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The dynamic structure factor (DSF) is a mathematical function that contains information about inter-particle correlations and their time evolution. Mostly the classical molecular dynamics is used to calculate the DSF of the classical systems. On the contrary this article deals with quantum systems and the quantum dynamic structure factor. The Wigner formulation of quantum mechanics was used to derive the path integral representation of the DSF, which is based on the Wiener-Khinchin theorem showing relation of the the power spectrum of a random paths to their correlation function. The $3 {\rm D} $ quantum system of strongly correlated soft-sphere fermions was considered as an interesting physical example. The developed Wigner path integral Monte Carlo (WPIMC) approach has been developed to calculate the spin--resolved DSFs, the radial distribution functions (RDFs) and other thermodynamic functions in a wide range of density and temperatures. The physical meaning of the peaks arising on the RDFs and DSF have been analyzed and explained by the manifestation of the interference effects of the exchange and interparticle interactions and, as well as, the wave interference between multiple-scattering. This phenomenon in the system of the soft-sphere scatterers may to be the precursor effect of the Anderson localization, which finds its origin in the wave interference between multiple-scattering paths., Comment: arXiv admin note: text overlap with arXiv:2305.07601, arXiv:2306.05430

The paper discusses the problem of stability of a two-component plasma and proposes a consistent consideration of quantum and long-range effects to calculate the thermodynamic properties of such a plasma. We restrict ourselves by the case of a non-degenerate plasma to avoid the fermionic sign problem and consider the weakly coupled regime. Long-range interaction effects are taken into account using the angular-averaged Ewald potential (AAEP). To calculate thermodynamic properties, we apply both classical Monte Carlo (CMC) and path integral Monte Carlo (PIMC) methods. A special method is developed to correctly calculate potential energy in PIMC simulations with long-range interaction effects. Our theoretical estimations show that the probability of a bound state formation is very low at a coupling parameter $\Gamma~\le~0.01$, so both classical and quantum simulations give the same energy at $\Gamma~\leq~0.01$, and the thermodynamic limit coincides with the Debye--H\"uckel theory. At higher $\Gamma$, the $N$-convergence is lost due to the formation of bound states.

In this work, we consider the pressure of Coulomb systems, in which particles interact via a volume-dependent potential (in particular, the Ewald potential). We confirm that the expression for virial pressure should be corrected in this case. We show that the corrected virial pressure coincides with the formula obtained by differentiation of free energy if the potential energy is a homogeneous function of particle coordinates and a cell length. As a consequence, we find out that the expression for pressure in the recent paper by J. Liang \textit{et al.} [\href{https://doi.org/10.1063/5.0107140}{J. Chem. Phys. \textbf{157}, 144102 (2022)}] is incorrect.

Path integral Monte Carlo simulations in the Wigner approach to quantum mechanics has been applied to calculate momentum and spin--resolved radial distribution functions of the strongly correlated soft--sphere quantum fermions. The obtained spin--resolved radial distribution functions demonstrate arising triplet clusters of fermions, that is the consequence of the interference of exchange and interparticle interactions. The semiclassical analysis in the framework of the Bohr--Sommerfeld quantization condition applied to the potential of the mean force corresponding to the same--spin radial distribution functions allows to detect exchange--correlation bound states in triplet clusters and to estimate corresponding averaged energy levels. The obtained momentum distribution functions demonstrate the narrow sharp separated peaks corresponding to bound states and disturbing the Maxwellian distribution., Comment: arXiv admin note: substantial text overlap with arXiv:2305.07601

The Wigner formulation of quantum mechanics is used to derive a new path integral representation of quantum density of states. A path integral Monte Carlo approach is developed for the numerical investigation of density of states, internal energy and spin--resolved radial distribution functions for a 2D system of strongly correlated soft--sphere fermions. The peculiarities of the density of states and internal energy distributions depending on the hardness of the soft--sphere potential and particle density are investigated and explained. In particular, at high enough densities the density of states rapidly tends to a constant value, as for an ideal system of 2D fermions.

Discovery of material properties at extremes, which are essential for high energy density physics development, requires the most advanced experimental facilities, theories, and computations. Nowadays it is possible to model properties of matter in such conditions using the state-of-the-art density functional theory (DFT) or path-integral Monte--Carlo (PIMC) approaches with remarkable precision. However, fundamental and computational limitations of these methods impede their practical usage while wide-range thermodynamic and transport models of plasma are required. As a consequence, an average atom (AA) framework is still relevant today and has been attracting more and more attention lately. The self-consistent field and electron density in an atomic cell is usually obtained using the Thomas--Fermi (TF), Hartree--Fock (HF), Kohn--Sham (KS) approaches, or their extensions. In this study we present the AA model, where semiclassical wave functions are used for bound states, while free electrons are approximated by the TF model with a thermodynamically consistent energy boundary. The model is compared in various regions of temperatures and pressures with the reference data: Saha model for rarefied plasma, DFT for warm dense matter, and experimental shock Hugoniot data. It is demonstrated that a single AA model may provide a reasonable agreement with the established techniques at low computational cost and with stable convergence of the self-consistent field., Comment: 11 pages

