Chaotic Symmetry Breaking and Dissipative Two-Field Dynamics

TL;DR

This paper investigates chaotic dynamics and symmetry breaking in a two-field dissipative model, using numerical solutions and fractal dimension analysis to characterize the complex behavior of the system.

Contribution

It introduces a numerical study of chaos in a two-field symmetry-breaking model with dissipation, highlighting the role of strange attractors and phase space trajectories.

Findings

Strong chaotic behavior observed in the model

Fractal dimension used to quantify chaos

Symmetry breaking leads to transitory strange attractors

Abstract

The dynamical symmetry breaking in a two-field model is studied by numerically solving the coupled effective field equations. These are dissipative equations of motion that can exhibit strong chaotic dynamics. By choosing very general model parameters leading to symmetry breaking along one of the field directions, the symmetry broken vacua make the role of transitory strange attractors and the field trajectories in phase space are strongly chaotic. Chaos is quantified by means of the determination of the fractal dimension, which gives an invariant measure for chaotic behavior. Discussions concerning chaos and dissipation in the model and possible applications to related problems are given.