Quantum pump for spin and charge transport in a Luttinger liquid

We study two different parametric pumps for interacting quantum wires, one for pumping spin currents, the other for charge currents. We find that the spin or charge pumped per cycle has a non-universal crossover, depending on pumping details, between two universal fixed point values of 0 and twice the electronic spin or charge quantum number. These universal values are independent of interactions, but the direction of flow between the two values depends on whether the interactions are repulsive or attractive.