Spectral, statistical, and vertex functions in scalar quantum field theory far from equilibrium

Abstract

We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in 3+1 spacetime dimensions starting from over-occupied initial conditions. We determine universal scaling exponents and functions for two-point correlators and the four-vertex in a self-similar regime in time and space or momenta. The scaling form of the momentum-dependent four-vertex exhibits a dramatic fall-off towards low momenta. Comparing spectral functions (commutators) and statistical correlations (anti-commutators) of field operators allows us to detect strong violations of the fluctuation-dissipation relation in this non-perturbative infrared regime. Based on a self-consistent expansion in the number of field components to next-to-leading order, a wide range of interaction strengths is analyzed and compared to weak-coupling estimates in effective kinetic theory and classical-statistical field theory.

QCD thermalization: Ab initio approaches and interdisciplinary connections

“…These analytical estimates were numerically verified using 2PI effective action techniques in Refs. [319,320] for an N -component scalar field theory with quartic self-interactions. In classicalstatistical simulations, which construct the ensemble averages from individual runs with a non-zero field value, the observed scaling exponents are consistent with the estimates in the presence of an effective three-vertex [50].…”

“…The non-equilibrium infrared dynamics for scalars starting from over-occupation has been studied in great detail [26,52,320,[333][334][335][336][337][338][339][340][341][342][343][344]. The emergence of selfsimilar scaling behavior is closely related to the existence of non-thermal fixed points [26,[345][346][347].…”

“…Although the inflaton dynamics is described by a relativistic field theory, the self-similar scaling behavior at sufficiently low momenta below the screening mass scale is predicted to exhibit universal properties of a nonrelativistic system [334]. The non-equilibrium infrared dynamics for scalars starting from overoccupation has been theoretically studied in great detail [26,52,320,333,[335][336][337][338][339][340][341][342][343][344]. However important aspects of this farfrom-equilibrium dynamics can be probed experimentally using Bose gases in an optical trap.…”

Broad excitations in a 2+1D overoccupied gluon plasma

“…In the isotropic 3+1D theory, we observed in [40] that the spectral and statistical correlation functions in our considered far-from-equilibrium system are related by the generalized fluctuation-dissipation relation fluctuation-dissipation relation, which for low momenta p T below the temperature reads EE α (ω, p) = Tρ α (ω, p). In contrast, out of equilibrium their connection may be much more complicated or even absent, as observed for scalar theories [41,42,59]. The HTL framework predicts a generalized fluctuation-dissipation relation [60] with a timedependent effective temperature…”

Broad excitations in a 2+1D overoccupied gluon plasma

“…In thermal equilibrium both correlations are connected by the fluctuationdissipation relation, which for low momenta p T below the temperature reads EE α (ω, p) = T ρα (ω, p). In contrast, out of equilibrium their connection may be much more complicated or even absent, as observed for scalar theories [41,42,58]. The HTL framework predicts a generalized fluctuation-dissipation relation [59] with a time-dependent effective temperature T eff (t) = EE α (t, ∆t=0, p)/ ρα (t, ∆t=0, p)…”