Transient phenomena in the Unruh effect

We derive an expression for the excitation rate of a DeWitt detector moving along an arbitrary world-line in Minkowski vacuum. For the special case of a uniformly accelerated detector this gives the well-known Unruh effect. It is shown here that, in general, for an arbitrarily moving detector Unruh's relation between temperature and acceleration does not hold even locally. Moreover, in some cases the response function exhibits oscillatory transient phenomena.