Search Results (4)

The current developments in the theory of quantum static triplet correlations and their associated structures (real r-space and Fourier k-space) in monatomic fluids are reviewed. The main framework utilized is Feynman’s path integral formalism (PI), and the issues addressed cover quantum diffraction effects and zero-spin bosonic exchange. The structures are associated with the external weak fields that reveal their nature, and due attention is paid to the underlying pair-level structures. Without the pair, level one cannot fully grasp the triplet extensions in the hierarchical ladder of structures, as both the pair and the triplet structures are essential ingredients in the triplet response functions. Three general classes of PI structures do arise: centroid, total continuous linear response, and instantaneous. Use of functional differentiation techniques is widely made, and, as a bonus, this leads to the identification of an exact extension of the “classical isomorphism” when the centroid structures are considered. In this connection, the direct correlation functions, as borrowed from classical statistical mechanics, play a key role (either exact or approximate) in the corresponding quantum applications. Additionally, as an auxiliary framework, the traditional closure schemes for triplets are also discussed, owing to their potential usefulness for rationalizing PI triplet results. To illustrate some basic concepts, new numerical calculations (path integral Monte Carlo PIMC and closures) are reported. They are focused on the purely diffraction regime and deal with supercritical helium-3 and the quantum hard-sphere fluid. Full article

The main purpose of this paper is to derive a new perturbation theory (PT) that has converging series. Such series arise in the nonlocal scalar quantum field theory (QFT) with fractional power potential. We construct a PT for the generating functional (GF) of complete Green functions (including disconnected parts of functions) $\mathcal{Z}\left[j\right]$ as well as for the GF of connected Green functions $\mathcal{G}\left[j\right]=ln\mathcal{Z}\left[j\right]$ in powers of coupling constant g. It has infrared (IR)-finite terms. We prove that the obtained series, which has the form of a grand canonical partition function (GCPF), is dominated by a convergent series—in other words, has majorant, which allows for expansion beyond the weak coupling g limit. Vacuum energy density in second order in g is calculated and researched for different types of Gaussian part $S_0\left[\varphi \right]$ of the action $S\left[\varphi \right]$. Further in the paper, using the polynomial expansion, the general calculable series for $\mathcal{G}\left[j\right]$ is derived. We provide, compare and research simplifications in cases of second-degree polynomial and hard-sphere gas (HSG) approximations. The developed formalism allows us to research the physical properties of the considered system across the entire range of coupling constant g, in particular, the vacuum energy density. Full article

We present computer simulation and theoretical results for a system of N Quantum Hard Spheres (QHS) particles of diameter $\sigma$ and mass m at temperature T, confined between parallel hard walls separated by a distance $H\sigma$, within the range $1\le H\le \infty$. Semiclassical Monte Carlo computer simulations were performed adapted to a confined space, considering effects in terms of the density of particles ${\rho }^{*}=N/V$, where V is the accessible volume, the inverse length $H^{-1}$ and the de Broglie’s thermal wavelength ${\lambda }_B=h/\sqrt{2\pi mkT}$, where k and h are the Boltzmann’s and Planck’s constants, respectively. For the case of extreme and maximum confinement, $0.5<H^{-1}<1$ and $H^{-1}=1$, respectively, analytical results can be given based on an extension for quantum systems of the Helmholtz free energies for the corresponding classical systems. Full article

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 $0.2\le {\lambda }_B^{*}<2$, densities $0.1\le {\rho }_N^{*}\le 0.925$). 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 (${\rho }_N^{*}=0.9, 0.925)$. 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). Full article