Hot Accelerated Qubits: Decoherence, Thermalization, Secular Growth and Reliable Late-time Predictions

Abstract

We compute how an accelerating qubit coupled to a scalar field - i.e. an Unruh-DeWitt detector - evolves in flat space, with an emphasis on its late-time behaviour. When calculable, the qubit evolves towards a thermal state for a field prepared in the Minkowski vacuum, with the approach to this limit controlled by two different time-scales. For a free field we compute both of these as functions of the difference between qubit energy levels, the dimensionless qubit/field coupling constant, the scalar field mass and the qubit's proper acceleration. Both time-scales differ from the Candelas-Deutsch-Sciama transition rate traditionally computed for Unruh-DeWitt detectors, which we show describes the qubit's early-time evolution away from the vacuum rather than its late-time approach to equilibrium. For small enough couplings and sufficiently late times the evolution is Markovian and described by a Lindblad equation, which we derive in detail from first principles as a special instance of Open EFT methods designed to handle a breakdown of late-time perturbative predictions due to the presence of secular growth. We show how this growth is resummed in this example to give reliable information about late-time evolution including both qubit/field interactions and field self-interactions. By allowing very explicit treatment, the qubit/field system allows a systematic assessment of the approximations needed when exploring late-time evolution, in a way that lends itself to gravitational applications. It also allows a comparison of these approximations with those - e.g. the `rotating-wave' approximation - widely made in the open-system literature (which is aimed more at atomic transitions and lasers).