  We have investigated collective breathing modes of a unitary Fermi gas in
deformed harmonic traps. The ground state is studied by the Superfluid Local
Density Approximation (SLDA) and small-amplitude collective modes are studied
by the iterative Quasiparticle Random Phase Approximation (QRPA). The results
illustrate the evolutions of collective modes of a small system in traps from
spherical to elongated or pancake deformations. For small spherical systems,
the influences of different SLDA parameters are significant, and, in
particular, a large pairing strength can shift up the oscillation frequency of
collective mode. The transition currents from QRPA show that the compressional
flow patterns are nontrivial and dependent on the deformation. Finally, the
finite size effects are demonstrated to be reasonable when progressing towards
larger systems. Our studies indicate that experiments on small and medium
systems are valuable for understanding effective interactions in systems with
varying sizes and trap deformations.
