Memory effects in the spin relaxation within and without rotating wave approximation

In the frame of the time-convolutionless generalized master equation approach, an analysis of a spin relaxation is made within and without the rotating wave approximation. The non-Markovian reduced dynamics is investigated, giving explicit expressions for the time-dependent involved coefficients, and numerical results are presented for the Ohmic reservoir model. The comparisons between these results and those obtained with the Markovian approximation are developed, analyzing the positivity of the reduced dynamics in the short transient time