Abstract
The instantaneous and centroid triplet structure factors, , of liquid (one-center) para-hydrogen are computed on the crystallization line for temperatures T/K ≤ 33. The focus is on salient equilateral and isosceles features, and the methods utilized are path integral Monte Carlo (PIMC) simulations and Ornstein-Zernike (OZ) integral equations, which involve Jackson-Feenberg convolution (JF3) and other distinct closures. Long path integral simulation runs are carried out in the canonical ensemble, so as to obtain sufficiently accurate direct PI triplet results. Conclusions are drawn regarding general triplet structure features and the role and usefulness of the OZ closures. The equilateral features are studied in more detail, and one finds that (a) PIMC results point to the existence of regularity in the centroid main peak amplitudes; (b) some of the studied closures give qualitative descriptions for wave numbers below k ≈ 1 Å-1, but they all fail to describe the main peak amplitude regions (1.75 < k/Å-1 < 2.5); and (c) JF3 plays the role of a limit closure that is valid for increasing wave numbers (k ≥ 2.6 Å-1). In addition, representative isosceles PI features turn out to be reasonably bounded (within Δk = 0.1 Å-1) by those of some closures.
Highlights
The study of static triplet structures in 3D homogeneous and isotropic fluids is a key issue in statistical mechanics.1–6 Its interest is formal, owing to the hierarchical character of the structural functions,5–8 and practical in that triplet structures are needed to achieve a more complete understanding of condensed matter problems.14–19 In this regard, note that there is no known direct determination of the related triplet structures via radiation scattering experiments because of their very small contribution to the total differential cross section.20–23 this sort of study in both the real space (r-space) and the Fourier k-space (k-space) must be via computer simulations, Monte Carlo (MC), and molecular dynamics (MD) or via theoretical approaches.PI provides the most accurate framework for carrying out quantum triplet computations
The instantaneous and centroid triplet structure factors, S(3)(k1, k2), of liquid parahydrogen are computed on the crystallization line for temperatures T /K ≤ 33
The equilateral features are studied in more detail, and one finds that (a) path integral Monte Carlo (PIMC) results point to the existence of regularity in the centroid main peak amplitudes; (b) some of the studied closures give qualitative descriptions for wave numbers below k ≈ 1 Å−1, but they all fail to describe the main peak amplitude regions (1.75 < k/Å−1 < 2.5); and (c) JF3 plays the role of a limit closure that is valid for increasing wave numbers (k ≥ 2.6 Å−1)
Summary
The study of static triplet structures in 3D homogeneous and isotropic fluids is a key issue in statistical mechanics. Its interest is formal, owing to the hierarchical character of the structural functions, and practical in that triplet structures are needed to achieve a more complete understanding of condensed matter problems (e.g., elementary excitations in quantum fluids, freezing, fluid mixtures, and glassforming liquids). In this regard, note that there is no known direct determination of the related triplet structures via radiation scattering experiments because of their very small contribution to the total differential cross section. this sort of study in both the real space (r-space) and the Fourier k-space (k-space) must be via computer simulations, Monte Carlo (MC), and molecular dynamics (MD) or via theoretical approaches. Its interest is formal, owing to the hierarchical character of the structural functions, and practical in that triplet structures are needed to achieve a more complete understanding of condensed matter problems (e.g., elementary excitations in quantum fluids, freezing, fluid mixtures, and glassforming liquids).14–19 In this regard, note that there is no known direct determination of the related triplet structures via radiation scattering experiments because of their very small contribution to the total differential cross section.. A wide range of general computer simulation techniques, namely, path integral Monte Carlo (PIMC) and path integral molecular dynamics (PIMD), are available to study quantum fluids at equilibrium.27,30,31,34–37 These PI techniques are regarded as “exact” in that they produce results with controllable errors.
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