  We consider two-level detectors coupled to a scalar field and moving on
arbitrary trajectories in Minkowski space-time. We first derive a generic
expression for the response function using a (novel) regularization procedure
based on the Feynmann prescription that is explicitly causal, and we compare it
to other expressions used in the literature. We then use this expression to
study, analytically and numerically, the time dependence of the response
function in various non-stationarity situations. We show that, generically, the
response function decreases like a power in the detector's level spacing, $E$,
for high $E$. It is only for stationary world-lines that the response function
decays faster than any power-law, in keeping with the known exponential
behavior for some stationary cases. Under some conditions the (time dependent)
response function for a non-stationary world-line is well approximated by the
value of the response function for a stationary world-line having the same
instantaneous acceleration, torsion, and hyper-torsion. While we cannot offer
general conditions for this to apply, we discuss special cases; in particular,
the low energy limit for linear space trajectories.
