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

TL;DR

This paper uses numerical simulations to explore deep inelastic vortex scattering in nonlinear Maxwell-Klein-Gordon equations, revealing new critical behaviors, scaling laws, and scattering angles for vortex collisions across various parameters.

Contribution

It introduces the first detailed analysis of deep inelastic vortex scattering, identifying a $ ext{kappa}$-specific static attractor and novel scattering angles at critical impact parameters.

Findings

Time-scaling laws for scattering duration with $ ext{log}$ dependence.

Existence of a $ ext{kappa}$-specific $m=2$ vortex attractor at critical velocity.

Scattering angle of 135° for small impact parameters, differing from classical values.

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 ($v_0^*$) 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^*) $, with $\kappa$-dependent scaling exponents, $\alpha$, and have $v_0^*$ that appear not to have the previously reported upper bound. The arbitrarily long-lived static intermediate attractor at criticality ($v_0=v_0^*$) is observed to be the $\kappa$-specific $m=2$ vortex solution. Scattering angles are observed for off-axis ($b\neq 0$) collisions for a wide range of $b$, $v_0$, and $\kappa$. It is shown that for arbitrarily small impact parameters ($b\rightarrow 0$), 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 $b=0$.