Differential cross sections and escape plots for low-energy solitonic SU(2) BPS magnetic monopole dynamics

Abstract

We compute the low-energy classical differential scattering cross section for solitonic BPS SU(2) magnetic monopoles using the geodesic approximation to the actual dynamics and 32K virtual parallel processors on a CM2. We compare the classical solitonic differential cross section to the low-energy quantum BPS SU(2) magnetic monopole differential cross section obtained by Schroers. Our numerical experiments suggest that the classical solitonic BPS magnetic monopole differential cross section approximates well the quantum BPS magnetic monopole differential cross section. In particular, the expected quantum interference of identical bosons at scattering angle θ = π 2 (centre-of-mass frame) is not observed numerically, and indeed is contradicted. We argue that the lack of singularities in the two-body configuration space, related to the solitonic qualities of the BPS SU(2) magnetic monopole, is responsible for the agreement observed between the classical solitonic and the quantum mechanical cross sections. We also study the scattering and bounded classical motions of BPS SU(2) dyons and their global structure in phase space by constructing “escape plots”. The escape plots contain a surprising amount of structure. The escape plots suggest that the classical dynamics of two BPS SU(2) magnetic monopoles is non-integrable and that there are closed and bounded two-monopole motions with isolated energies.