Transport and Dissipation in Quantum Pumps

TL;DR

This paper investigates adiabatic transport in quantum pumps, emphasizing the role of energy shift in determining various currents and exploring the geometric and topological aspects, including limitations of Chern number-based quantization.

Contribution

It introduces the concept of energy shift as a key operator in analyzing quantum pump transport and clarifies the topological constraints on quantized transport mechanisms.

Findings

Energy shift determines current, dissipation, noise, and entropy in quantum pumps.

Chern number-based quantization cannot occur in these systems due to topological constraints.

The paper highlights the geometric and topological structure underlying adiabatic quantum transport.

Abstract

This paper is about adiabatic transport in quantum pumps. The notion of ``energy shift'', a self-adjoint operator dual to the Wigner time delay, plays a role in our approach: It determines the current, the dissipation, the noise and the entropy currents in quantum pumps. We discuss the geometric and topological content of adiabatic transport and show that the mechanism of Thouless and Niu for quantized transport via Chern numbers cannot be realized in quantum pumps where Chern numbers necessarily vanish.