Master equation for the Unruh-DeWitt detector and the universal relaxation time in de Sitter space

TL;DR

This paper derives a master equation for the Unruh-DeWitt detector in arbitrary backgrounds, revealing a universal relaxation time in de Sitter space linked to its curvature, and explores nonequilibrium thermodynamics.

Contribution

It provides a general master equation for the detector's evolution and identifies a universal relaxation time in de Sitter space, extending previous thermodynamic analyses.

Findings

The relaxation time is universally half the curvature radius of de Sitter space.

The detector's behavior indicates nonequilibrium thermodynamic properties of de Sitter space.

A method to compute relaxation times for various initial states of the scalar field.

Abstract

We derive the master equation that completely determines the time evolution of the density matrix of the Unruh-DeWitt detector in an arbitrary background geometry. We apply the equation to reveal a nonequilibrium thermodynamic character of de Sitter space. This generalizes an earlier study on the thermodynamic property of the Bunch-Davies vacuum that an Unruh-DeWitt detector staying in the Poincare patch and interacting with a scalar field in the Bunch-Davies vacuum behaves as if it is in a thermal bath of finite temperature. In this paper, instead of the Bunch-Davies vacuum, we consider a class of initial states of scalar field, for which the detector behaves as if it is in a medium that is not in thermodynamic equilibrium and that undergoes a relaxation to the equilibrium corresponding to the Bunch-Davies vacuum. We give a prescription for calculating the relaxation times of the nonequilibrium processes. We particularly show that, when the initial state of the scalar field is the instantaneous ground state at a finite past, the relaxation time is always given by a universal value of half the curvature radius of de Sitter space. We expect that the relaxation time gives a nonequilibrium thermodynamic quantity intrinsic to de Sitter space.