Unstable Behaviours of Classical Solutions in Spinor-type Conformal Invariant Fermionic Models

TL;DR

This paper investigates how external periodic forcing induces bifurcations and chaos in classical solutions of conformal invariant spinor fermionic models, enhancing understanding of their dynamical behaviors.

Contribution

It introduces an analysis of the unstable behaviors of classical solutions in spinor-type conformal invariant fermionic models under external forcing, highlighting bifurcations and chaos.

Findings

External forcing causes bifurcations in the models.

Chaos emerges depending on excitation amplitude.

Different dimensions and spinor numbers exhibit similar dynamical phenomena.

Abstract

It is well known that instantons are classical topological solutions existing in the context of quantum field theories that lie behind the standard model of particles. To provide a better understanding for the dynamical nature of spinor-type instanton solutions, conformal invariant pure spinor fermionic models that admit particle-like solutions for the derived classical field equations are studied in this work under cosine wave forcing. For this purpose the effects of external periodic forcing on two systems having different dimensions and quantum spinor numbers and have been obtained under the use of Heisenberg ansatz are investigated by constructing their Poincar\'e sections in phase space. As a result, bifurcations and chaos are observed depending on the excitation amplitude of the external forcing in both pure spinor fermionic models.