2010/04/29 by Pye-Ton How, André LeClair · 1 citation
Mathematics · Physics and Astronomy · #Bose gas #Bose–Einstein condensate #Boson #Cold Atom Physics and Bose-Einstein Condensates #Exponent #Fermion #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Renormalization group #Scattering #Scattering length #Unitary matrix #Unitary state #cond-mat.quant-gas #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1742-5468/2010/07/p07001
published as J. Stat. Mech. (2010) P07001 · 26 pages, 16 figures
arxiv created 2010/04/29 · openalex publication_date 2010/07/01 · arxiv updated 2015/05/18 · openalex created_date 2022/01/25 · openalex updated_date 2026/08/05
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 ≈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 λ T 3 ≈1.3, where n is the density and λ T the thermal wavelength, which is lower than the ideal gas value of ζ(3/2) = 2.61.