  Exact conditions for antiUnruh effect in (1+1)-dimensional spacetime are
obtained. For detectors with Gaussian switching functions, the analytic results
are similar to previous ones, indicating that antiUnruh effect occurs when the
energy gap matches the characteristic time scale. However, this conclusion does
not hold for detectors with square wave switching functions, in which case the
condition turns out to depend on both the energy gap and the characteristic
time scale in some nontrivial way. We also show analytically that there is no
antiUnruh effect for detectors with Gaussian switching functions in
(3+1)-dimensional spacetime.
