paper

Open system dynamics in interacting quantum field theories

arXiv:2403.18907 · doi:10.1103/kjph-9z8l

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.

19 pages, 6 figures. Edited to highlight QFT-specific subtleties in section III, added details about constructing the two-point function in section IV, expanded discussions of the renormalization procedure, Markov approximation, and Markovian limit in section VI, and added discussion about renormalization for open systems in section VIII. Matches published version

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