  We use a careful treatment of time-dependent wave-mechanical scattering to
determine the conditions under which a dilute, non-degenerate quantum gas can
obey a Boltzmann equation. If the gas possesses weak long-range coherence, such
as may occur when a gas is quantum mechanically throttled by tunnelling through
a barrier, collisions within the gas will suppress this long range coherence.
We calculate its decay rate and find it to be related to the Boltzmann
equation's loss term.
