  In this paper we investigate the non-Markovian dynamics of a qubit by
comparing two generalized master equations with memory. In the case of a
thermal bath, we derive the solution of the post-Markovian master equation
recently proposed in Ref. [A. Shabani and D.A. Lidar, Phys. Rev. A {\bf 71},
020101(R) (2005)] and we study the dynamics for an exponentially decaying
memory kernel. We compare the solution of the post-Markovian master equation
with the solution of the typical memory kernel master equation. Our results
lead to a new physical interpretation of the reservoir correlation function and
bring to light the limits of usability of master equations with memory for the
system under consideration.
