Large-N kinetic theory for highly occupied systems

TL;DR

This paper develops a large-N kinetic theory framework for quantum many-body systems with high occupation numbers, extending previous models to include next-to-leading order effects, and compares the results with lattice simulations.

Contribution

It introduces a large-N kinetic theory at next-to-leading order capable of describing highly occupied, far-from-equilibrium quantum systems beyond standard perturbative methods.

Findings

Derived analytical effective scattering matrix elements.

Numerically solved the kinetic equation for highly occupied systems.

Identified the universal scaling form at an infrared nonthermal fixed point.

Abstract

We consider an effective kinetic description for quantum many-body systems, which is not based on a weak-coupling or diluteness expansion. Instead, it employs an expansion in the number of field components N of the underlying scalar quantum field theory. Extending previous studies, we demonstrate that the large-N kinetic theory at next-to-leading order is able to describe important aspects of highly occupied systems, which are beyond standard perturbative kinetic approaches. We analyze the underlying quasiparticle dynamics by computing the effective scattering matrix elements analytically and solve numerically the large-N kinetic equation for a highly occupied system far from equilibrium. This allows us to compute the universal scaling form of the distribution function at an infrared nonthermal fixed point within a kinetic description and we compare to existing lattice field theory simulation results.