Adiabatic charge pumping in open quantum systems

TL;DR

This paper develops a mathematical framework for understanding charge transport in quantum pumps connected to external leads, demonstrating that in the adiabatic limit, the current can be described by a formula linking it to the frozen S-matrix and its time derivative.

Contribution

It provides a rigorous mathematical proof that the adiabatic charge current in quantum pumps follows a known formula under general Hamiltonian assumptions.

Findings

Current in quantum pumps is given by Buttiker, Pretre, and Thomas formula.

The formula relates current to the frozen S-matrix and its time derivative.

The proof applies under broad conditions on the Hamiltonian.

Abstract

We introduce a mathematical setup for charge transport in quantum pump connected to a number of external leads. It is proved that under rather general assumption on the Hamiltonian describing the system, in the adiabatic limit, the current through the pump is given by a formula of Buttiker, Pretre, and Thomas, relating it to the frozen S-matrix and its time derivative.