We study a variational multiparticle correlation theory for the ground state of inhomogeneous Bose fluids at zerotemperature. The ground state wave function of a many-boson system is written as a generalized Jastrow–Feenberg function including multiparticle correlation functions. Euler–Lagrange equations for the one, two, three and four particle correlation functions are derived using a systematic functional theoretical approach within the framework of the generalized hypernetted chain theory (HNC2 equations). The Euler–Lagrange equations for the optimal one and two particle correlation functions are analyzed including the infinite series of the elementary diagrams summed by integral equations. For the determination of the optimal triplet correlation factor we propose a novel iterative procedure in which the HNC2 equation is used to calculate the triplet distribution function.
We investigate the thermodynamic ground state of binary boson mixtures using a variational ansatz. With a pair-independent trial function we map the isotopic boson mixture onto a quantum theorem of corresponding-states picture which enables us to conclude that all such isotopic boson mixtures completely phase-separate at zero temperature. We also investigate mixtures of spin-aligned hydrogen (H\ensuremath{\uparrow}) and spin-aligned tritium (T\ensuremath{\uparrow}) with
4He. We find that these systems also prefer to completely phase-separate. However, due to important differences in the sizes of "cores" of the interaction, allowance must be made for different correlations between different types of pairs. We then find that at zero pressure the zero-concentration chemical potential for H\ensuremath{\uparrow} in
4He is 40 K and for T\ensuremath{\uparrow} in
4He it is 0.5 K.
A system of fermions or bosons interacting in one dimension via a two-body potential of the form
V(r)=r2g is known to have a ground state of Jastrow type. The boson system is explored in this paper within the hypernetted-chain scheme to study the various ground-state properties, and the results are compared with the exact results available for this system. The results are expected to have important bearing on spin correlations in the Gutzwiller state.
The variational density-matrix approach introduced by Campbell, K\"urten, Ristig, and Senger [Phys. Rev. B 30, 3728 (1984)], to study finite-temperature Bose fluids is reformulated to avoid dealing directly with the entropy of the trial density matrix. We obtain exact expressions for the Euler-Lagrange equations for a finite-temperature trial statistical density matrix, which is the simplest finite-temperature generalization of a Jastrow trial ground-state wave function. A multicomponent hypernetted-chain method is developed to solve approximately these Euler-Lagrange equations at low temperatures. In leading order the results are shown to be equivalent to those obtained by Campbell et al. The current formalism provides a scheme to improve results of the previous approach.
The ground state of a many-boson system is studied within the range of the Bijl-Dingle-Jastrow-type description when the radial distribution function
g(r) differs little from its asymptotic value. The treatment of the problem is based on the development of power series in $\ensuremath{\alpha}=1\ensuremath{-}g(0)$ for all physical quantities which depend on the particle density. The
n-particle distribution functions
p(n) are evaluated to order ${\ensuremath{\alpha}}^{4}$ as functionals in the
g(r) function for
n=3and4 using the cluster-expansion procedure outlined by Abe. These results are used in connection with the improvement of the ground-state description when the wave function is not the optimum choice. Using
p(3) function obtained, the Bogoliubov-Born-Green-Kirkwood-Yvon equation is solved, also to order ${\ensuremath{\alpha}}^{4}$, for the two-particle correlation function
U(r), and the first two leading corrections to the hypernetted-chain (HNC) approximation are obtained. The variational calculation along with the series expansion for
U(r) yields formulas for the ground-state properties, including some corrections to known results. For a charged boson gas, numerical values of
U(r),
p(3),
p(4), and the ground-state energy are computed using the Gaussian approximation for
g(r), and the results show that the errors associated with the HNC approximation are small. A brief discussion is presented on the method of determining the general expansion coefficients of the correlation functions of
p(n) in terms of
g(r).
The energy and structure of a dilute hard-disks Bose gas are studied in the framework of a variational many-body approach based on a Jastrow correlated ground-state wave function. The asymptotic behaviors of the radial distribution function and the one-body density matrix are analyzed after solving the Euler equation obtained by a free minimization of the hypernetted chain energy functional. Our results show important deviations from those of the available low density expansions, already at gas parameter values $x\ensuremath{\sim}0.001$. The condensate fraction in 2D is also computed and found generally lower than the 3D one at the same
x.