We consider a model of the evolution of one and two qubits embedded in an environment. In contrast to the well-known spin-boson model, used to model a translation invariant and macroscopic environment, we model the environment by random matrices of large size that are widely used to describe multi-connected disordered environments of mesoscopic and even nanoscopic size. An important property of the model is that it incorporates non-Markovian evolution allowing for the backflow of energy and information from the environment to the qubits.
We obtain an asymptotically exact in size of the environment expression for the reduced density matrix of qubits valid for all typical realizations of the disordered environment. By using detailed analytical and numerical analysis of expressions, we find several interesting patterns of the qubit evolution, including the disappearance of entanglement in the finite moments and, especially, its subsequent reappearance. These patterns are known in quantum information science as the sudden death and the sudden birth of entanglement. They were found earlier in special versions of the spin-boson model. Our results obtained for a non microscopic and disordered environment demonstrate the robustness and universality of the patterns. When combined with certain tools of quantum information science (e.g., entanglement distillation), the results can lead to a much slower decay entanglement down to its asymptotic persistence.