Dynamics of interaction of topological localized structures in reversed time

TL;DR

This paper presents numerical simulations of topological soliton interactions in a reversed time (2+1)-dimensional O(3) non-linear sigma model, revealing decay, annihilation, and restoration processes that confirm T-invariance.

Contribution

The study develops new models for topological vortex interactions in reversed time and introduces a specialized numerical algorithm for simulating these complex processes.

Findings

Observed decay and annihilation of vortices depending on parameters

Confirmed T-invariance of the topological field model

Developed a numerical algorithm for reversed time interactions

Abstract

The results of numerical simulation of the interaction of topological solitons (2+1)-dimensional O(3) non-linear sigma model in reversed time are presented. At the first stage, models of interactions of topological vortices are developed, where, depending on the dynamic parameters, processes of their decay into localized perturbations and phased annihilation are observed. Also, models for the phased annihilation of topological vortices during their interaction with 180-degree domain walls are considered. On the basis of the models obtained, initial conditions for numerical simulation of interaction processes in reversed time are developed. The models describing the complete restoration of the initial topological field of interacting solitons at the combination of localized perturbations and radiation waves are obtained. Also, models are obtained that describe the formation of topological vortices in the plane of the domain wall and their subsequent emission. Thus, the T-invariance property of the field-theoretic model under study is confirmed. Numerical calculations were carried out in a stratified space on the basis of methods of the theory of finite difference schemes, using the properties of a stereo-graphic projection. The experiments were carried out for different values of the Kronecker-Hopf index of topological vortices. A complex program module is proposed that implements a special algorithm for the numerical calculation of the evolution of the interaction of space-time topological structures in reversed time.