Over-populated gauge fields on the lattice

TL;DR

This paper investigates the nonequilibrium dynamics of over-populated SU(2) gauge fields on the lattice, revealing a scaling behavior linked to weak wave turbulence and energy cascades, with insights comparable to scalar theories.

Contribution

It demonstrates that the scaling exponent in over-populated gauge fields can be understood through leading order interactions and draws parallels with scalar field turbulence phenomena.

Findings

Quick evolution towards a 3/2 scaling exponent

Scaling behavior explained by leading O(g^2) contributions

Energy cascade resembles scalar field turbulence

Abstract

We study nonequilibrium dynamics of SU(2) pure gauge theory starting from initial over-population, where intense classical gauge fields are characterized by a single momentum scale Q_s. Classical-statistical lattice simulations indicate a quick evolution towards an approximate scaling behavior with exponent 3/2 at intermediate times. Remarkably, the value for the scaling exponent may be understood as arising from the leading O(g^2) contribution in the presence of a time-dependent background field. The phenomenon is associated to weak wave turbulence describing an energy cascade towards higher momenta. This particular aspect is very similar to what is observed for scalar theories, where an effective cubic interaction arises because of the presence of a time-dependent Bose condensate.