Collective coordinate models for 2-vortex shape mode dynamics

Models are developed for the motion of charge-2 Abelian Higgs vortices through the 2-vortex moduli space <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">M</a:mi></a:math>, with the vortices excited by their shape mode oscillations. The models simplify to the well-known geodesic flow on <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"><d:mi mathvariant="script">M</d:mi></d:math>, modified by a potential, when the mode oscillations are fast relative to the moduli space motion and their amplitudes are small. When the lowest-frequency mode is excited with a large amplitude, the geodesic flow is not a correct description. Instead, a chaotic, or even fractal, multibounce structure in vortex-vortex collisions is predicted.