Exact 1/N and Optimized Perturbative Evaluation of mu_c for Homogeneous Interacting Bose Gases

TL;DR

This paper evaluates the critical chemical potential in dilute Bose gases using large N expansion and optimized perturbative methods, showing good agreement with numerical simulations and providing insights into the critical temperature shift.

Contribution

It introduces an exact 1/N expansion and optimized perturbative approaches to accurately estimate the critical chemical potential in homogeneous Bose gases.

Findings

Large N approximation performs well for N=2.

Optimized perturbative methods yield excellent results.

Results agree with recent numerical lattice simulations.

Abstract

In the framework of the O(N) three-dimensional effective scalar field model for homogeneous dilute weakly interacting Bose gases we use the 1/N expansion to evaluate, within the large N limit, the parameter r_c which is directly related to the critical chemical potential mu_c. This quantity enters the order-a^2 n^{2/3} coefficient contributing to the critical temperature shift Delta T_c where a represents the s-wave scattering length and n represents the density. Compared to the recent precise numerical lattice simulation results, our calculation suggests that the large N approximation performs rather well even for the physical case N=2. We then calculate the same quantity but using different forms of the optimized perturbative (variational) method, showing that these produce excellent results both for the finite N and large-N cases.