2013/07/23 by Fabio Briscese
Mathematics · Physics and Astronomy · #Ab initio #Atomic physics #Bose–Einstein condensate #Cold Atom Physics and Bose-Einstein Condensates #Field (mathematics) #Hartree–Fock method #Lambda #Mathematics #Order (exchange) #Physics #Quantum #Quantum mechanics #Quantum, superfluid, helium dynamics #Semiclassical physics #Strong Light-Matter Interactions #cond-mat.quant-gas #cond-mat.stat-mech
paper · pdf · doi:10.1140/epjb/e2013-40551-y
published as Eur. Phys. J. B (2013) 86: 343 · 6 pages, to appear in Eur. Phys. J. B (2013)
arxiv created 2013/07/23 · openalex publication_date 2013/07/27 · arxiv updated 2013/08/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss the effect of inter-atoms interactions on the condensation temperature Tc of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift ΔTc/Tc0 ≈ b1 (a/λTc) + b2 (a/λTc)2 + ψ[a/λTc] with a the s-wave scattering length, λT the thermal wavelength and ψ[a/λTc] a non-analytic function such that ψ[0] = ψ'[0] = ψ"[0] = 0 and |ψ"'[0]| = ∞. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in a/λTc and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for b2 ≃ 18.8 which improves a previous numerical result. We also discuss how the discrepancy between b2 and the empirical value of b2 = 46 ± 5 may be explained with no need to resort to beyond-mean field effects.