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S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case
A new analytic treatment of three-dimensional homogeneous Bose and Fermi
gases in the unitary limit of negative infinite scattering length is presented,
based on the S-matrix approach to statistical mechanics we recently developed.
The unitary limit occurs at a fixed point of the renormalization group with
dynamical exponent z=2 where the S-matrix equals -1. For fermions we find T_c
/T_F is approximately 0.1. For bosons we present evidence that the gas does not
collapse, but rather has a critical point that is a strongly interacting form
of Bose-Einstein condensation. This bosonic critical point occurs at n lambda^3
approximately 1.3 where n is the density and lambda the thermal wavelength,
which is lower than the ideal gas value of 2.61.Comment: 26 pages, 16 figure