Kadanoff-Baym Equations with Non-Gaussian Initial Conditions: The Equilibrium Limit

TL;DR

This paper extends the Kadanoff-Baym equations to include non-Gaussian initial states, specifically vacuum and thermal correlations, improving the accuracy of nonequilibrium quantum field dynamics simulations.

Contribution

It derives Kadanoff-Baym equations for non-Gaussian initial states from the 2PI effective action and provides a diagrammatic method to construct these correlations.

Findings

Non-Gaussian initial conditions improve equilibrium approximation.

Numerical solutions show significant qualitative and quantitative improvements.

Thermal 4-point correlations enhance the accuracy of nonequilibrium dynamics.

Abstract

The nonequilibrium dynamics of quantum fields is an initial-value problem, which can be described by Kadanoff-Baym equations. Typically, and in particular when numerical solutions are demanded, these Kadanoff-Baym equations are restricted to Gaussian initial states. However, physical initial states are non-Gaussian correlated initial states. In particular, renormalizability requires the initial state to feature n-point correlations that asymptotically agree with the vacuum correlations at short distances. In order to identify physical nonequilibrium initial states, it is therefore a precondition to describe the vacuum correlations of the interacting theory within the nonequilibrium framework. In this paper, Kadanoff-Baym equations for non-Gaussian correlated initial states describing vacuum and thermal equilibrium are derived from the 2PI effective action. A diagrammatic method for the explicit construction of vacuum and thermal initial correlations from the 2PI effective action is provided. We present numerical solutions of Kadanoff-Baym equations for a real scalar Phi^4 quantum field theory which take the thermal initial 4-point correlation as the leading non-Gaussian correction into account. We find that this minimal non-Gaussian initial condition yields an approximation to the complete equilibrium initial state that is quantitatively and qualitatively significantly improved as compared to Gaussian initial states.