In this paper, a method for deriving master equation is developed for a generic small quantum system, which is locally coupled to an environment as a many-body quantum chaotic system that satisfies the eigenstate thermalization hypothesis ansatz, resorting to neither the Born approximation nor the Markov approximation. The total system undergoes Schr\"{ o}dinger evolution, under an initial condition in which the environmental branches possess no correlation with the interaction Hamiltonian. Derivation of the master equation is based on piecewise usage of a second-order expansion of a formal expression, which is derived for the evolution of the environmental branches. Approximations used in the derivation are mainly based on dynamic properties of the environment.
Categories: quant-ph