Simulating Magnetic Monopole-Defect Dynamics

TL;DR

This paper simulates the dynamics of magnetic monopoles interacting with defects using explicit solutions and collective coordinate mechanics, providing both numerical and analytical insights into monopole-defect interactions.

Contribution

It introduces a comprehensive simulation framework for monopole-defect interactions, combining explicit solutions, animations, and analytical treatment of single-defect cases.

Findings

Energy density plots from simulations

Trajectories from collective coordinate mechanics

Analytic solutions for single-defect interactions

Abstract

We present simulations of one magnetic monopole interacting with multiple magnetic singularities. Three-dimensional plots of the energy density are constructed from explicit solutions to the Bogomolny equation obtained by Blair, Cherkis, and Durcan. Animations follow trajectories derived from collective coordinate mechanics on the multi-centered Taub--NUT monopole moduli space. We supplement our numerical results with a complete analytic treatment of the single-defect case.