Elementary Excitations in a BEC with Isotropic Harmonic Trap: Bogoliubov Equations versus Hydrodynamic Formalism

TL;DR

This paper compares Bogoliubov equations and hydrodynamic formalism to analyze elementary excitations in a trapped BEC, revealing how scattering length and trap influence excitation frequencies and angular momentum information.

Contribution

It introduces a parameter that explains the influence of scattering length and trap on excitation frequencies beyond the Thomas-Fermi approximation.

Findings

Outside the Thomas-Fermi regime, excitation frequencies do not encode angular momentum.

The comparison clarifies the validity range of hydrodynamic versus Bogoliubov approaches.

A new parameter links scattering length, trap, and excitation characteristics.

Abstract

The elementary excitations for a BEC trapped by means of an isotropic harmonic oscillator are studied in the present work. The analysis of these perturbations is done in the context of the Bogoliubov equations and not resorting to the hydrodynamic version. The comparison between these two approaches will allow us to deduce a parameter explaining the role that the scattering length and the trap play in the way in which the frequency of these elementary excitations acquires information about the angular momentum of the corresponding solutions. It will be shown that outside the validity realm of the Thomas_fermi approximation the frequencies of the perturbations cannot inherit the information of the angular momentum codified in the functions escribing the elementary excitations.