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The strong system-bath correlation is a typical initial condition in manycondensed matter and some quantum optical systems. Here, the dynamics of a spininteracting with a spin bath through an intermediate spin are studied. Initialcorrelations between the spin and the intermediate spin are taken into account.The exact analytical expression for the evolution operator of the spin isfound. Furthermore, correlated projection superoperator techniques are appliedto the model and a time-convolutionless master equation to second order isderived. It is shown that the time-convolutionless master equation to secondorder reproduces the exact dynamics for time-scales of the order 1/{\gamma},where {\gamma} is the coupling of the central spin to the intermediate spin. Itis found that there is a strong dependence on the initial system-bathcorrelations in the dynamics of the reduced system, which cannot be neglected.

Initial correlation in a system of a spin coupled to a spin bath through an intermediate spin