We have measured the damped motion of a trapped Bose–Einstein condensate, oscillating with
respect to a thermal cloud. The cigar-shaped trapping potential provides enough transverse
confinement that the dynamics of the system are intermediate between three-dimensional and onedimensional.
We find that the scaling of the damping rate with temperature is consistent with Landau
theory, but that the damping rate for axial oscillations at a given temperature is consistently smaller
than expected for a three-dimensional gas. We attribute this to the suppressed density of states for
low-energy transverse excitations(essential excitations for axial Landau damping), which results from
the quantization of the radial motion.