S-matrix approach to quantum gases in the unitary limit I: the two-dimensional case

Abstract

In three spatial dimensions, in the unitary limit of a non-relativistic quantum Bose or Fermi gas, the scattering length diverges. This occurs at a renormalization group fixed point, thus these systems present interesting examples of interacting scale-invariant models with dynamical exponent z=2. We study this problem in two and three spatial dimensions using the S-matrix based approach to the thermodynamics we recently developed. It is well suited to the unitary limit where the S-matrix equals -1, since it allows an expansion in the inverse coupling. We define a meaningful scale-invariant, unitary limit in two spatial dimensions, where again the scattering length diverges. In the two-dimensional case, the integral equation for the pseudo-energy becomes transcendentally algebraic, and we can easily compute the various universal scaling functions as a function of μ/T, such as the energy per particle. The ratio of the shear viscosity to the entropy density is above the conjectured lower bound of for all cases except attractive bosons. For attractive 2-component fermions, the ratio is greater than 6.07 times the conjectured lower bound, whereas for attractive bosons it is greater than 0.4 times it.

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Cited by in corpus (5)

• Fisher zeros of a unitary Bose gas
• On the viscosity to entropy density ratio for unitary Bose and Fermi Gases
• S-matrix approach to quantum gases in the unitary limit II: the three-dimensional case
• 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