On the anomalous density for Bose gases at finite temperature

TL;DR

This paper investigates the temperature-dependent behavior of anomalous density in Bose gases, highlighting its significance for condensate stability and how it varies with interaction strength.

Contribution

It provides a variational analysis of anomalous density at finite temperatures, confirming its importance and revealing effects of weak interactions on density profiles.

Findings

Anomalous density remains higher than normal density at low temperatures.

Neglecting anomalous density can destabilize the condensate.

Weak interactions eliminate the central density dip.

Abstract

We analyze the behavior of the anomalous density as function of the radial distance at different temperatures in a variational framework. We show that the temperature dependence of the anomalous density agrees with the Hartree-Fock-Bogoliubov (HFB) calculations. Comparisons between the normal and the anomalous fractions at low temperature show that the latter remains higher and consequently the neglect of the anomalous density may destabilize the condensate. These results are compatible with those of Yukalov. Surprisingly, the study of the anomalous density in terms of the interaction parameter shows that the dip in the central density is destroyed for sufficiently weak interactions. We explain this effect.