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Adiabatic Pumping in Interacting Systems

A dc current can be pumped through an interacting system by periodically varying two independent parameters such as magnetic field and a gate potential. We present a formula for the adiabatic pumping current in general interacting systems, in terms of instantaneous properties of the system, and find the limits for its applicability. This formula generalizes the scattering approach for noninteracting pumps. We study the pumped spin in a system that exhibits the two-channel Kondo effect as an application of the adiabatic pumping formula. We find that a quantized spin of $\hbar$ is transferred between the two channels as the temperature approaches zero, and discuss the non-Fermi liquid features of this system at finite temperatures.