We have studied the dynamics of quantum correlations such as entanglement,
Bell-nonlocality and quantum discord between identical as well as unidentical
atoms interacting with a single-mode cavity field and subject to cavity decay.
The effect of single atom detuning, cavity decay rate and initial preparation
of the atoms on the corresponding correlation measures have been investigated.
It is found that even under strong dissipation, time evolution can create high
quantum discord while entanglement and Bell nonlocality stay zero for an
initially separable state. Quantum discord increases while entanglement
decreases in a certain time period under dissipation for the initial state that
both atoms are in the excited state if the qubits are identical. For some type
of initial states, cavity decay is shown to drive the system to a stationary
state with high entanglement and quantum discord