Bose-Einstein condensation temperature of a homogenous weakly interacting Bose gas in variational perturbation theory through seven loops

2003/09/11 by Boris Kastening · 4 citations
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #Quantum, superfluid, helium dynamics #cond-mat.stat-mech #hep-ph #quant-ph

paper · pdf · doi:10.1103/physreva.69.043613

published as Phys.Rev. A69 (2004) 043613 · 8 pages; typos and errors of presentation fixed; beautifications; results unchanged

arxiv created 2003/09/11 · openalex publication_date 2004/04/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a is computed for given particle density n. Variational perturbation theory is used to resum the corresponding perturbative series for \ensuremathΔ⟨\ensuremathφ²⟩∕Nu in a classical three-dimensional scalar field theory with coupling u and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte Carlo simulations; for N=2, we obtain \ensuremathΔT_c∕T₀=(1.27\ifmmode±\else\textpm\fi0.11)an^1∕3. We use seven-loop perturbative coefficients, extending earlier work by one loop order.

Citations

• Asymptotically improved convergence of optimized perturbation theory in the Bose-Einstein condensation problem
• Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas in variational perturbation theory through six loops

Cited by

• Non-Perturbative Renormalization Group calculation of the transition temperature of the weakly interacting Bose gas
• Critical temperature of dilute Bose gases
• Heat-kernel approach for scattering
• Theory of the weakly interacting Bose gas
• Scattering theory without large-distance asymptotics