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Formally exact time-convolutionless master equation was derived by means of the projection operator method for the reduced statistical operator of a multi-level quantum system interacting with arbitrary external deterministic fields and dissipative environment simultaneously. While being closed and homogeneous in the reduced statistical operator, this equation accounts for thermodynamically equilibrium correlations between the multi-level system and the environment at the initial moment of time. On the basis of the exact master equation, an approximate time-convolutionless master equation for the reduced statistical operator was derived in the second order of the system-environment interaction strength. It was shown that the analysis of this equation can be simplified if the free Hamiltonian dynamics of an arbitrary quantum multi-level system driven by the external fields is described in terms of the SU(N) algebra representation, so the master equation in question can be reduced to a set of ordinary differential equations for a finite number of time-dependent coefficients. As a consequence, efficient numerical methods can be employed to solve this master equation for various physically realistic quantum models of theoretical and practical importance.

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