Thomas Fermi approximation and large-$N$ quantum mechanics

TL;DR

This paper unifies the Thomas Fermi approximation with the large-$N$ quantum mechanics limit to improve the modeling of Bose-Einstein condensates in harmonic traps.

Contribution

It introduces a modified Thomas Fermi approximation by combining insights from the Thomas Fermi limit and large-$N$ quantum mechanics, enhancing accuracy.

Findings

Accurately predicts condensate energy in harmonic traps.

Demonstrates the effectiveness of the combined approximation.

Provides a new perspective on large-$N$ quantum systems.

Abstract

We note that the Thomas Fermi limit of Gross Pitaevskii equation and $N>>1$ limit of quantum mechanics, where $N$ is the dimensionality of space, are based on the same point of view. We combine these two to produce a modified Thomas Fermi approximation which gives a very good account of the energy of the condensate in harmonic trap.