Geometric phases in a scattering process

Abstract

The study of geometric phase in quantum mechanics has so far been confined to discrete (or continuous) spectra and trace-preserving evolutions. By considering 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 the scattering process by taking only the transmission process into account. We find that the geometric phase can be calculated by the same method as in 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.