Abstract
Path integral Monte Carlo and closure computations are utilized to study real space triplet correlations in the quantum hard-sphere system. The conditions cover from the normal fluid phase to the solid phases face-centered cubic (FCC) and cI16 (de Broglie wavelengths , densities ). The focus is on the equilateral and isosceles features of the path-integral centroid and instantaneous structures. Complementary calculations of the associated pair structures are also carried out to strengthen structural identifications and facilitate closure evaluations. The three closures employed are Kirkwood superposition, Jackson–Feenberg convolution, and their average (AV3). A large quantity of new data are reported, and conclusions are drawn regarding (i) the remarkable performance of AV3 for the centroid and instantaneous correlations, (ii) the correspondences between the fluid and FCC salient features on the coexistence line, and (iii) the most conspicuous differences between FCC and cI16 at the pair and the triplet levels at moderately high densities (. This research is expected to provide low-temperature insights useful for the future related studies of properties of real systems (e.g., helium, alkali metals, and general colloidal systems).
Highlights
The study of equilibrium triplet structures in 3D N-particle systems with quantum behavior remains a pending task in condensed matter research at low temperatures
Not much is known about the behavior of quantum triplets, the interest in undertaking this task
This is a logical step further in current statistical mechanics, allowing one to formulate thermodynamic properties beyond the pairwise approach [19], and it is central to outstanding condensed matter properties
Summary
The study of equilibrium triplet structures in 3D N-particle systems with quantum behavior remains a pending task in condensed matter research at low temperatures. Not much is known about the behavior of quantum triplets, the interest in undertaking this task This is a logical step further in current statistical mechanics, allowing one to formulate thermodynamic properties beyond the pairwise approach [19], and it is central to outstanding condensed matter properties. Among the latter, one can mention the following: phonon–phonon interactions in helium-II [4], the N-particle interpretation of fluid entropies [20,21,22], multiple scattering [23], theories of phase transitions [24,25], and glassy dynamics [26,27,28]. The whole PI quantum triplet task is computationally daunting at the present time, one can always seek to identify the main triplet features that may serve as a guide for the necessary future work on this topic
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