  Exchange in a Boltzmann gas of bosons with several internal states leads to
collective transport of internal polarization. The internal dynamics can be
understood as Larmor precession in the presence of a torque induced by atoms on
each other via exchange coupling. A generalized Bloch equation that includes
interatomic exchange effects as well as orbital motion in the gas is derived
and used to interpret recent experiment by Lewandowski et al. as an excitation
of a collective wave of internal state polarization. It is shown that exchange
leads to formation of domains in which precession frequencies are synchronized.
