Interaction correction to the conductance of a ballistic conductor

In disordered metals, electron-electron interactions are the origin of a small correction to the conductivity, the Altshuler-Aronov correction. Here we investigate the Altshuler-Aronov correction of a conductor in which the electron motion is ballistic and chaotic. We consider the case of a double quantum dot, which is the simplest example of a ballistic conductor in which the Altshuler-Aronov correction is nonzero. The fact that the electron motion is ballistic leads to an exponential suppression of the correction if the Ehrenfest time is larger than the mean dwell time or the inverse temperature.