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Abstract
We consider a model of a quantum system of two qubits embedded into an environment. We assume that the environment parts of the system Hamiltonian are described by hermitian random matrices of size N. We obtain the large N limit of the time dependent reduced density matrix of the qubits. We then work out an analog of the Bogolyubov-van Hove asymptotic regime of the theory of open systems in statistical mechanics. This regime does not imply in general the Markovian dynamics of the reduced density matrix of our model.
This model allows for a analytical and numerical analysis of the evolution of widely used quantifiers of quantum correlations, mainly entanglement. We find a variety of interesting patterns of qubit dynamics. The patterns demonstrate the important role of the environment in the enhancement and the diversification of the evolution of quantum correlations. Our results can also 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 models where the environment is described by free bosons.