Abstract
We compute the far-from-equilibrium dynamics of relativistic scalar quantum fields in $3+1$ space-time 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 toward low momenta. Comparing spectral functions (commutators) and statistical correlations (anticommutators) 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.
Highlights
Nonequilibrium dynamics of relativistic scalar quantum field theory is an important cornerstone in our understanding of the evolution of the early universe
While at sufficiently high momenta we recover the expected quasiparticle structure with a generalized fluctuation-dissipation relation, we demonstrate that significant violations occur in the nonperturbative infrared regime
Our results for scaling exponents and scaling functions are in agreement within errors with previous weak-coupling estimates for equal-time correlations using effective kinetic theory or classical-statistical field theory
Summary
Nonequilibrium dynamics of relativistic scalar quantum field theory is an important cornerstone in our understanding of the evolution of the early universe. A self-consistent expansion in powers of 1=N to next-to-leading order (NLO) provides a nonperturbative account of the dynamics, such that we may analyze the highly occupied infrared for a wide range of interaction strengths This has been previously employed to study far-from-equilibrium dynamics of this model, focusing on the role of a symmetry breaking field expectation value for its evolution [25]. The question of whether some generalized fluctuation-dissipation relation may be defined, such as underlying effective kinetic descriptions of the dynamics, has been recently addressed in this context with the help of classical-statistical simulations [26,27] We compute both spectral and statistical correlation functions directly based on the underlying quantum field. Three Appendices provide details about the error estimates for the extraction of the scaling exponents, the Wigner transformation employed in the read-out of the spectral function, and the procedure for the numerical computation of the time evolution
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