  Abstract We discuss the quantum dynamics of the central spin model in a
regime where the central spin and bath are slaved to each other. The exact
solution is found when the bath is static, and is compared with the effect of
an external field, finding that they are inequivalent due to the quantum nature
of the environment. When the bath has dynamics, we analyze the differences
between the numerical simulation using time-dependent perturbation theory and
the equation of motion technique, which shows better accuracy. We demonstrate
that the use of dynamical Renormalization Group (dRG), simultaneously with the
equation of motion technique, provides a suitable analytical tool to understand
the physics, to capture the main physical processes, and a powerful method to
eliminate secular terms. In addition, this approach allows to separate
classical non-linear behavior from corrections due to quantum correlations.
