Ground-state properties of bosons in three- and two-dimensional traps

TL;DR

This paper investigates the ground-state properties of bosons in 2D and 3D traps using series expansions and Padé approximants within the Gross-Pitaevskii framework, providing analytical estimates for energy and chemical potential.

Contribution

It introduces a method to derive analytical estimates of ground-state properties of trapped bosons using series expansions and Padé approximants in the Gross-Pitaevskii regime.

Findings

Derived series expansions for ground-state energy and chemical potential.

Presented explicit Padé approximants for key properties.

Validated the applicability of the approach in both noninteracting and strong-coupling limits.

Abstract

We study trapped systems of bosons at zero temperature in three and two dimensions. Conditions are fulfilled for the application of Gross-Pitaevskii theory with a positive scattering length. Series expansions for ground-state properties are obtained in both the noninteracting and the strong-coupling (Thomas-Fermi) limits. From these expansions, analytic estimates are presented in the form of two-point Pad\'e approximants. We explicitly show the approximants for the total energy per particle and the chemical potential.