Bose-Einstein Condensation of Atoms in a Trap

TL;DR

This paper discusses the local density approximation's validity in describing Bose-Einstein condensates in traps, providing a quantitative result for positive scattering lengths and critiquing the many-body physics interpretation.

Contribution

It clarifies the application of the local density approximation to Bose-Einstein condensation and offers a testable quantitative prediction for positive scattering lengths.

Findings

LDA is valid when b5 = b5b5b5 <<1

Provides a quantitative result (14') for positive scattering length cases

Critiques the physics of the many-body problem in terms of scattering length a

Abstract

We point out that the local density approximation (LDA) of Oliva is an adaptation of the Thomas-Fermi method, and is a good approximation when $\varepsilon = \hbar\omega/kT <<1$. For the case of scattering length $a > 0$, the LDA leads to a quantitative result (14') easily checked by experiments. Critical remarks are made about the physics of the many body problem in terms of the scattering length $a$.