Feshbach resonances and dynamics of BPS solitons

TL;DR

This paper explores how Feshbach resonances influence the dynamics of BPS solitons, revealing a mode-generated force and the persistence of spectral walls, with implications for monopole scattering.

Contribution

It introduces the concept of mode-generated forces affecting BPS soliton dynamics via Feshbach resonances in a toy model, linking to monopole scattering.

Findings

Feshbach resonances modify soliton geodesic dynamics.

Spectral walls remain unaffected by exponential decay of resonant modes.

Potential existence of spectral walls in monopole scattering in three dimensions.

Abstract

We demonstrate that the geodesic dynamics of BPS solitons can be modified by the excitation of Feshbach resonances, or quasi-bound modes, in a toy model of two scalar fields. A mode-generated force emerges, with a strength determined by the spectral flow of the frequency on the moduli space, and weakened by the coupling between the bound and scattering components of the resonance. Notably, spectral walls persist unaffected by the resonant mode's exponential decay, as the decay constant vanishes at the spectral wall. Our motivation comes from the 't Hooft-Polyakov monopoles, which do not present true bound states but long lived semi-bound excitations. Our findings suggest the existence of spectral walls in the scattering of excited monopoles in three dimensions, whose trajectories may significantly deviate from the geodesic motion in the moduli space of unexcited monopoles.