Geometric gauge potentials and forces in low-dimensional scattering systems

TL;DR

This paper explores low-dimensional scattering systems exhibiting geometric phase phenomena, analyzing exact solutions and approximations to understand geometric gauge forces and their practical implications.

Contribution

It introduces fully solvable low-dimensional models demonstrating geometric gauge effects and compares exact solutions with approximation methods, highlighting universality and symmetry breaking.

Findings

Geometric magnetism manifests in the models.

Exact solutions align with approximation methods.

Systems can mimic charged particle behavior in magnetic fields.

Abstract

We introduce and analyze several low-dimensional scattering systems that exhibit geometric phase phenomena. The systems are fully solvable and we compare exact solutions of them with those obtained in a Born-Oppenheimer projection approximation. We illustrate how geometric magnetism manifests in them, and explore the relationship between solutions obtained in the diabatic and adiabatic pictures. We provide an example, involving a neutral atom dressed by an external field, in which the system mimics the behavior of a charged particle that interacts with, and is scattered by, a ferromagnetic material. We also introduce a similar system that exhibits Aharonov-Bohm scattering. We propose some practical applications. We provide a theoretical approach that underscores universality in the appearance of geometric gauge forces. We do not insist on degeneracies in the adiabatic Hamiltonian, and we posit that the emergence of geometric gauge forces is a consequence of symmetry breaking in the latter.