J.E. Avron, A. Elgart, G.M. Graf and L. Sadun Optimal Quantum Pumps (27K, LaTeX2e with RevTeX and with 2 PS Figures) ABSTRACT. Optimal pumps saturate a lower bound on energy dissipation. We give a characterization of optimal pumps in terms of the energy shift matrix, which is computed from the on-shell, frozen, scattering matrix. The energy shift determines the charge transport, the dissipation and entropy production in adiabatic pumps. We give a geometric characterization of optimal pumps and discuss an example.