Non-Markovian Dynamics of Quantum and Classical Correlations in the Presence of System-Bath Coherence

We present a detailed study on the dynamics of two-qubit correlations in non-Markovian environments, applying the hierarchy equations approach. This treatment is free from the limitation of perturbative, Markovian or rotating wave approximations. It is shown that crossovers and sudden changes in the classical and quantum correlations can appear when the strength of the interaction between qubits is gradually reduced. For some special initial states, there are even sudden transitions between the classical and quantum correlations.