Nonthermal Fixed Points: Effective Weak Coupling for Strongly Correlated Systems Far from Equilibrium

Abstract

Strongly correlated systems far from equilibrium can exhibit scaling solutions with a dynamically generated weak coupling. We show this by investigating isolated systems described by relativistic quantum field theories for initial conditions leading to nonequilibrium instabilities, such as parametric resonance or spinodal decomposition. The nonthermal fixed points prevent fast thermalization if classical-statistical fluctuations dominate over quantum fluctuations. We comment on the possible significance of these results for the heating of the early Universe after inflation and the question of fast thermalization in heavy-ion collision experiments.

Basin of attraction for turbulent thermalization and the range of validity of classical-statistical simulations

“…Stated differently, this concerns the large field or large occupancy limit, which is relevant for important phenomena such as nonequilibrium instabilities or wave turbulence encountered in our study. The classicality condition has been verified in detail by comparing quantum to classical-statistical results in the context of scalar quantum field dynamics [2,32,33,39] and coupled to fermions [41,42].…”

“…In these examples, attractor solutions with self-similar scaling behavior are associated with the phenomenon of Kolmogorov wave turbulence [4,5] and strong turbulence with fluid-like behavior [2,[6][7][8] which leads to Bose condensation far from equilibrium [9][10][11]. A turbulent thermalization mechanism has also been predicted for non-Abelian gauge theories using classical-statistical simulations in a fixed box, where different groups obtain consistent results [12][13][14].…”

“…In this limit, we observe turbulent thermalization, where we point out that 1. the inverse particle cascade, which has so far only been established for O(N ) symmetric theories with N ≥ 2 [2,8,35], also occurs for the single component theory.…”

“…The important advantage for scalars is that powerful resummation techniques exist for the description of the entire evolution in quantum field theory. It has been demonstrated that classical-statistical descriptions have a well understood range of validity for which they accurately describe the dynamics of the underlying quantum theory [2,[32][33][34].…”

“…The self-similar time-evolution within a given universality class of different models can then be mapped onto each other by simple rescalings. The universal properties are described in terms of nonthermal fixed points [2] in renormalization group theory [3]. While the notion of thermal fixed points describing different universality classes is well established for systems in thermal equilibrium, the corresponding classification for nonequilibrium scaling phenomena is a rapidly progressing research topic.…”