Numberconserving model for boson pairing
Abstract
An independentpair ansatz is developed for the manybody wave function 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 closedform exactly solvable equations for the optimized pair correlation. The model involves both condensate and coherent pairing with number conservation and kineticenergy 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 twobody 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 offdiagonal longrange order resulting from the structural properties of the twoparticle density matrix. The connections with the lowdensity expansion and Bogoliubov theory are analyzed at different density values, including the density and scattering length regime of interest of trappedatom BoseEinstein condensates. Comparison with the available diffusion Monte Carlo results is also made.
 Publication:

Physical Review A
 Pub Date:
 September 2002
 DOI:
 10.1103/PhysRevA.66.033604
 arXiv:
 arXiv:condmat/0205282
 Bibcode:
 2002PhRvA..66c3604F
 Keywords:

 03.75.Fi;
 05.30.Jp;
 67.40.Db;
 Boson systems;
 Quantum statistical theory;
 ground state elementary excitations;
 Condensed Matter
 EPrint:
 21 pages, 12 figures