Quantum Dynamics, Master Equation and Equilibrium for a Qubit Coupled to a Thermal Boson Field

Abstract

We analytically derive the exact -- though formal -- master equation for a two-level quantum system (qubit) interacting with a bosonic environment within the rotating-wave approximation, assuming the environment is initially in an arbitrary thermal state. The long-time behavior of the evolution operator governing the dynamics of both the system and the environment is analyzed, and the conditions under which the system approaches thermal equilibrium are examined.