Chaotic thermalization in Yang-Mills-Higgs theory on a spacial lattice

TL;DR

This paper investigates the chaotic thermalization process in classical SU(2) Yang-Mills-Higgs theory on a lattice, focusing on energy transfer, Lyapunov exponents, and the influence of Higgs fields on gauge field instabilities.

Contribution

It provides a detailed analysis of energy dynamics, Lyapunov exponents, and the effects of Higgs fields on magnetic field instabilities in lattice Yang-Mills-Higgs theory.

Findings

Energy transfer and equilibration among gauge and Higgs sectors.

Lyapunov exponents related to plasmon damping rates.

Higgs fields influence magnetic field instability.

Abstract

We analyze the Hamiltonian time evolution of classical SU(2) Yang-Mills-Higgs theory with a fundamental Higgs doublet on a spacial lattice. In particular, we study energy transfer and equilibration processes among the gauge and Higgs sectors, calculate the maximal Lyapunov exponents under randomized initial conditions in the weak-coupling regime, where one expects them to be related to the high-temperature plasmon damping rate, and investigate their energy and coupling dependence. We further examine finite-time and finite-size errors, study the impact of the Higgs fields on the instability of constant non-Abelian magnetic fields, and comment on the implications of our results for the thermalization properties of hot gauge fields in the presence of matter.