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Boson, fermion, and super oscillators and (statistical) mechanism of cosmological constant; finite approximation of the zeta-function and fermion factorization of the bosonic statistical sum concidered.
In this study, we have performed the first-principles investigation of the structural, electronic, magnetic, and optical properties of TbNi{sub 5}, TbNi{sub 3}Ru{sub 2}, and TbNi{sub 3}Rh{sub 2} compounds. The full-potential linearized augmented plane waves with local orbitals method is used in the framework of density functional theory (DFT) employing the generalized gradient approximation (GGA) for the exchange correlation functional as implemented in WIEN2k package. The structural properties are reposed on the evaluation of the equilibrium lattice parameters of these compounds under hexagonal structure such as lattice constants (a and c), bulk modulus (B), and its first pressure derivative (B{sup ′}). The spin-polarized electronic structures, including band structure and density of states, are calculated employing the GGA plus band correlated Hubbard parameter (GGA + U) scheme. The results show that density of states and magnetic moment of the pure TbNi{sub 5} compound are changed by doping. These changes are observed in the appearance of additional peaks on the spectral density of states (DOS) and in the augmentation of the total magnetic moment of TbNi{sub 3}X{sub 2} (X = Ru and Rh) intermetallic compounds. Based on the electronic structure results, the frequency dependents of optical conductivity are estimated in all the spectra and interpreted in the interband optical absorption part.
The optical properties of the tetragonal phase of BaTiO 3 have been studied using density functional methods, applying the generalized gradient approximation at room temperature and a hybrid functional for static lattice analysis.
We have performed the first-principles calculations to study the structural, electronic and elastic properties of RERu{sub 2} (RE = Pr and Nd) Laves phase intermetallic compounds using full-potential linearized augmented plane wave (FP-LAPW) method based on density functional theory (DFT) within the generalized gradient approximation (GGA) for exchange and correlation potential. The optimized lattices constant are in reasonable agreement with available experimental data. The electronic properties are analyzed in terms of band structures, total and partial density of states, which confirm their metallic character. The calculated elastic constants infer that these compounds are mechanically stable in C15 (MgCu{sub 2} type) structure and found to be ductile in nature.
We apply a novel phase-space interpolation technique referred to as the simplex-in-cell (SIC) method to analyze two- and three-dimensional particle-in-cell (PIC) simulations of electromagnetic plasmas. SIC relies on a discretization of the initial phase-space distribution function into simplices, which allows an approximation to the full, continuously defined distribution function to be constructed at any later time in the simulation. This allows densities, currents, and even full momentum distribution functions to be measured at any point in the simulation domain without averaging over control volumes. The SIC approach applies to any PIC simulation for which a tessellation of the initial particle distribution can be constructed. In this study, we use outputs from standard PIC simulations of the Weibel instability and compare physical quantities such as charge and current densities calculated in postprocessing using SIC and standard particle deposits. Using 2D simulations with 1–65 536 particles-per-cell, we find that SIC eliminates discrete particle noise and in some cases can reach a given noise level using ~1000 times fewer simulation particles than with standard particle deposition schemes. In regions of low density, such as between current filaments, SIC is able to capture small amplitude features even with fewer particles than gridpoints due to the deformable nature of the SIC volume elements. Here, by calculating momentum distributions, we show how SIC can capture low density tails in the spectrum using far fewer particles than are necessary for standard particle deposits. We calculate the charge density on spatial grids of increasing resolution to demonstrate the ability of SIC to reveal fine-scale details that are not accessible with standard particle deposits. Finally, we show how SIC can be extended to 3D and give an example of its use to calculate the charge density from 3D PIC simulations of the Weibel instability. These results motivate the future implementation of SIC directly in the simulation force calculation for a novel low-noise electromagnetic plasma simulation method.
