Some geometric features of Berry's phase

TL;DR

This paper explores the geometric structure of Berry's phase by constructing Berry bundles from physical data, providing insights into the differential geometric elements underlying this quantum phenomenon.

Contribution

It introduces a general method to identify and construct geometric elements of Berry's phase from physical data, applied to various quantum systems.

Findings

Berry bundles constructed from physical data reveal geometric features of Berry's phase

Application to specific systems illustrates the geometric structures involved

Provides a framework for analyzing Berry's phase in different quantum contexts

Abstract

In this letter, we elaborate on the identification and construction of the differential geometric elements underlying Berry's phase. Berry bundles are built generally from the physical data of the quantum system under study. We apply this construction to typical and recently investigated systems presenting Berry's phase to explore their geometric features.