A new kind of geometric phases in open quantum systems and higher gauge theory

TL;DR

This paper introduces a novel geometric phase concept for open quantum systems using higher gauge theory, revealing how environmental decoherence manifests geometrically in a categorical bundle framework.

Contribution

It extends geometric phases to open quantum systems with a new higher gauge theory approach based on categorical principal bundles.

Findings

Defines geometric phases for mixed states in open quantum systems.

Connects decoherence effects to higher gauge structures.

Proposes a mathematical framework using non-abelian bundle gerbes.

Abstract

A new approach extending the concept of geometric phases to adiabatic open quantum systems described by density matrices (mixed states) is proposed. This new approach is based on an analogy between open quantum systems and dissipative quantum systems which uses a $C^*$-module structure. The gauge theory associated with these new geometric phases does not take place in an usual principal bundle structure but in an higher structure, a categorical principal bundle (so-called principal 2-bundle or non-abelian bundle gerbes) which is sometimes a non-abelian twisted bundle. This higher degree in the gauge theory is a geometrical manifestation of the decoherence induced by the environment on the quantum system.