Quantum anholonomies in time-dependent Aharonov-Bohm rings

TL;DR

This paper investigates quantum anholonomies in eigenstates caused by time-dependent magnetic flux in Aharonov-Bohm rings, revealing persistent effects beyond adiabatic conditions and emphasizing the importance of gauge choice for understanding eigenspace properties.

Contribution

It demonstrates the persistence of eigenstate anholonomies beyond adiabatic regimes and clarifies the role of gauge choice in relating these to eigenspace anholonomy using non-Abelian connections.

Findings

Anholonomies persist beyond adiabatic regimes.

Gauge choice affects the interpretation of anholonomies.

Eigenspace anholonomy described by non-Abelian connection.

Abstract

Anholonomies in eigenstates are studied through time-dependent variations of a magnetic flux in an Aharonov-Bohm ring. The anholonomies in the eigenenergy and the expectation values of eigenstates are shown to persist beyond the adiabatic regime. The choice of the gauge of the magnetic flux is shown to be crucial to clarify the relationship of these anholonomies to the eigenspace anholonomy, which is described by a non-Abelian connection in the adiabatic limit.