Geometric phases in a scattering process

TL;DR

This paper investigates the geometric phase in quantum scattering processes focusing on transmission channels, revealing how it can be computed similarly to unitary evolutions and how it depends on system parameters.

Contribution

It extends the concept of geometric phase to scattering processes with internal degrees of freedom, a setting not previously explored in detail.

Findings

Geometric phase in scattering can be calculated using methods similar to unitary evolution.

Interference visibility depends on transmission amplitude.

Geometric phase varies with barrier strength and spin-spin coupling.

Abstract

The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is neither a discrete spectrum problem nor a trace preserving process. We explore the geometric phase in a scattering process taking only the transmission process into account. We find that the geometric phase can be calculated by the some method as in an unitary evolution. The interference visibility depends on the transmission amplitude. The dependence of the geometric phase on the barrier strength and the spin-spin coupling constant is also presented and discussed.