Numerous indications suggest that subtle changes occurring in the structures of liquids on supercooling are connected to the phenomenon of the glass transition and that detailed understanding of these changes is crucial for the development of new glasses with desired properties. J.D. Bernal in his 1962 Bakerian lecture, in particular, reported about an observation of approximately linear chains of several particles, referred to as collineations. He found that in the studied hard sphere system, these collineations can contain up to eight particles. Since then, the collineations of three particles have been discussed in many papers in the context of the splitting of the second peak in pair density functions of supercooled liquids and glasses. However, it appears that longer collineations involving more that three particles have not been systematically studied. Here, we report on our study of such collineations for the Kob-Andersen system of particles on cooling for the parent and inherent structures. Contrary to intuition, our findings reveal that below the potential energy landscape crossover temperature, the number of collineations in the parent structures can exceed that of the corresponding inherent structures. We also introduce a model that connects long collineations with the pair density and angular density distribution functions and demonstrate that this model describes long collineations quite well. The second part of the paper explores potential connections between collineations and: 1) the disclination lines associated with the geometric frustration approach, 2) low-energy clusters from the topological cluster classification approach, 3) chain-like cooperative motion of particles in low-temperature supercooled liquids. For the studied system, according to the used methods, no clear connection was found between collineations and these phenomena., Comment: 25 pages, 13 figures (with supplemental materials)

In this work, we derive a correct expression for the one--component plasma (OCP) energy via the angular--averaged Ewald potential (AAEP). Unlike E.~Yakub and C.~Ronchi (J. Low Temp. Phys. 139, 633 (2005)), who had tried to obtain the same energy expression from a two--component plasma model, we used the original Ewald potential for an OCP. A constant in the AAEP was determined using the cluster expansion in the limit of weak coupling. The potential has a simple form suitable for effective numerical simulations. To demonstrate the advantages of the AAEP, we performed a number of Monte--Carlo simulations for an OCP with up to a million particles in a wide range of the coupling parameter. Our computations turned out at least two orders of magnitude more effective than those with a traditional Ewald potential. A unified approach is offered for the determination of the thermodynamic limit in the whole investigated range. Our results are in good agreement with both theoretical data for a weakly coupled OCP and previous numerical simulations. We hope that the AAEP will be useful in path integral Monte Carlo simulations of the uniform electron gas.

The density matrix for a system of particles interacting via the Coulomb potential is obtained in the high--temperature limit following almost entirely the original work by Kelbg. For this purpose the Bl\"och equation is solved in the first order of perturbation theory. We tried to explain all the transformations in the derivation in order to simplify the understanding of this non-trivial theory. The solution of Kelbg is widely used in path integral simulations of Coulomb systems.

Intense heat-mass transfer in a gas flow to a condensation surface is studied with the consistent atomistic and kinetic theory methods. The simple moment method is utilized for solving the Boltzmann kinetic equation (BKE) for the nonequilibrium gas flow and its condensation, while molecular dynamics (MD) simulation of a similar flow is used for verification of BKE results. We demonstrate that BKE can provide the steady flow profiles close to those obtained from MD simulations in both subsonic and supersonic regimes of steady gas flows. Surprisingly, the elementary theory of condensation is shown with BKE results to have a good accuracy in a wide range of gas flow parameters. MD confirms that a steady supersonic gas flow condensates on a surface at the distinctive temperature after formation of a standing shock front in reference to this surface, which can be interpreted as a permeable condensating piston. The last produces the shock compression but completely absorbs incoming gas flow in contrast to a common impermeable piston. The shock front divides the vapor flow on the supersonic and subsonic zones, and condensation of compressed gas happens in the subsonic regime. The complete and partial condensation regimes are discussed. It is shown that above the certain surface temperatures determined by the shock Hugoniot the runaway shock front stops an inflow gas and condensation is ceased., Comment: 12 pages, 14 figures

In this work we provide a step by step derivation of an angular--averaged Ewald potential suitable for numerical simulations of disordered Coulomb systems. The potential was first introduced by E.\,Yakub and C.\,Ronchi without a clear derivation. Two methods are used to find the coefficients of the series expansion of the potential: based on the Euler--Maclaurin and Poisson summation formulas. The expressions for each coefficient is represented as a finite series containing derivatives of Jacobi theta functions. We also demonstrate the formal equivalence of the Poisson and Euler--Maclaurin summation formulas in the three-dimensional case. The effectiveness of the angular--averaged Ewald potential is shown by the example of calculating the Madelung constant for a number of crystal lattices.

In this paper we continued our research of the uniform electron gas, using the single--momentum path integral Monte Carlo method, and studied the momentum distribution functions and the pair correlation functions in the warm dense matter regime. We discovered that the single--particle momentum distribution function deviates from the Fermi distribution and forms so-called "quantum tails" at high momenta, if non-ideality is strong enough in both degenerate and non-degenerate cases. This effect is always followed by the appearance of the short--range order on the pair distribution functions and can be explained via the tunneling through the effective potential wells surrounding the electrons. Also we calculated the average kinetic and potential energies in the wide range of states, expanding our previous results significantly.

We investigate the degree of local structural similarity between the parent-liquid and children-crystal states for a model soft-matter system of particles interacting through the harmonic-repulsive pair potential. At different pressures, this simple system crystallizes into several significantly different crystal structures. Therefore, the model is well suited for addressing the question under consideration. In our studies, we carefully analyze the developments of the pair and triple correlation functions for the parent-liquid as the pressure increases. In particular, these considerations allow us to address the similarities in the orientational orderings of the corresponding liquid and solid phases. It is demonstrated that the similarities in the orientational ordering between the two states extend beyond the first and second neighbors. Currently, it is widely accepted that orientational ordering is important for understanding the behaviors of liquids, supercooled liquids, and the development of detailed theories of the crystalization process. Our results suggest that, up to a certain degree, it might be possible to predict the structures of the children-solids from studies of the parent-liquids. Our results raise anew a general question of how much insight into the properties of the liquid-state can be gained from drawing a parallel with the solid-state., Comment: The pdf file includes the manuscript (the version from the 1st submission to Physica A) and two supplementary materials files. In total, there are 21 pages and 8 figures