In this paper, a method is developed for the study of a generic small central quantum system, which is locally coupled to an environment as a many-body chaotic quantum system that satisfies the eigenstate-thermalization-hypothesis (ETH) ansatz. The approach is based on properties of environmental branches of the total system's state, the overlaps of which give the reduced density matrix (RDM) of the central system. To study the evolution of the RDM within a finite time period, the period is divided into a series of short intervals, within each of which the RDM is computed by making use of a formal solution to the time evolution of the environmental branches. The expressions thus obtained are simplified by the ETH ansatz and, further, by decay of phase correlations among the environmental branches, the latter of which also originates from chaotic dynamics of the environment. This gives a generic method of deriving a master equation. As an application, a master equation is derived in the simplest nontrivial case, which predicts a decoherence rate in agreement with that predicted by the random-matrix theory. Furthermore, the Born approximation, which is employed in the ordinary approach to the master equation, can be justified within the proposed framework, and a Markovian feature is shown for the RDM's evolution in an effective sense.

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• Eigenstate thermalization
• Open quantum systems & decoherence
• Quantum chaos
• Master equation