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

TL;DR

This paper develops an analytic S-matrix approach to study three-dimensional quantum gases at the unitary limit, revealing a critical point for bosons and estimating the transition temperature for fermions.

Contribution

It introduces a new analytic method for analyzing 3D quantum gases at unitarity, providing insights into their critical behavior and phase transitions.

Findings

Fermionic T_c/T_F is approximately 0.1.

Bosonic gas has a critical point at nλ^3 ≈ 1.3.

Bosons do not collapse but undergo a strongly interacting Bose-Einstein condensation.

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.