Computational study of the structures of gaseous helium-3 at low temperature

A Glimpse into Quantum Triplet Structures in Supercritical 3He

A methodological study of triplet structures in quantum matter is presented. The focus is on helium-3 under supercritical conditions (4 < T/K < 9; 0.022 < ρN/Å-3 < 0.028), for which strong quantum diffraction effects dominate the behavior. Computational results for the triplet instantaneous structures are reported. Path integral Monte Carlo (PIMC) and several closures are utilized to obtain structure information in the real and the Fourier spaces. PIMC involves the fourth-order propagator and the SAPT2 pair interaction potential. The main triplet closures are: AV3, built as the average of the Kirkwood superposition and the Jackson-Feenberg convolution, and the Barrat-Hansen-Pastore variational approach. The results illustrate the main characteristics of the procedures employed by concentrating on the salient equilateral and isosceles features of the computed structures. Finally, the valuable interpretive role of closures in the triplet context is highlighted.

Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres

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).

Computation of static quantum triplet structure factors of liquid para-hydrogen

The instantaneous and centroid triplet structure factors, S ( 3 ) ( k 1 , k 2 ) , 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.

On static triplet structures in fluids with quantum behavior

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.

Path-integral and Ornstein-Zernike study of quantum fluid structures on the crystallization line

Liquid neon, liquid para-hydrogen, and the quantum hard-sphere fluid are studied with path integral Monte Carlo simulations and the Ornstein-Zernike pair equation on their respective crystallization lines. The results cover the whole sets of structures in the r-space and the k-space and, for completeness, the internal energies, pressures and isothermal compressibilities. Comparison with experiment is made wherever possible, and the possibilities of establishing k-space criteria for quantum crystallization based on the path-integral centroids are discussed. In this regard, the results show that the centroid structure factor contains two significant parameters related to its main peak features (amplitude and shape) that can be useful to characterize freezing.

A study of the pair and triplet structures of the quantum hard-sphere Yukawa fluid

The pair and triplet structures of the quantum hard-sphere Yukawa fluid, evaluated for equilateral and isosceles correlations in both the r and the k spaces for a range of conditions and with a particular focus on a region where the onset of increasing number fluctuations takes place (for densities 0.4<or=rho(N) ( *)<or=0.5, along the isotherm lambda(B) ( *)=0.6), are computed via path-integral Monte Carlo simulations in the canonical ensemble and an appropriate Ornstein-Zernike framework. For a given type of correlation (instantaneous, continuous linear response, and centroids), the structural results in r space display how the correlation functions approach each other with decreasing densities as a result of the increasing fluctuations. An attempt at obtaining improved isothermal compressibilities by using a simplified grand-canonical correction to the canonical pair radial functions is also discussed in detail. The results for triplets in k space are based on triplet direct correlation function calculations and are restricted to the higher-density region of the interval studied. Complementary results report an assessment of the performances of the Kirkwood superposition and the Jackson-Feenberg convolution. Comparisons with results also obtained in this work for the bare quantum and the classical hard-sphere fluids are made, allowing one to draw conclusions on the interplay between the inclusion of Yukawa attractions and the quantum diffraction effects in hard-sphere fluids.