Five-Loop Critical Temperature Shift in Weakly Interacting Homogeneous Bose-Einstein Condensate

TL;DR

This paper calculates the five-loop correction to the critical temperature shift in a weakly interacting homogeneous Bose-Einstein condensate using variational perturbation theory, providing a more precise theoretical estimate.

Contribution

It presents a five-loop calculation of the critical temperature shift in Bose-Einstein condensates, extending previous lower-order theoretical results.

Findings

Calculated Delta T_c/T_c^{(0)} approx 1.14(11) an^{1/3}

Result is lower than recent Monte Carlo simulations

Uses variational perturbation theory for high-order loop calculations

Abstract

Using variational perturbation theory, we calculate the shift in the critical temperature T_c up to five loops to lowest order in the scattering length a and find Delta T_c/T_c^{(0)} approx (1.14\pm0.11)an^{1/3}, where n is the particle density. Our result is lower than the latest Monte Carlo result (1.32\pm0.02)an^{1/3}.