Unraveling the nature of universal dynamics in $O(N)$ theories

TL;DR

This paper investigates the universal dynamics of highly-occupied $N$-component scalar systems, revealing distinct phenomena for different $N$ values and clarifying the dominant excitations using unequal-time correlators.

Contribution

It identifies for the first time two fundamentally different universal phenomena in $N$-component systems, challenging previous assumptions of universality across all $N$.

Findings

All $N extgreater=3$ systems are dominated by a Lorentzian large-$N$ peak.

$N=1$ systems exhibit a non-Lorentzian peak with different properties.

$N=2$ systems show a mixture of two contributions.

Abstract

Many-body quantum systems far from equilibrium can exhibit universal scaling dynamics which defy standard classification schemes. Here, we disentangle the dominant excitations in the universal dynamics of highly-occupied $N$-component scalar systems using unequal-time correlators. While previous equal-time studies have conjectured the infrared properties to be universal for all $N$, we clearly identify for the first time two fundamentally different phenomena relevant at different $N$. We find all $N\geq3$ to be indeed dominated by the same Lorentzian ``large-$N$'' peak, whereas $N=1$ is characterized instead by a non-Lorentzian peak with different properties, and for $N=2$ we see a mixture of two contributions.