The field of 2D materials has grown dramatically in the past two decades. 2D materials can be utilized for a variety of next-generation optoelectronic, spintronic, clean energy, and quantum computing applications. These 2D structures, which are often exfoliated from layered van der Waals materials, possess highly inhomogeneous electron densities and can possess short- and long-range electron correlations. The complexities of 2D materials make them challenging to study with standard mean-field electronic structure methods such as density functional theory (DFT), which relies on approximations for the unknown exchange-correlation functional. To overcome the limitations of DFT, highly accurate many-body electronic structure approaches such as diffusion Monte Carlo (DMC) can be utilized. In the past decade, DMC has been used to calculate accurate magnetic, electronic, excitonic, and topological properties in addition to accurately capturing interlayer interactions and cohesion and adsorption energetics of 2D materials. Here, this approach has been applied to 2D systems of wide interest, including graphene, phosphorene, MoS 2 , CrI 3 , VSe 2 , GaSe, GeSe, borophene, and several others. In this review article, we highlight some successful recent applications of DMC to 2D systems for improved property predictions beyond standard DFT.
The correctness of the known plane single-ended probe method for measuring the anisotropic ion distribution functions in a gas-discharge plasma has been considered. Analysis has been performed for positive probe potentials relative to the plasma with magnitudes on the order of the mean ion energy, which as a rule is much lower than the mean electron energy. We have analyzed the dependence of the collection surface area of a plane probe on its potential in this range. The structure of the near-probe layer has been determined for an isotropic electron distribution function of the Maxwellian or Druvestein type and an anisotropic ion distribution function. These results are used to derive analytic relations for the correction to the second derivative of the probe current with respect to the plane probe potential. It has been shown that, when the ion distribution function is measured in a wide range of conditions in the gas-discharge plasma, when the approximation of a collisionless probe layer is applicable, and the probe does not perturb the plasma, the dependence of the collection surface area of the probe on the potential can be disregarded in this range.
The information required to specify a liquid structure equals, in suitable units, its thermodynamic entropy. Hence, an expansion of the entropy in terms of multi-particle correlation functions can be interpreted as a hierarchy of information measures. Utilizing first principles molecular dynamics simulations, we simulate the structure of liquid aluminum to obtain its density, pair and triplet correlation functions, allowing us to approximate the experimentally measured entropy and relate the excess entropy to the information content of the correlation functions. We discuss the accuracy and convergence of the method.
A data-driven procedure for identifying the dominant transport barriers in a time-varying flow from limited quantities of Lagrangian data is presented. Our approach partitions state space into coherent pairs, which are sets of initial conditions chosen to minimize the number of trajectories that “leak” from one set to the other under the influence of a stochastic flow field during a pre-specified interval in time. In practice, this partition is computed by solving an optimization problem to obtain a pair of functions whose signs determine set membership. From prior experience with synthetic, “data rich” test problems, and conceptually related methods based on approximations of the Perron-Frobenius operator, we observe that the functions of interest typically appear to be smooth. We exploit this property by using the basis sets associated with spectral or “mesh-free” methods, and as a result, our approach has the potential to more accurately approximate these functions given a fixed amount of data. In practice, this could enable better approximations of the coherent pairs in problems with relatively limited quantities of Lagrangian data, which is usually the case with experimental geophysical data. We apply this method to three examples of increasing complexity: The first is the double gyre, the second is the Bickley Jet, and the third is data from numerically simulated drifters in the Sulu Sea.
We detail a mixed complementarity problem (MCP) formulation of continuous state dynamic programming problems (DP-MCP). We write the solution to projection methods in value function iteration (VFI) as a joint set of optimality conditions that characterize maximization of the Bellman equation; and approximation of the value function. The MCP approach replaces the iterative component of projection based VFI with a one-shot solution to a square system of complementary conditions. We provide three numerical examples to illustrate our approach.
