Dynamical simulations of colliding superconducting strings

We study the collisions of elastic superconducting strings, also referred to as current-carrying strings, formed in a $U_{\rm local}(1) \times U_{\rm global}(1)$ field-theory model, using three-dimensional numerical field-theoretic simulations. The breaking of $U_{\rm local}(1)$ leads to string formation via the Higgs mechanism, while the scalar field of the second $U_{\rm global}(1)$ carries the current, which condenses onto the string. We construct straight and static superconducting string solutions numerically and identify the regions in which they exist in the model parameter space. We then perform dynamical simulations for colliding superconducting strings with various collision angles and collision velocities. We explore the kinematic parameter space for six sets of model parameters characterising the coupling between the two scalar fields and the current on the string. The final states of the strings (after the collision) are reported diagrammatically. We classify them into four categories: (i) regular intercommutation, (ii) double intercommutation, (iii) bound state, and (iv) expanding string solution. We find that the outcome of the collision process is the regular intercommutation of the colliding strings in most of the kinematic parameter space while they form bound states for small velocities and small angles. We also find that the strings undergo two successive intercommutations and, therefore, pass through one other in a small region corresponding to relatively small angles and velocities of order c/2. The string structure breaks down when there is a relatively large coupling between the two scalar fields, even if each string is stable before the occurrence of the collision.