The Aharonov-Casher Phase: Considerations Regarding Force, Time-Dependence, and Berry Phase

TL;DR

This paper investigates the Aharonov-Casher effect, deriving its Hamiltonian, exploring geometries for phase calculation, and relating it to the Berry phase, with specific results for arbitrary electric fields.

Contribution

It provides a derivation of the AC Hamiltonian using the Dirac equation and analyzes the phase in various geometries, connecting it to the Berry phase.

Findings

AC phase is quadratic in small electric fields.

AC phase is linear in large electric fields.

Explicit phase expressions for specific geometries.

Abstract

The relation of the Aharonov-Casher (AC) effect and the force on a particle having a magnetic moment is explored. The general form of the AC Hamiltonian is derived using the Foldy-Wouthuysen transformation to the Dirac equation. Geometries in which an analytic expression for the phase can be obtained are examined, as well as the relation of the AC phase to the Berry phase. The AC phase is determined for an arbitrary homogeneous electric field; it is quadratic (linear) in the field strength for small (large) electric field strengths.