Dirac phase and replicating adiabaticity in isotropically moving wall confinement

TL;DR

This paper investigates the geometric Dirac phase in a quantum particle confined by isotropically moving walls, revealing how it depends on the rate of change of the confinement and how to replicate adiabatic evolution in finite time.

Contribution

It introduces a new approach to explain the physical origin of the Dirac phase and identifies external potentials that can replicate adiabatic evolution quickly.

Findings

Dirac phase depends on the relative rate of change of the spatial scale.

External potentials can replicate adiabatic evolution in finite time.

Examples include uniform, accelerating walls, and cosmic expansion effects.

Abstract

Geometric phase in the wave function is important with regard to quantum non-locality and adiabatic evolution. We study the confinement of a particle by three-dimensional isotropically moving walls, of relevance to experimental trapping techniques, via a proposed approach that explains the physical origin of the geometric Dirac phase induced in the wave function. This phase depends only on the relative rate of change of the spatial scale factor. The approach also yields the class of external potentials that replicate adiabatic evolution in finite time. As illustrative examples, we consider uniform and accelerating walls, and the case where the Dirac phase is due to cosmic expansion.