Adiabatic Process and Chern Numbers

TL;DR

This paper explores the topological properties of quantum systems with multiple adiabatic parameters, linking Chern numbers to physical phenomena like the AC Josephson effect and spin Hall effect.

Contribution

It introduces a topological framework using Chern numbers for quantum processes with multiple adiabatic parameters, applied to specific physical effects.

Findings

Chern numbers characterize quantum processes with multiple parameters.

Topological formulation explains the AC Josephson and spin Hall effects.

Integer Chern numbers relate to quantized physical phenomena.

Abstract

We study quantum processes with two or more adiabatic parameters. When the parameters are compactified, a derivative of the Hamiltonian gives a first Chern number, hence an integer. This topological formulation is applied to the AC Josephson effect and the spin Hall effect in semiconductors.