Quantum pumping: The charge transported due to a translation of a scatterer

TL;DR

This paper investigates the fundamental aspects of quantum pumping, specifically how charge transport relates to scatterer displacement, using a network model and Kubo formula to explore dependencies on system openness, transmission, chaos, and environment coupling.

Contribution

It provides a detailed analysis of the quantum pumping mechanism using network models and the Kubo formula, addressing open questions about system dependence and chaos effects.

Findings

Charge transport relates to scatterer displacement via a conductance G.

G depends on system openness, transmission, and chaos.

The study clarifies fundamental aspects of quantum pumping theory.

Abstract

The amount of charge which is pushed by a moving scatterer is $dQ = -G dX$, where $dX$ is the displacement of the scatterer. The question is what is $G$. Does it depend on the transmission $g_0$ of the scatterer? Does the answer depend on whether the system is open (with leads attached to reservoirs) or closed? In the latter case: what are the implications of having ``quantum chaos" and/or coupling to to the environment? The answers to these questions illuminate some fundamental aspects of the theory of quantum pumping. For the analysis we take a network (graph) as a model system, and use the Kubo formula approach.