Anomalous Effects in a Trapped Bose-Einstein Condensate

TL;DR

This paper investigates the anomalous density in trapped Bose-Einstein condensates across different dimensions, revealing divergence behaviors and proposing a reliable renormalization method within a variational framework.

Contribution

It introduces a variational approach to analyze anomalous densities in Bose gases, providing insights into divergence patterns and a compatible renormalization scheme.

Findings

Anomalous density is finite in 1D.

Logarithmic divergence in 2D.

Linear divergence in 3D.

Abstract

We study the anomalous density in an ultra-cold trapped bose gas in a variational framework, for both zero and finite temperature. We show that it is finite in 1D, while it is logarithmically and linearly divergent in 2D and 3D. The renormalization that we adopt is more reliable and compatible with the variational scheme. The main outcome is that the anomalous and non condensate densities are of the