Berry's phase under topology change

TL;DR

This paper explores how Hamiltonians on metric graphs can exhibit non-trivial Berry's phase due to topology changes, linking geometric phases to topological transformations.

Contribution

It demonstrates that real-valued eigenfunction Hamiltonians can have non-trivial Berry's phase through topology change in metric graph Laplacians.

Findings

Hamiltonians with real eigenfunctions can have non-trivial Berry's phase

Topology change in metric graphs affects geometric phase

Connections between Berry's phase and topology are discussed

Abstract

Laplacians on metric graphs are used to construct continuous families of Hamiltonians with different topological structure. One such family is used to demonstrate that Hamiltonians with real-valued eigenfunctions may possess non-trivial geometric Berry's phase. Connections between non-trivial Berry's phase and topology change are discussed.