  For adiabatically and periodically manipulated dissipative quantum systems we
derive, using Floquet theory, a simple Markovian master equation. Contrary to
some previous works we explicitly take into account the time dependence of the
Hamiltonian and, therefore, obtain a master equation with a time-dependent
dissipative part. We illustrate our theory with two examples and compare our
results with the previously proposed master equations. In particular, we
consider the problem of Cooper pair pumping and demonstrate the inadequacy of
the secular (rotating wave) approximation when calculating the pumped charge.
The secular approximation producing a master equation of the Lindblad type
approximates well the quantum state (density matrix) of the system, while to
determine the pumped charge a non-Lindblad master equation beyond the rotating
wave approximation is necessary.
