Quantum stirring of particles in closed devices

TL;DR

This paper investigates quantum pumping in closed devices by translating a scatterer, revealing counterintuitive current directions and connecting quantum chaos considerations with the quantum-classical correspondence.

Contribution

It introduces a novel approach to quantum pumping in closed systems using the Kubo formula and line integrals around Dirac monopoles, linking quantum chaos to transport phenomena.

Findings

Counterintuitive current flow when moving scatterers

Relation between quantum chaos and pumping efficiency

Connection to S matrix formalism in open systems

Abstract

We study the quantum analog of stirring of water inside a cup using a spoon. This can be regarded as a prototype example for quantum pumping in closed devices. The current in the device is induced by translating a scatterer. Its calculation is done using the Kubo formula approach. The transported charge is expressed as a line integral that encircles chains of Dirac monopoles. For simple systems the results turn out to be counter intuitive: e.g. as we move a small scatterer "forward" the current is induced "backwards". One should realize that the route towards quantum-classical correspondence has to do with "quantum chaos" considerations, and hence assumes greater complexity of the device. We also point out the relation to the familiar $S$ matrix formalism which is used to analyze quantum pumping in open geometries.