Stable and unstable perturbations in universal scaling phenomena far from equilibrium

TL;DR

This paper investigates the stability of universal scaling phenomena in quantum many-body systems far from equilibrium, identifying stable and unstable perturbations and elucidating the mechanisms behind their dynamics.

Contribution

It introduces a large-N expansion analysis of perturbation stability at nonthermal fixed points, revealing the role of scaling instabilities and quasi-particle cascades.

Findings

Unstable perturbations cause quasi-exponential deviations in the infrared.

A tower of quasi-particle states with specific dispersion relations is identified.

Scaling instability leads to a self-similar cascade towards the infrared.

Abstract

We study the dynamics of perturbations around nonthermal fixed points associated to universal scaling phenomena in quantum many-body systems far from equilibrium. For an N-component scalar quantum field theory in 3+1 space-time dimensions, we determine the stability scaling exponents using a self-consistent large-N expansion to next-to-leading order. Our analysis reveals the presence of both stable and unstable perturbations, the latter leading to quasi-exponential deviations from the fixed point in the infrared. We identify a tower of far-from-equilibrium quasi-particle states and their dispersion relations by computing the spectral function. With the help of linear response theory, we demonstrate that unstable dynamics arises from a competition between elastic scattering processes among the quasi-particle states. What ultimately renders the fixed point dynamically attractive is the phenomenon of a scaling instability, which is the universal scaling of the unstable regime towards the infrared due to a self-similar quasi-particle cascade. Our results provide ab initio understanding of emergent stability properties in self-organized scaling phenomena.