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

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).

The Solid Phase of 4He: A Monte Carlo Simulation Study

“…In that case, three-body terms are included as separate contributions, and this is the spirit in which the original Aziz potential has been subsequently refined and other versions proposed. The result has been typically that of slightly worsening the agreement between theory and experiment, which would then be improved by the explicit inclusion of three-body terms [ 41 , 42 ]. As mentioned above, however, no systematic comparison has been carried out of different versions of the Aziz pair potential when it comes to reproducing the physical properties of the solid phase of helium at low pressure, where the effect of three-body interactions is expected to be small.…”

Density of states of a 2D system of soft-sphere fermions by path integral Monte Carlo simulations

“…DOS is a fundamental function of a system and can be defined as Ω(E) = Tr{δ(E Î − Ĥ)} [35]. Ω(E)d E determines the number of states between E and E + d E per unit volume [36] ( Î is the unit operator, while δ is the delta function). The DOS can be used to compute important thermodynamic properties such as, for example, internal energy, entropy and heat capacity.…”

Statistical Mechanics and Thermodynamics of Liquids and Crystals

“…Yet, triplet correlations convey crucial information for any statistical analysis aiming to go beyond the traditional pairwise approximation. Reference [28] investigates triplet correlations in a fluid of quantum hard spheres, as well as in two crystalline phases of the same system. Using path-integral Monte Carlo simulations, the author of [28] delves into the accuracy of a few closure relations expressing the triplet distribution function in terms of two-body terms, eventually identifying a combination of closures that performs well in rather disparate conditions.…”