Equivalence of topological and scattering approaches to quantum pumping

TL;DR

This paper demonstrates the equivalence between topological and scattering approaches to quantum pumping, unifying two previously separate descriptions of charge transport in adiabatic quantum systems.

Contribution

It generalizes the topological description of quantum pumping and proves its equivalence to the scattering matrix approach.

Findings

Topological and scattering descriptions are mathematically equivalent.

The work applies to both infinite gapped systems and finite systems with leads.

Provides a unified framework for understanding quantum pumping mechanisms.

Abstract

The Schroedinger equation with a potential periodically varying in time is used to model adiabatic quantum pumps. The systems considered may be either infinitely extended and gapped or finite and connected to gapless leads. Correspondingly, two descriptions of the transported charge, one relating to a Chern number and the other to a scattering matrix, have been available for some time. Here we generalize the first one and establish its equivalence to the second.