Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas

TL;DR

This paper develops a refined theoretical model for a trapped Bose-Einstein condensate, accounting for boundary layer effects and providing more accurate predictions of energy and excitation frequencies beyond the Thomas-Fermi approximation.

Contribution

It introduces boundary layer corrections and extends the hydrodynamic density-fluctuation amplitudes for a more precise description of the condensate.

Findings

Corrections to energy are of order R^{-4}ln R and R^{-4}.

First-order correction to excitation frequencies is of order R^{-4}.

Provides a uniform description of the condensate including the boundary layer.

Abstract

Corrections to the zero-temperature Thomas-Fermi description of a dilute interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap arise due to the presence of a boundary layer near the condensate surface. Within the Bogoliubov approximation, the various contributions to the ground-state condensate energy all have terms of order R^{-4}ln R and R^{-4}, where R is the number-dependent dimensionless condensate radius in units of the oscillator length. The zero-order hydrodynamic density-fluctuation amplitudes are extended beyond the Thomas-Fermi radius through the boundary layer to provide a uniform description throughout all space. The first-order correction to the excitation frequencies is shown to be of order R^{-4}.