Number--conserving model for boson pairing

TL;DR

This paper introduces a number-conserving boson pairing model using an independent pair ansatz, providing a rigorous energy bound and exact equations for pair correlations, with applications to dilute Bose systems and comparisons to Monte Carlo results.

Contribution

It develops a novel number-conserving pairing model for dilute Bose systems with exact sum rules and solvable equations, improving upon previous approaches.

Findings

Computed two-body distribution function and energy per particle.

Analyzed the connection with Bogoliubov theory at various densities.

Compared results with Diffusion Monte Carlo simulations.

Abstract

An independent pair ansatz is developed for the many body wavefunction of dilute Bose systems. The pair correlation is optimized by minimizing the expectation value of the full hamiltonian (rather than the truncated Bogoliubov one) providing a rigorous energy upper bound. In contrast with the Jastrow model, hypernetted chain theory provides closed-form exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kinetic energy sum rules satisfied exactly and the compressibility sum rule obeyed at low density. We compute, for bulk boson matter at a given density and zero temperature, (i) the two--body distribution function, (ii) the energy per particle, (iii) the sound velocity, (iv) the chemical potential, (v) the momentum distribution and its condensate fraction and (vi) the pairing function, which quantifies the ODLRO resulting from the structural properties of the two--particle density matrix. The connections with the low--density expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trapped-atoms Bose--Einstein condensates. Comparison with the available Diffusion Monte Carlo results is also made.