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Universal Thermodynamics of Degenerate Quantum Gases in the Unitarity Limit

We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study makes use of a "Universality Hypothesis" for the relevant energy scales of a many-body system at unitarity. This Hypothesis is supported by recent experiments and can be proven in Boltzmann regime. It implies a universal form for the grand potential which is characterized by only a few universal numbers in degenerate limit. This universal form provides a simple way to determine the density profile of a trapped fermion superfluid as well as the second sound velocity of a homogeneous superfluid at unitarity.