Deep inelastic vortex scattering: A third outcome for head-on collisions

Abstract

Results are presented from numerical simulations of the flat-space nonlinear Maxwell-Klein-Gordon equations demonstrating deep inelastic scattering of $m=1$ vortices for a range of Ginzburg-Landau (or Abelian-Higgs) parameters ($\kappa$), impact parameters ($b$), and initial velocities ($v_0$). The threshold ($v_0^{\ast }$) of right-angle scattering is explored for head-on ($b=0$) collisions by varying $v_0$. Solutions obey time-scaling laws, $T\propto \alpha \ln (v_0-v_0^{\ast })$, with $\kappa$-dependent scaling exponents, $\alpha$, and have $v_0^{\ast }$ that appear not to have the previously reported upper bound. The arbitrarily long-lived static intermediate attractor at criticality ($v_0=v_0^{\ast }$) is observed to be the $\kappa$-specific $m=2$ vortex solution. Scattering angles are observed for off-axis ($b\ne 0$) collisions for a wide range of $b$, $v_0$, and $\kappa$. It is shown that for arbitrarily small impact parameters ($b\to 0$), the unstable %but arbitrarily long-lived $\kappa$-dependent $m=2$ "critical" vortex is an intermediate attractor and decays with a $\kappa$-\emph{independent} scattering angle of $135^{\circ }$, as opposed to either of the well-known values of $180^{\circ }$ or $90^{\circ }$ for $b=0$.

Comments: 13 pages, 14 figures, 3 tables