Differential scattering cross section of the non-Abelian Aharonov-Bohm effect in multiband systems

TL;DR

This paper develops a unified theoretical framework for the non-Abelian Aharonov-Bohm effect in multiband systems, deriving scattering states and cross sections that depend on polarization, with applications to condensed matter and particle physics.

Contribution

It introduces a complex contour integral method for non-Abelian AB scattering in multiband systems, extending previous Abelian results to more complex gauge fields.

Findings

Angular dependence matches original AB effect but varies with polarization.

Explicit calculation of cross sections for three multiband systems.

Visualization of probability and current distributions for different incoming waves.

Abstract

We develop a unified treatment of the non-Abelian Aharonov-Bohm (AB) effect in isotropic multiband systems, namely, the scattering of particles on a gauge field corresponding to a noncommutative Lie group. We present a complex contour integral representation of the scattering states for such systems, and, using their asymptotic form, we calculate the differential scattering cross section. The angular dependence of the cross section turns out to be the same as that obtained originally by Aharonov and Bohm in their seminal paper, but this time it depends on the polarization of the incoming plane wave. As an application of our theory, we perform the contour integrals for the wave functions explicitly and calculate the corresponding cross section for three non-trivial isotropic multiband systems relevant to condensed matter and particle physics. To have a deeper insight into the nature of the scattering, we plot the probability and current distributions for different incoming waves. This paper is a generalization of our recent results on the Abelian AB effect providing an extension of exactly solvable AB scattering problems.