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| It is shown that, if the reduced density matrix (RDM) of an open system may reach a stationary solution for long times, and if the environment of the system has certain random feature, then, in the limit of large Hilbert space of the environment, the stationary RDM is commutable with a renormalized Hamiltonian of the system. Here, the renormalized Hamiltonian is given by the unperturbed Hamiltonian plus certain average of the interaction Hamiltonian over the environmental degrees of freedom. Under the above-mentioned conditions, the eigenbasis of the renormalized Hamiltonian is usually a preferred basis in view of the long-time evolution of the RDM. |
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| Keywords:open quantum system, reduce density matrix, decoherence, pointer state, statistically preferred basis, renormalization, dynamical randomization |
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