  The dynamics of an open quantum system is usually studied by performing a
weak-coupling and weak-correlation expansion in the system-bath interaction.
For systems exhibiting strong couplings and highly non-Markovian behavior this
approach is not justified. We apply a recently proposed correlated projection
superoperator technique to the model of a central spin coupled to a spin bath
via full Heisenberg interaction. Analytical solutions to both the
Nakajima-Zwanzig and the time-convolutionless master equation are determined
and compared with the results of the exact solution. The correlated projection
operator technique significantly improves the standard methods and can be
applied to many physical problems such as the hyperfine interaction in a
quantum dot.
