  A finite-dimensional quantum system is coupled to a bath of oscillators in
thermal equilibrium at temperature $T>0$. We show that for fixed, small values
of the coupling constant $\lambda$, the true reduced dynamics of the system is
approximated by the completely positive, trace preserving Markovian semigroup
generated by the Davies-Lindblad generator. The difference between the true and
the Markovian dynamics is $O(|\lambda|^{1/4})$ for all times, meaning that the
solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is
approximating the true dynamics to accuracy $O(|\lambda|^{1/4})$ for all times.
Our method is based on a recently obtained expansion of the full system-bath
propagator. It applies to reservoirs with correlation functions decaying in
time as $1/t^{4}$ or faster, which is a significant improvement relative to the
previously required exponential decay.
