We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study is based on a “universality hypothesis” for the relevant energy scales which is supported by experiments and can be proven in the Boltzmann regime. It implies a universal form for the grand potential, which is specified by only a few universal numbers in the degenerate limit. This hypothesis provides a simple way to determine the density profile of a trapped fermion superfluid. It implies a superfluid bump in the density and gives the general expression of the second sound velocity of a homogeneous superfluid at unitarity.

• Received 4 September 2003

DOI:https://doi.org/10.1103/PhysRevLett.92.090402