Quantum corrections to the Classical Statistical Approximation for the expanding quantum field

TL;DR

This paper investigates how quantum corrections affect the equation of state in an expanding scalar field, highlighting the limitations of the Classical Statistical Approximation in nonequilibrium quantum dynamics.

Contribution

It provides analytical and numerical analysis of quantum corrections to the energy-momentum tensor in expanding quantum fields, extending the understanding beyond classical approximations.

Findings

Quantum corrections cause deviations from the ultrarelativistic equation of state.

A nontrivial intermediate regime with significant quantum effects is identified.

The Keldysh-Schwinger framework is used to analyze energy-momentum evolution.

Abstract

We found the deviation of the equation of state from ultrarelativistic one due to quantum corrections for a nonequilibrium longitudinally expanding scalar field. Relaxation of highly excited quantum field is usually described in terms of Classical Statistical Approximation (CSA). However, the expansion of the system reduces the applicability of such a semiclassical approach as the CSA making quantum corrections important. We calculate the evolution of the trace of the energy-momentum tensor within the Keldysh-Schwinger framework for static and longitudinal expanding geometries. We provide analytical and numerical arguments for the appearance of the nontrivial intermediate regime where quantum corrections are significant.