  The dynamics of a central spin-1/2 in presence of a local magnetic field and
a bath of N spin-1/2 particles is studied in the thermodynamic limit. The
interaction between the spins is Heisenberg XY type and the bath is considered
to be a perfect thermal reservoir. In this case, the evolution of the
populations of the reduced density matrix are obtained for different
temperatures. A Born approximation is made but not a Markov approximation
resulting a non-Markovian dynamics. The measure of the way that the system
mixes is obtained by means of the von Neumann entropy. For low temperatures,
results show that there are oscillations of populations and of the von Neumann
entropy, indicating that the central spin becomes a pure state with
characteristic time periods in which it is possible to extract or recuperate
information. In the regime of high temperatures, the evolution shows a final
maximum mixed state with entropy S=ln 2 as it is expected for a two level
system.
