Collision, mechanism, and $Z_4$ operation among chiral and nonchiral kinks in coupled double-field $\phi^4$ model

TL;DR

This paper explores collision processes among chiral and nonchiral kinks in a coupled double-field $$ model, revealing a $Z_4$ group structure and mechanisms for chirality switching during collisions.

Contribution

It introduces a classification of twelve kinks in the coupled model and demonstrates the $Z_4$ group operation governing their collisions and topological charge changes.

Findings

Kinks follow $Z_4$ abelian group operation during collisions.

Three types of collision behaviors observed depending on initial conditions.

Chirality charges switch during collisions while preserving the $Z_4$ structure.

Abstract

In this work, we investigate collision processes and their mechanism among chiral and nonchiral kinks in the coupled double-field $\phi^4$ model and show that the kink collisions follow the $Z_4$ abelian group operation. Unlike the single-field $\phi^4$ model, this model has twelve kinks, which are classified into chiral and nonchiral kinks depending on their topological chiral charges. This enriches the variety of the collision processes. From the numerical simulation, we observe three kinds of collisions depending on the initial configuration and initial velocities of colliding kinks. During a collision, the topological chiral charges of kinks switch while preserving the $Z_4$ abelian group operation. To understand the collision and chirality switching mechanism, we investigate the detailed collision process, energy densities, the field gradients, internal modes, energy exchange between two fields, coherent vibration of two bions located in different fields, and the orbits of colliding kinks in the two-dimensional field space.