Orbital Variational Adiabatic Hyperspherical Method Applied to Bose-Einstein Condensates

TL;DR

This paper introduces a variational hyperspherical method for Bose-Einstein condensates that improves upon mean-field predictions by incorporating multi-orbital correlations, providing better ground state and excitation descriptions.

Contribution

It develops a multi-orbital variational approach within the adiabatic hyperspherical framework, enhancing the modeling of correlations and critical phenomena in Bose-Einstein condensates.

Findings

Single-orbital basis reproduces Gross-Pitaevskii ground state properties.

Multi-orbital basis improves correlation and collapse predictions.

Method shows deviations from Bogoliubov theory for excitation frequencies.

Abstract

A variational basis set motivated by mean-field theory is utilized to describe the Bose-Einstein condensate within the adiabatic hyperspherical coordinate framework. The simplest single-orbital variant of this treatment reproduces many of the ground state properties predicted by the Gross-Pitaevskii equation. But a multi-orbital improvement to the basis set yields a better representation of particle correlations and of the critical number where the condensate collapses for a negative two-body scattering length. The method also produces systematic deviations from Bogoliubov theory for the fundamental monopole excitation frequency.