Chaotic behavior in classical Yang-Mills dynamics

TL;DR

This paper investigates the chaotic dynamics of classical Yang-Mills theories to understand rapid thermalization in high-energy heavy ion collisions, analyzing Lyapunov exponents across different regimes.

Contribution

It characterizes distinct Lyapunov exponent regimes in classical Yang-Mills dynamics and discusses their implications for gauge-field thermalization times.

Findings

Thermalization occurs within a few femtometers per c for pure gauge theories.

Different spectral regimes of Lyapunov exponents are identified and characterized.

Inclusion of fermions and specific initial conditions can reduce thermalization time.

Abstract

Understanding the underlying mechanisms causing rapid thermalization deduced for high-energy heavy ion collisions is still a challenge. To estimate the thermalization time, entropy growth for classical Yang-Mills theories is studied, based on the determination of Lyapunov exponents. Distinct regimes for short, medium and long sampling times are characterized by different properties of their spectrum of Lyapunov exponents. Clarifying the existence of these regimes and their implications for gauge-field dynamics is one of the results of this contribution. As a phenomenological application we conclude that for pure gauge theories with random initial conditions thermalization occurs within few fm/c, an estimate which can be reduced by the inclusion of fermions, specific initial conditions, etc.