  We derive a quantum Langevin equation for a quantum spin in the presence of a
magnetic field and study its dynamics in the Markovian limit using the Ohmic
bath model. We extend our analysis to the Drude bath with a finite memory. We
study the time evolution of the expectation values of the magnetic moments. The
spin auto-correlation functions exhibit a damped oscillatory behaviour with the
randomization time being determined by the damping rate and also the memory
time for the Drude bath model. We also analyse the spin response function of
the system for the Ohmic bath model. Our results are consistent with findings
in cold atom experiments. In addition we make predictions which can be tested
in future ultra cold atom experiments.
