  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).
