  Dynamics of an open two-qubit system is investigated in the post-Markovian
regime, where the environments have a short-term memory. Each qubit is coupled
to separate environment which is held in its own temperature. The inter-qubit
interaction is modeled by XY-Heisenberg model in the presence of spin-orbit
interaction and inhomogeneous magnetic field. The dynamical behavior of
entanglement and discord has been considered. The results show that, quantum
discord is more robust than quantum entanglement, during the evolution. Also
the asymmetric feature of quantum discord can be monitored by introducing the
asymmetries due to inhomogeneity of magnetic field and temperature difference
between the reservoirs. By employing proper parameters of the model, it is
possible to maintain non-vanishing quantum correlation at high degree of
temperature. The results can provide a useful recipe for studying of dynamical
behavior of two-qubit systems such as trapped spin-electrons in coupled quantum
dots.
