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

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.

Figure 1

Two-point function $F_{\perp }(t,t;\mathbf{p})$ as a function of momentum $|\mathbf{p}|$ for three different times. Quantum (solid line) and classical (dashed line) evolution agree well even where $F_{\perp }(\mathbf{p})\ll 1$.

Figure 2

NLO contributions to the fixed point Eq. (4).

Figure 3

The effective vertex at $t=240$ as a function of spatial momentum $\mathbf{p}$ for different frequencies $\omega \equiv p_0$.

Figure 4

Occupation number as a function of momentum for different times. The solid line corresponds to $t=8000$, along with fits $\sim |\mathbf{p}{|}^{-4}$ for low and $\sim |\mathbf{p}{|}^{-3/2}$ for higher momenta.