  We consider two systems of harmonically trapped particles in a typical pure
state of the Hilbert space defined by given values of the particle numbers and
energies of the two gases. Such a state is entangled but we show that, for
large systems, the resulting correlations between the two gases are identical
to those of a separable mixture. This result can be generalized to other
physical systems. We discuss the relation of this effective separability to the
well-known existence of quantum correlations in any entangled state. We study
in detail a small bipartite system and find that its correlations are well
explained by the large systems results.
