Stability analysis of non-thermal fixed points in longitudinally expanding kinetic theory

TL;DR

This paper analyzes the stability of non-thermal fixed points in non-Abelian plasmas using Hamiltonian kinetic theory, deriving stability equations and relaxation rates to understand prescaling phenomena in QCD and Bose gases.

Contribution

It introduces a Hamiltonian kinetic theory approach with a perturbative expansion to analyze stability and relaxation near non-thermal fixed points.

Findings

Reproduces known non-thermal fixed point scaling exponents

Derives stability equations for scaling exponents

Calculates relaxation rates to fixed points

Abstract

We use the Hamiltonian formulation of kinetic theory to perform a stability analysis of non-thermal fixed points in a non-Abelian plasma. We construct a perturbative expansion of the Fokker-Planck collision kernel in an adiabatic approximation and show that the (next-to-)leading order solutions reproduce the known non-thermal fixed point scaling exponents. Working at next-to-leading order, we derive the stability equations for scaling exponents and find the relaxation rate to the non-thermal fixed point. This approach provides the basis for an understanding of the prescaling phenomena observed in QCD kinetic theory and non-relativistic Bose gas systems.