S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case

Abstract

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.

26 pages, 16 figures

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• On the viscosity to entropy density ratio for unitary Bose and Fermi Gases
• Viscosity Bound Violation in Viscoelastic Fermi Liquids
• Virial coefficients for Bose and Fermi trapped gases beyond the unitary limit: an S-Matrix approach
• Quantum Bose and Fermi gases with large negative scattering length in the 2-body S-matrix approximation
• Unitary Fermi superfluid near the critical temperature: thermodynamics and sound modes from elementary excitations
• Thermodynamic Properties of Universal Fermi Gases
• Metastability of Bose and Fermi gases on the upper branch