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" 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 P-0.4 and the collisions are approximately elastic until P-0.3. This suggests that higher-order modes arising from the collisions are not excited until 6-0.3. When vortices and antivortices collide at highly relativistic speeds (P-0.9) it is found that the direction into which they reform depends upon the coupling constant. The metric on the moduli space 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.

Knotty inflation and the dimensionality of spacetime

“…This is e.g. supported by twodimensional simulations of vortex collisions, where it has been shown that colliding vortices only overlap above a critical velocity [52]. We expect typical velocities to be indeed small in our scenario due to the large number density of mutually repelling flux tubes formed during the phase transition, as discussed above.…”

Kinematic constraints on formation of bound states of cosmic strings: Field theoretical approach

“…The link forms and unforms, the two strings becoming separately visible again. This is not surprising; the process is essentially right-angle scattering which is well-established by numerical experiments with vortices [25,26]. Analytically, right-angle scattering after a head-on collision is understood at critical coupling (β = 1) [27], in terms of geodesic motion in the moduli space approximation.…”

Kink interactions in the(1+1)-dimensionalφ6model

“…8 is not symmetric with respect to the vertical line passing through its maximum. As in the previous case, we also studied the evolution of the initial configuration of the type (21), solving the exact equation of motion (2) reproduces the corresponding result of Ref. [28].…”

“…Special attention should be paid to configurations of strings or vortices [1, 14,15]. In particular, there are important results on quantum stabilization of strings [16][17][18] and strings/vortices/monopoles dynamics [19][20][21][22][23].…”