  For confined systems of identical particles, either bosons or fermions, we
argue that the parabolic nature of the confinement potential is a prerequisite
for the non-dissipative character of the center of mass response to a uniform
probe. For an excitation in a parabolic confining potential, the half width of
the density response function depends nevertheless quantitatively on properties
of the internal degrees of freedom, as is illustrated here for an ideal
confined gas of identical particles with harmonic interparticle interactions.

Statistical Mechanics