Topological Aspects of the Non-adiabatic Berry Phase

TL;DR

This paper explores the topological properties of the non-adiabatic Berry phase, revealing a critical frequency where the topology changes and relating the Chern number to angular momentum.

Contribution

It introduces the topological analysis of non-adiabatic Berry phase bundles and identifies a critical frequency where the topology becomes ill-defined.

Findings

Topology change at a critical frequency

Chern number proportional to angular momentum

Non-adiabatic bundle is ill-defined at critical frequency

Abstract

The topology of the non-adiabatic parameter space bundle is discussed for evolution of exact cyclic state vectors in Berry's original example of split angular momentum eigenstates. It turns out that the change in topology occurs at a critical frequency. The first Chern number that classifies these bundles is proportional to angular momentum. The non-adiabatic principal bundle over the parameter space is not well-defined at the critical frequency.