no role. This raises doubts concerning whether lasing actually plays any role in the experiment. Even though our simulations do not take quantum fluctuations into account, the mean field behavior they reveal would persist in the presence of quantum fluctuations, and it already seems to account for the observed mean field behavior. On the other hand, even if the conditions for lasing existed in the system, we may not have seen that instability because of the absence of the necessary seed fluctuations.

There is an important feature of the experimental measurements that our simulations in this paper do not address, and that is the connected density-density correlation function. This is because our simulations are deterministic. In order to understand the relation between this correlation function and the mean field behavior, as well as to check for lasing instability in the presence of quantum fluctuations, in another paper [@correlations] we have studied the system in the presence of both quantum fluctuations, and fluctuations in atom number from one run to the next. We find there that the correlation function is engendered by fluctuation-induced modulation of the deterministic standing wave. In fact, it results primarily from the varying number of atoms in 