Chaotic behavior in a Z_2 x Z_2 field theory

TL;DR

This paper explores chaotic dynamics in a two-scalar field system with Z_2 x Z_2 symmetry, revealing how chaos varies with the parameter r and energy, and identifying distinct behaviors in different topological sectors.

Contribution

It demonstrates the presence of chaos in a Z_2 x Z_2 symmetric field theory and analyzes how chaos depends on the parameter r and energy levels, highlighting differences between topological sectors.

Findings

Chaos is prevalent in the system for most parameter values.

Complex dynamics are observed for r>0, with chaos decreasing as energy increases.

For r<0, the system exhibits simpler, less chaotic behavior.

Abstract

We investigate the presence of chaos in a system of two real scalar fields with discrete Z_2 x Z_2 symmetry. The potential that identify the system is defined with a real parameter r and presents distinct features for r>0 and for r<0. For static field configurations, the system supports two topological sectors for r>0, and only one for r<0. Under the assumption of spatially homogeneous fields, the system exhibts chaotic behavior almost everywhere in parameter space. In particular a more complex dynamics appears for r>0; in this case chaos can decrease for increasing energy, a fact that is absent for r<0.