Two-body density matrix of bose fluids

A detailed cluster analysis of the two-body density matrix $\text{n(}\text{r}{}_1\text{,}\text{r}{}_2\text{,}\text{r}\text{′}{}_1\text{,}\text{r}\text{′}{}_2\text{)}$ and the associated pairing matrix elements is performed for a strongly interacting system of bosons described by a Jastrow wave function. The study employs a multiplicative cluster procedure as suggested by Feenberg. It is demonstrated that the density matrix has a structure $\text{f(r)f(r′)n(r)n(r′)}\text{exp}\text{[?R(}\text{r}{}_1\text{,}\text{r}{}_2\text{,}\text{r}\text{′}{}_1\text{,}\text{r}\text{′}{}_2\text{)]}$ where f(r) is the conventional Jastrow factor and n(r) the one-body density matrix corresponding to the Jastrow trial state $\text{(r  |}\text{r}{}_1\text{?}\text{r}{}_2\text{|, r′  |}\text{r}\text{′}{}_1\text{?}\text{r}\text{′}{}_2\text{|)}$. The function R may be expressed by a series of irreducible cluster contributions which are given by a compact expressions in terms of spatial distribution functions. The density matrix exhibits off-diagonal long range order of the type $\text{n(}\text{r}{}_1\text{,}\text{r}{}_2\text{,}\text{r}\text{′}{}_1\text{,}\text{r}\text{′}{}_2\text{) → f(r)n(r)f(r′)n(r′)}\text{as}\text{|}\text{r}{}_1\text{?}\text{r}\text{′}{}_1\text{| → ∞,r,r′ < ∞}$. The associated pairing matrix elements and pairing energy of a Bose fluid are derived upon proper specialization of our results for the two-body density matrix.