Open system dynamics in interacting quantum field theories

TL;DR

This paper develops a non-Markovian Redfield master equation for a quantum scalar field interacting with another field, providing a more accurate perturbative solution and analyzing the conditions under which Markovian approximations are valid.

Contribution

The paper constructs a non-Markovian Redfield master equation for interacting quantum fields and compares its solutions to traditional methods, highlighting its improved accuracy in certain regimes.

Findings

Redfield solution closely matches the exact solution for bilinear interactions.

Markovian approximation performs poorly with oscillatory environment correlations.

Redfield equation offers a perturbative resummation beyond second-order Dyson series.

Abstract

A quantum system that interacts with an environment generally undergoes nonunitary evolution described by a non-Markovian or Markovian master equation. In this paper, we construct the non-Markovian Redfield master equation for a quantum scalar field that interacts with a second field through a bilinear or nonlinear interaction on a Minkowski background. We use the resulting master equation to set up coupled differential equations that can be solved to obtain the equal-time two-point function of the system field. We show how the equations simplify under various approximations including the Markovian limit and argue that the Redfield equation-based solution provides a perturbative resummation to the standard second-order Dyson series result. For the bilinear interaction, we explicitly show that the Redfield solution is closer to the exact solution compared to the perturbation theory-based one. Further, the environment correlation function is oscillatory and nondecaying in this case, making the Markovian master equation a poor approximation. For the nonlinear interaction, on the other hand, the environment correlation function is sharply peaked and the Redfield solution matches that obtained using a Markovian master equation in the late-time limit.