Exact scaling transform for a unitary quantum gas in a time dependent harmonic potential

A unitary quantum gas is a gas of quantum particles with a binary interaction of infinite scattering length and negligible range. It has been produced in recent experiments with gases of fermionic atoms by means of a Feshbach resonance. Using the Fermi pseudo-potential model for the atomic interaction, we show that the time evolution of such a gas in an isotropic three-dimensional time dependent harmonic trap is exactly given by a gauge and scaling transform. (C) 2004 Academie des sciences. Published by Elsevier SAS. All rights reserved.