We investigate a scale-invariant two-component Fermi gas in a time-dependentView original: http://arxiv.org/abs/1202.0584
isotropic harmonic potential. The exact time evolution of the density
distribution in position space in any spatial dimension is obtained. Two
experimentally relevant examples, an abrupt change and a periodic modulation of
the trapping frequency are solved. Small deviations from scale invariance and
isotropy of the confinement are considered. We discuss the consequences for
experiments with ultracold quantum gases such as the excitation of a tower of
undamped breathing modes and a new alternative for measuring the Tan contact.