In the context of managing distributed energy resources (DERs) within distribution networks (DNs), this work focuses on the task of developing local controllers. We propose an unsupervised learning framework to train functions that can closely approximate optimal power flow (OPF) solutions. The primary aim is to establish specific conditions under which these learned functions can collectively guide the network towards desired configurations asymptotically, leveraging an incremental control approach. The flexibility of the proposed methodology allows to integrate fairness-driven components into the cost function associated with the OPF problem. This addition seeks to mitigate power curtailment disparities among DERs, thereby promoting equitable power injections across the network. To demonstrate the effectiveness of the proposed approach, power flow simulations are conducted using the IEEE 37-bus feeder. The findings not only showcase the guaranteed system stability but also underscore its improved overall performance.
We provide a simple derivation of the constant factor in the short-distance asymptotics of the tau-function associated with the 2-point function of the two-dimensional Ising model. This factor was first computed by Tracy (Commun Math Phys 142:297–311, 1991) via an exponential series expansion of the correlation function. Further simplifications in the analysis are due to Tracy and Widom (Commun Math Phys 190:697–721, 1998) using Fredholm determinant representations of the correlation function and Wiener–Hopf approximation results for the underlying resolvent operator. Our method relies on an action integral representation of the tau-function and asymptotic results for the underlying Painlevé-III transcendent from McCoy et al. (J Math Phys 18:1058–1092, 1977).
Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wave function. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step. From this perspective, arbitrary probability distributions can be used in the projection step, allowing the user to prioritize accuracy in different regions of state space. Motivated by this theoretical perspective, the paper tests a weighted VMC method on the antiferromagnetic Heisenberg model for a periodic spin chain. Compared to traditional VMC, weighted VMC reduces the error in the ground state energy by a factor of 2, and it reduces the errors in the local energies away from the mode by large factors of 10 2 –10 4 .
In this report, we present recent development in semi-classical description of static properties of nuclei. By employing the Wigner transform, we derive simple semiclassical approximations for evaluating properties of nuclear system. We present results of calculations of static properties, using the energy density functional associated with Skyrme effective nucleon–nucleon interaction. In particular, we consider properties of the Wigner distribution function, line of beta stability, Coulomb and symmetry energies, deformation energies, equation of state, nuclear radii, and single-particle level density.
We have investigated dielectric function related optical properties such as refractive index, absorption coefficient of two-dimensional hexagonal system of aluminum antimony (AlSb). We have also find structural and electronic properties of AlSb which show direct/indirect band gap with planar structure, employing the density functional theory using the generalized gradient approximation (GGA) given by Perdew-Burke-Ernzerhof (PBE) functional for exchange-correlation potential. The refractive index n(ω) increases with frequency in the near infrared region but in visible region n(ω) increasing after decrease.
Here, we describe an iterative formalism to compute influence functionals that describe the general quantum dynamics of a subsystem beyond the assumption of linear coupling to a quadratic bath. We use a space-time tensor network representation of the influence functional and investigate its approximability in terms of its bond dimension and time-like entanglement in the tensor network description. We study two numerical models, the spin-boson model and a model of interacting hard-core bosons in a 1D harmonic trap. We find that the influence functional and the intermediates involved in its construction can be efficiently approximated by low bond dimension tensor networks in certain dynamical regimes, which allows the quantum dynamics to be accurately computed for longer times than with direct time evolution methods. However, as one iteratively integrates out the bath, the correlations in the influence functional can first increase before decreasing, indicating that the final compressibility of the influence functional is achieved via non-trivial cancellation.
Structural, optical and electronic properties and elastic constants of Cd1{sub -x-y}Zn{sub x} Hg{sub y}Te alloys have been studied by employing the commercial code Castep based on density functional theory. The generalized gradient approximation and local density approximation were utilized as exchange correlation. Using elastic constants for compounds, bulk modulus, band gap, Fermi energy and Kramers–Kronig relations, dielectric constants and the refractive index have been found through calculations. Apart from these, X-ray measurements revealed elastic constants and Vegard’s law. It is seen that results obtained from theory and experiments are all in agreement.