  The question, whether an open system dynamics is Markovian or non-Markovian
can be answered by studying the direction of the information flow in the
dynamics. In Markovian dynamics, information must always flow from the system
to the environment. If the environment is interacting with only one of the
subsystems of a bipartite system, the dynamics of the entanglement in the
bipartite system can be used to identify the direction of information flow.
Here we study the dynamics of a two-level system interacting with an
environment, which is also a heat bath, and consists of a large number of
two-level quantum systems. Our model can be seen as a close approximation to
the `spin bath' model at low temperatures. We analyze the Markovian nature of
the dynamics, as we change the coupling between the system and the environment.
We find the Kraus operators of the dynamics for certain classes of couplings.
We show that any form of time-independent or time-polynomial coupling gives
rise to non-Markovianity. Also, we witness non-Markovianity for certain
parameter values of time-exponential coupling. Moreover, we study the
transition from non-Markovian to Markovian dynamics as we change the value of
coupling strength.
