The Master Equation for Two-Level Accelerated Systems at Finite Temperature

TL;DR

This paper derives a master equation for a two-level quantum system interacting with a thermal reservoir, incorporating finite temperature effects, and applies it to analyze energy dynamics and acceleration effects in quantum systems.

Contribution

It introduces a novel master equation formalism for two coupled quantum systems at finite temperature using Thermofield Dynamics, with applications to atomic and oscillator systems.

Findings

Derived a master equation at finite temperature for two-level systems.

Analyzed energy variation rates and population dynamics.

Explored effects of acceleration on quantum systems as Unruh detectors.

Abstract

In this work we study the behaviour of two weakly coupled quantum systems, described by a separable density operator; one of them is a single oscillator, representing a microscopic system, while the other is a set of oscillators which perform the role of a \emph{reservoir} in thermal equilibrium. From the Liouville-Von Neumann equation for the reduced density operator, we devise the master equation that governs the evolution of the microscopic system, incorporating the effects of temperature via Thermofield Dynamics formalism by suitably redefining the vacuum of the macroscopic system. As applications, we initially investigate the behaviour of a Fermi oscillator in the presence of a heat bath consisting of a set of Fermi oscillators and that of an atomic two-level system interacting with a scalar radiation field, considered as a \emph{reservoir}, by constructing the corresponding master equation which governs the time evolution of both sub-systems at finite temperature. Finally, we calculate the energy variation rates for the atom and the field, as well as the atomic population levels, both in the inertial case and at constant proper acceleration, considering the two-level system as a prototype of an Unruh detector, for admissible couplings of the radiation field.