The dynamics of quantum correlations of two qubits in a common environment

We consider a model of quantum system of two qubits embedded into a common environment assuming that the environment parts of the system Hamiltonian are described by hermitian random matrices of size $N$. We obtain the infinite $N$ limit of the time dependent reduced density matrix of qubits. We then work out an analog of the Bogolyubov-van Hove asymptotic regime of the theory of open systems and statistical mechanics. The regime does not imply in general the Markovian dynamics of the reduced density matrix of our model and allows for a analytical and numerical analysis of the evolution of several widely used quantifiers of quantum correlation, mainly entanglement. We find a variety of new patterns of qubits dynamics absent in the case of independent random matrix environments studied in our paper [8]. The patterns demonstrate the important role of common environment in the enhancement and the diversification of quantum correlations via the indirect (via environment) interaction between qubits. Our results, partly known and partly new, can be viewed as a manifestation of the universality of certain properties of the decoherent qubit evolution that have been found in various exact and approximate versions of the two qubit models with macroscopic bosonic environment.