 
Summary: VOLUME 87, NUMBER 23 P H Y S I C A L R E V I E W L E T T E R S 3 DECEMBER 2001
Optimal Quantum Pumps
J. E. Avron,1 A. Elgart,2 G. M. Graf,3 and L. Sadun4
1
Department of Physics, Technion, 32000 Haifa, Israel
2
Department of Physics, Jadwin Hall, Princeton University, Princeton, New Jersey 08544
3
Theoretische Physik, ETHHönggerberg, 8093 Zürich, Switzerland
4
Department of Mathematics, University of Texas, Austin, Texas 78712
(Received 8 May 2001; published 13 November 2001)
We study adiabatic quantum pumps on time scales that are short relative to the cycle of the pump. In
this regime the pump is characterized by the matrix of energy shift which we introduce as the dual to
Wigner's time delay. The energy shift determines the charge transport, the dissipation, the noise, and
the entropy production. We prove a general lower bound on dissipation in a quantum channel and define
optimal pumps as those that saturate the bound. We give a geometric characterization of optimal pumps
and show that they are noiseless and transport integral charge in a cycle. Finally we discuss an example
of an optimal pump related to the Hall effect.
DOI: 10.1103/PhysRevLett.87.236601 PACS numbers: 72.10.Bg, 73.23.b
