Study of the interaction and scattering of vortices in the Abelian Higgs (or Ginzburg-Landau) model.

Abstract

Line vortices arising in the Ginzburg-Landau or Abelian Higgs model are studied numerically. For a wide range of parameters simulations of parallel line vortices and antivortices were performed and the results are reported. The head-on 90\ifmmode^\circ\else\textdegree\fi{} scattering is demonstrated to be independent of initial conditions provided that the vortex zeros first completely overlap. For critically coupled vortices the scattering behavior seems to be approximately velocity independent until \ensuremath{\beta}\ensuremath{\sim}0.4 and the collisions are approximately elastic until \ensuremath{\beta}\ensuremath{\sim}0.3. This suggests that higher-order modes arising from the collisions are not excited until \ensuremath{\beta}\ensuremath{\sim}0.3. When vortices and antivortices collide at highly relativistic speeds (\ensuremath{\beta}\ensuremath{\sim}0.9) it is found that the direction into which they reform depends upon the coupling constant. The metric on the moduli space ${\mathit{M}}_{2}$ is calculated from its field-kinetic definition. The scattering angles directly calculated from the metric components are shown to agree with the numerical simulations. The nontrivial forms of the components are discussed in relation to the scattering results.