Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops

TL;DR

This paper calculates the shift in Bose-Einstein condensation temperature for a weakly interacting homogeneous Bose gas using advanced seven-loop variational perturbation theory, aligning results with recent Monte-Carlo simulations.

Contribution

It extends previous work by computing the temperature shift using seven-loop perturbative coefficients and generalizes the analysis to arbitrary N in the scalar field theory.

Findings

Results agree with recent Monte-Carlo simulations.

For N=2, the temperature shift ratio is 1.27 +/- 0.11 a n^(1/3).

Extended the perturbative calculation by one loop order.

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 Delta<phi^2>/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 Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop perturbative coefficients, extending earlier work by one loop order.