Heat current in parametric quantum pump
  We investigate the heat flow in the parametric quantum pump. Using the time dependent scattering matrix theory, we have developed a general theory for the pumped heat current at finite pumping amplitude and frequency. We have applied our theory to a double barrier structure and studied pumped heat current in both the weak and strong pumping regimes as different system parameters vary. By comparing the pumped heat current and the power of Joule heat generated in the system, we found that the double barrier structure can function as an optimal pump in the strong pumping regime. 
Baigeng Wang and Jian Wang