Band structure in classical field theory

TL;DR

This paper investigates the emergence of band structure phenomena in classical field theory, specifically analyzing the stability of dynamic embedded kinks and their implications for defect lifetimes.

Contribution

It introduces the concept that dynamic embedded kinks can exhibit stability in certain parameter bands, extending the understanding of stability in classical field configurations.

Findings

Dynamic kinks can be stable in specific parameter bands.

Embedded kink stability depends on its motion and parameters.

Results inform estimates of defect and Z-string loop lifetimes.

Abstract

Stability and instability bands in classical mechanics are well-studied in connection with systems such as described by the Mathieu equation. We examine whether such band structure can arise in classical field theory in the context of an embedded kink in 1+1 dimensions. The static embedded kink is unstable to perturbations but we show that if the kink is dynamic it can exhibit stability in certain parameter bands. Our results are relevant for estimating the lifetimes of various embedded defects and, in particular, loops of electroweak Z-string.