Nonlinear amplification of instabilities with longitudinal expansion

TL;DR

This paper analyzes how nonlinear effects amplify instabilities in anisotropically expanding systems like the Glasma, revealing secondary amplification regimes that impact isotropization and thermalization.

Contribution

It introduces a generalized conformal time framework to analytically study nonlinear amplification of instabilities in boost-invariant expanding quantum fields.

Findings

Primary instabilities lead to secondary regimes with enhanced growth rates.

Nonlinear corrections significantly influence isotropization.

Power-counting scheme for weak coupling in secondary instabilities.

Abstract

We study the dynamics of nonequilibrium instabilities in anisotropically expanding systems. The most prominent example of such a system is the 'Glasma' in the context of relativistic heavy-ion collision experiments, where the expansion is a consequence of approximately boost-invariant initial conditions. Here we consider the problem of parametric resonance in scalar $N$-component quantum field theories with boost-invariant initial conditions, which is similar in spirit. We find that many aspects of the dynamics can be treated analytically by introducing a generalized conformal time. Primary instabilities, which are described by the linearized evolution equations, are seen to lead to a secondary regime of amplifications with strongly enhanced growth rates due to nonlinear corrections. For the secondary instabilities we present a power-counting scheme for weak coupling, and discuss their role for the question of isotropization and the establishment of an equation of state.