  The dynamics of atom lasers with a continuous output coupler based on
two-photon Raman transitions is investigated. With the help of the
time-convolutionless projection operator technique the quantum master equations
for pulsed and continuous wave (cw) atom lasers are derived. In the case of the
pulsed atom laser the power of the time-convolutionless projection operator
technique is demonstrated through comparison with the exact solution. It is
shown that in an intermediate coupling regime where the Born-Markov
approximation fails the results of this algorithm agree with the exact
solution. To study the dynamics of a continuous wave atom laser a pump
mechanism is included in the model. Whereas the pump mechanism is treated
within the Born-Markov approximation, the output coupling leads to
non-Markovian effects. The solution of the master equation resulting from the
time-convolutionless projection operator technique exhibits strong oscillations
in the occupation number of the Bose-Einstein condensate. These oscillations
are traced back to a quantum interference which is due to the non-Markovian
dynamics and which decays slowly in time as a result of the dispersion relation
for massive particles.
