LONG-RANGE ORDER IN BOSE FLUIDS

We are interested in the evaluation of the one- and two-body density matrices for extended boson matter. A trial function Ψ = Πi<jA{cauchy integral}(r of Bijl-Dingle-Jastrow form provides a reasonable first approximation to the ground state wave function of A bosons. The corresponding one-body density matrix has a structure n(r) = ρnc exp [-Q(r)] in the thermodynamic limit and shows off-diagonal long range order, n(r)→-ρnc > 0 as r→ ∞. The condensate fraction is given by nc = exp Q(0). A similar structure is found for the two-body density matrix, n(r1,r2,r'1,r'2) = χ(r)χ(r') exp[-R (r1, r2, r'1,r'2)] where r ≡ |r1 - r2|, r' ≡ |r'1 - r'2|. The behavior over macroscopic distances is characterized by off-diagonal long range order of pairing type, n(r1, r2, r'1, r'2) → χ(r)χ(r') as |r1 - r'1| → ∞ while r, r' < ∞, in close analogy to the pairing phenomenon in Fermi superfluids. The pairing function χ(r) is related to the one-body density matrix by χ(r) = {cauchy integral}(r)n(r). The basic quantities Q(r) and Q(0) are analysed (i) in terms of a standard factor cluster expansion, (ii) in terms of a highly summed cluster expansion in the compact portions of the successive distribution functions g(r12), g3(r1, r2, r3), ..., (iii) within the hypernetted chain (HNC) framework. The HNC equations for Q(r) are solved analytically for uniform Bose fluids described by |g(r) - 1| {less-than or approximate} K ≪ 1. We find in the uniform limit Q(r) = -(2π)-3(4ρ)-1 ∫ [S(k) - 1]2S-1(k) exp (ik · r)dk where S(k) is the liquid structure function. The HNC formalism for quantities Q(r) and Q(0) is employed in a numerical study of the long-range order in (i) the charged boson system, (ii) a model of neutron matter, (iii) liquid 4He. © 1979.