixed voltage.