Abstract
The problem of the equilibrium triplet structures in fluids with quantum behavior is discussed. Theoretical questions of interest to the real space structures are addressed by studying the three types of structures that can be determined via path integrals (instantaneous, centroid, and total thermalized-continuous linear response). The cases of liquid para-H2 and liquid neon on their crystallization lines are examined with path-integral Monte Carlo simulations, the focus being on the instantaneous and the centroid triplet functions (equilateral and isosceles configurations). To analyze the results further, two standard closures, Kirkwood superposition and Jackson-Feenberg convolution, are utilized. In addition, some pilot calculations with path integrals and closures of the instantaneous triplet structure factor of liquid para-H2 are also carried out for the equilateral components. Triplet structural regularities connected to the pair radial structures are identified, a remarkable usefulness of the closures employed is observed (e.g., triplet spatial functions for medium-long distances, triplet structure factors for medium k wave numbers), and physical insight into the role of pair correlations near quantum crystallization is gained.
Highlights
The study of triplets has received a great deal of attention from the classical point of view, there is a dearth of information on the quantum fluid side of this topic
Note that for homogeneous and isotropic monatomic fluids, structural triplet functions depend on three independent variables: (i) g3(r1,r2,r3) = g3(r12,r13,r23) = g3(r13,r23,cos θ13,23); (ii) c3(r1,r2,r3) = c3(r12,r13,r23) = c3(r13,r23,cos θ13,23); and (iii) in general S(3)(k1,k2) = S(3)(k1,k2,cos θ12). [Interatomic distances are denoted by rij = ri − rj, and the angles θ are defined by the pairs of vectors (r13,r23) and (k1,k2), respectively.] Apart from the complexity inherent in 4D calculations, another difficulty is the visualization of results
It is interesting to note that the gCM 3–p1 values diminish in a very slow fashion as the temperature and density increase, whereas for v1 and p2, the gCM 3 values remain far more stable showing slight oscillations. This contrasts sharply with the analogous PIMC instantaneous gET 3(r,r,r) features, which show steady trends that are noticeable for the three features upon increasing (T,ρN ): there is a rise in the p1 and p2 heights and a decrease in the v1 depth
Summary
Triplet structures play a crucial role in the statistical mechanics of fluids despite the fact that they cannot be determined in 3D many-body systems via radiation scattering experiments (their contribution to the total differential cross section is negligible). This is the most challenging since triplet structures serve to formulate the first step beyond the usual pair theories, and their usefulness for recent condensed matter studies may become essential (e.g., glassforming liquids). the study of triplets has received a great deal of attention from the classical point of view, there is a dearth of information on the quantum fluid side of this topic. Homogeneous and isotropic fluids, monatomic or describable by a monatomic model, will be considered in this article.triplet structures in general are needed to understand a number of condensed matter problems. Triplet structures play a crucial role in the statistical mechanics of fluids despite the fact that they cannot be determined in 3D many-body systems via radiation scattering experiments (their contribution to the total differential cross section is negligible).. Triplet structures play a crucial role in the statistical mechanics of fluids despite the fact that they cannot be determined in 3D many-body systems via radiation scattering experiments (their contribution to the total differential cross section is negligible).1,2 This is the most challenging since triplet structures serve to formulate the first step beyond the usual pair theories, and their usefulness for recent condensed matter studies may become essential (e.g., glassforming liquids).. Note that for homogeneous and isotropic monatomic fluids, structural triplet functions depend on three independent variables: (i) g3(r1,r2,r3) = g3(r12,r13,r23) = g3(r13,r23,cos θ13,23); (ii) c3(r1,r2,r3) = c3(r12,r13,r23) = c3(r13,r23,cos θ13,23); and (iii) in general S(3)(k1,k2) = S(3)(k1,k2,cos θ12).
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