Scattering approach to parametric pumping

Abstract

A dc current can be pumped through a quantum dot by periodically varying two independent parameters ${X}_{1}$ and ${X}_{2},$ like a gate voltage or magnetic field. We present a formula that relates the pumped current to the parametric derivatives of the scattering matrix ${S(X}_{1}{,X}_{2})$ of the system. As an application we compute the statistical distribution of the pumped current in the case of a chaotic quantum dot.