  We investigate the phenomenon of sudden transition between classical and
quantum decoherence in the study of quantum discord for a dissipative cavity
QED system, which consists of two noninteracting two-level atoms, each trapped
in a dissipative cavity. It is found that the quantum discord between two
atoms, which are prepared initially in the X-type quantum states, is not
destroyed by the dissipation of the cavities for a finite time interval and the
stationary quantum discord can arise in the interaction of atoms with cavities
as the time approach to infinite. The transition time is sensitive to the
initial state parameter of the two atoms and the mean photon number of the
coherent field. Interestingly, the quantum discord between the two atoms is
completely unaffected by the dissipation of the cavities if we choose the
suitable value of the ratio, which depends on the decay rate of two cavities
and the atom-field coupling constant.
