  Using random matrices, we study the reduced dynamics of a two level system
interacting with a generic environment. In the weak coupling limit, the result
can be obtained directly from known results for purity decay, and result in
Markovian dynamics. We then focus on the case of strong coupling, when the
dynamics is known to be non-Markovian. In this regime, the coupling dominates
over the local parts of the Hamiltonian, and thus we treat the latter as a
perturbation of the former. With the help of the linear response approximation,
this allows us to obtain an analytical description of the reduced dynamics.
Finally, we find a transition from non-Markovian to Markovian dynamics at a
point where the coupling and the local Hamiltonian are comparable in size.
