  We analyze several puzzling features of a recent experiment with a
noninteracting gas of atoms in a quadrupole trap. After an initial momentum
kick, the system reaches a stationary, quasi-thermal state even without
collisions, due to the dephasing of individual particle trajectories.
Surprisingly, the momentum distribution remains anisotropic at long times,
characterized by different "temperatures" along the different directions. In
particular, there is no transfer of the kick energy between the axial and
radial trap directions. To understand these effects we discuss and solve two
closely related models: a spherically symmetric trap $V(r)\simeq r^\alpha$ and
a strongly confined gas along one direction (a "pancake" trap). We find that in
the isotropic trap, the gas unexpectedly also preserves the anisotropy of the
kick at long times, which we are able to explain using the conservation of
angular momentum and the virial theorem. Depending on the value of $\alpha$ we
find that the kick can cool or heat the orthogonal directions. The pancake trap
case is quantitatively similar to the quadrupole one. We show that for the
former, the temperature anisotropy and memory of the kick direction are due to
the change in the 2D effective potential resulting from the kick, thereby also
explaining the quadrupole experimental results.
