Geometric magnetism in open quantum systems

TL;DR

This paper extends the concept of geometric magnetism from classical chaotic systems to open quantum systems, providing explicit formulas and demonstrating that heat baths do not affect the geometric magnetism in a damped quantum harmonic oscillator.

Contribution

It introduces a quantum fluctuation relation approach to define geometric magnetism in open quantum systems, expanding the Berry curvature concept.

Findings

Geometric magnetism persists in open quantum systems with heat baths.

Explicit expressions for geometric forces in open quantum systems are derived.

Geometric magnetism remains unaffected by thermal environments in the studied model.

Abstract

An isolated classical chaotic system, when driven by the slow change of several parameters, responds with two reaction forces: geometric friction and geometric magnetism. By using the theory of quantum fluctuation relations we show that this holds true also for open quantum systems, and provide explicit expressions for those forces in this case. This extends the concept of Berry curvature to the realm of open quantum systems. We illustrate our findings by calculating the geometric magnetism of a damped charged quantum harmonic oscillator transported along a path in physical space in presence of a magnetic field and a thermal environment. We find that in this case the geometric magnetism is unaffected by the presence of the heat bath.