Correlations in many-body systems with the Stochastic Variational Method

TL;DR

This paper uses an ab-initio correlated Gaussian approach to analyze few-body correlations in dilute Bose-Einstein condensates, providing insights into the importance of two-body correlations across different interaction regimes.

Contribution

It introduces a computational method that explicitly includes few-body correlations with complexity independent of particle number, applicable to many-body systems.

Findings

Two-body correlations dominate in weakly interacting regimes.

Higher-order correlations are significant in small systems.

Ground state energy varies with scattering length and correlation inclusion.

Abstract

Few-body correlations often express the distinguishing characteristic features of a many-body system. This thesis studies such correlations within dilute Bose-Einstein condensates in the case of arbitrary negative s-wave scattering length. The N-boson problem is solved by using an ab-initio approach based on correlated Gaussians that allows explicit inclusion of few-body correlations with a computational complexity that is independent of the number of particles. Calculations introducing all higher-order correlations are also done for small systems. In the weakly interacting regime, two-body correlations are not only the simplest but also the most important. By varying the scattering length and comparing the ground state energy for different explicitly correlated trial wave functions this assumption is investigated under both weakly and strongly interacting conditions.