Energy and Structure of Hard-Sphere Bose Gases in three and two dimensions

TL;DR

This paper investigates the energy and structural properties of dilute hard-sphere Bose gases in two and three dimensions using a variational Hypernetted Chain approach, revealing correlation effects and asymptotic behaviors.

Contribution

It introduces a variational HNC method with optimized Jastrow wavefunctions to analyze static properties of Bose gases across dimensions and interaction strengths.

Findings

Identification of a maximum in radial distribution and momentum distribution functions with increasing gas parameter

Analysis of asymptotic behavior of structural functions in dilute Bose gases

Comparison of 2D and 3D systems in terms of correlation effects

Abstract

The energy and structure of dilute gases of hard spheres in three dimensions is discussed, together with some aspects of the corresponding 2D systems. A variational approach in the framework of the Hypernetted Chain Equations (HNC) is used starting from a Jastrow wavefunction that is optimized to produce the best two--body correlation factor with the appropriate long range. Relevant quantities describing static properties of the system are studied as a function of the gas parameter $x=\rho a^d$ where $\rho$, $a$ and $d$ are the density, $s$--wave scattering length of the potential and dimensionality of the space, respectively. The occurrence of a maximum in the radial distribution function and in the momentum distribution is a natural effect of the correlations when $x$ increases. Some aspects of the asymptotic behavior of the functions characterizing the structure of the systems are also investigated.