Year: 2020
Type: article
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 ($\ensuremath{\kappa}$), 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, $T\ensuremath{\propto}\ensuremath{\alpha}\mathrm{ln}({v}_{0}\ensuremath{-}{v}_{0}^{*})$, with $\ensuremath{\kappa}$-dependent scaling exponents, $\ensuremath{\alpha}$, 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 $\ensuremath{\kappa}$-specific $m=2$ vortex solution. Scattering angles are observed for off-axis ($b\ensuremath{\ne}0$) collisions for a wide range of $b$, ${v}_{0}$, and $\ensuremath{\kappa}$. It is shown that for arbitrarily small impact parameters ($b\ensuremath{\rightarrow}0$), the unstable $\ensuremath{\kappa}$-dependent $m=2$ ``critical'' vortex is an intermediate attractor and decays with a $\ensuremath{\kappa}$-independent scattering angle of 135\ifmmode^\circ\else\textdegree\fi{}, as opposed to either of the well-known values of 180\ifmmode^\circ\else\textdegree\fi{} or 90\ifmmode^\circ\else\textdegree\fi{} for $b=0$.
Author: Ethan P. Honda
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W3082402365