  We consider an interacting, one-dimensional Bose gas confined in a split
trap, obtained by an harmonic potential with a localized barrier at its center.
We address its quantum-transport properties through the study of dipolar
oscillations, which are induced by a sudden quench of the position of the
center of the trap. We find that the dipole-mode frequency strongly depends on
the interaction strength between the particles, yielding information on the
classical screening of the barrier and on its renormalization due to quantum
fluctuations. Furthermore, we predict a parity effect which becomes most
prominent in the strongly correlated regime.
