Use of two-body correlated basis functions with van der Waals interaction to study the shape-independent approximation for a large number of trapped interacting bosons

TL;DR

This paper investigates the ground state and excitations of a trapped Bose gas across a wide range of particle numbers using correlated two-body basis functions and van der Waals interactions, comparing results with mean-field and Monte Carlo methods.

Contribution

It introduces a comprehensive many-body analysis incorporating shape-dependent van der Waals interactions and correlations for large particle numbers, extending beyond traditional mean-field approaches.

Findings

Effect of van der Waals tail on one-body density

Finite-size effects in Bose gases

Validation of hydrodynamic model for large N

Abstract

We study the ground state and the low-lying excitations of a trapped Bose gas in an isotropic harmonic potential for very small ($\sim 3$) to very large ($\sim 10^7$) particle numbers. We use the correlated two-body basis functions and the shape-dependent van der Waals interaction in our many-body calculations. We present an exhaustive study of the effect of inter-atomic correlations and the accuracy of the mean-field equations considering a wide range of particle numbers. We calculate the ground state energy and the one-body density for different values of the van der Waals parameter $C_{6}$. We compare our results with those of the modified Gross-Pitaevskii results, the correlated Hartree hypernetted-chain equations (which also utilize the two-body correlated basis functions), as well as of the Diffusion Monte Carlo for hard sphere interactions. We observe the effect of the attractive tail of the van der Waals potential in the calculations of the one-body density over the truly repulsive zero-range potential as used in the Gross-Pitaevskii equation and discuss the finite-size effects. We also present the low-lying collective excitations which are well described by a hydrodynamic model in the large particle limit.