Magnetic Force Exerted by the Aharonov-Bohm Line

TL;DR

This paper investigates the scattering of charges by an Aharonov-Bohm flux line, revealing an asymmetrical magnetic force due to forward scattering, and provides solutions within the paraxial approximation along with kinetic and quantization analyses.

Contribution

It introduces a finite width beam approach to analyze AB scattering, uncovering asymmetrical forces and deriving the scattering solution and S-matrix.

Findings

Charge scattering is asymmetrical despite symmetric cross-section.

The magnetic force arises from forward scattering within the incident wave's angular size.

Solutions for the scattering problem are obtained in the paraxial approximation.

Abstract

The problem of the scattering of a charge by the Aharonov-Bohm (AB) flux line is reconsidered in terms of finite width beams. It is shown that despite the left-right symmetry in the AB scattering cross-section, the charge is scattered asymmetrically. The asymmetry (i.e. magnetic force) originates from almost forward scattering within the angular size of the incident wave. In the paraxial approximation, the real space solution to the scattering problem of a beam is found as well as the scattering S-matrix. The Boltzmann kinetics and the Landau quantization in a random AB array are considered.