A nonextensive approach to Bose-Einstein condensation of trapped interacting boson gas

TL;DR

This paper applies nonextensive statistics to model Bose-Einstein condensation in interacting boson gases, providing a new way to estimate transition temperatures considering effective interactions.

Contribution

It introduces a nonextensive statistical framework to analyze Bose-Einstein condensation, deriving generalized temperatures and interaction parameters for different atomic gases.

Findings

Effective interactions are attractive for 87Rb, 23Na, and 7Li.

The model estimates q values consistent with observed transition temperatures.

Conventional theories underestimate the condensation temperatures.

Abstract

In the Bose-Einstein condensation of interacting atoms or molecules such as 87Rb, 23Na and 7Li, the theoretical understanding of the transition temperature is not always obvious due to the interactions or zero point energy which cannot be exactly taken into account. The S-wave collision model fails sometimes to account for the condensation temperatures. In this work, we look at the problem within the nonextensive statistics which is considered as a possible theory describing interacting systems. The generalized energy Uq and the particle number Nq of boson gas are given in terms of the nonextensive parameter q. q>1 (q<1) implies repulsive (attractive) interaction with respect to the perfect gas. The generalized condensation temperature Tcq is derived versus Tc given by the perfect gas theory. Thanks to the observed condensation temperatures, we find q ~ 0.1 for 87Rb atomic gas, q ~ 0.95 for 7Li and q ~ 0.62 for 23Na. It is concluded that the effective interactions are essentially attractive for the three considered atoms, which is consistent with the observed temperatures higher than those predicted by the conventional theory.