  We discuss the use of the Born and Markov approximations in describing the
dynamics of an atom laser. In particular, we investigate the applicability of
the quantum optical Born-Markov master equation for describing output coupling.
We derive conditions based on the atomic reservoir, and atom dispersion
relations for when the Born-Markov approximations are valid and discuss
parameter regimes where these approximations fail in our atom laser model.
Differences between the standard optical laser model and the atom laser are due
to a combination of factors, including the parameter regimes in which a typical
atom laser would operate, the different reservoir state which is appropriate
for atoms, and the different dispersion relations between atoms and photons. We
present results based on an exact method in the regimes in which the
Born-Markov approximation fails. The exact solutions in some experimentally
relavent parameter regimes give non-exponential loss of atoms from a cavity.
