Perturbation Theory Method Research Articles

Relativistic Configuration-Interaction and Perturbation Theory Calculations for Heavy Atoms

Heavy atoms present challenges to atomic theory calculations due to the large number of electrons and their complicated interactions. Conventional approaches such as calculations based on Cowan’s code are limited and require a large number of parameters for energy agreement. One promising approach is relativistic configuration-interaction and many-body perturbation theory (CI-MBPT) methods. We present CI-MBPT results for various atomic systems where this approach can lead to reasonable agreement: La I, La II, Th I, Th II, U I, Pu II. Among atomic properties, energies, g-factors, electric dipole moments, lifetimes, hyperfine structure constants, and isotopic shifts are discussed. While in La I and La II accuracy for transitions is better than that obtained with other methods, more work is needed for actinides.

Simulation of the Charge Carriers Distribution in the Active Region of the P-I-N-Diodes by the Perturbation Theory Methods

A mathematical model of the electron-hole plasma stationary distribution in the active region (i-region) of p-i-n-diodes in the dif-fusion-drift approximation is proposed. The model is represented in the form of a nonlinear singularly perturbed boundary value prob-lem for the system of equations of the electron-hole currents conti-nuity, the Poisson equation and the corresponding boundary condi-tions. The decomposition of the nonlinear boundary value problem of modeling the stationary distribution of charge carriers in the plasma of p-i-n-diodes is carried out on the basis of the solutions asymptotic representation. The model problem is reduced to a se-quence of the linear boundary value problems with a characteristic separation of the main (regular) components of the asymptotics and a boundary corrections. It was found that the formulation of the problem for finding the zero term of the asymptotics regular part coincides with the classical formulation of the p-i-n-diodes charac-teristics modeling problem, which is carried out in the approxima-tion of the ambipolar diffusion (approximation of a self-consistent electrostatic field).The proposed mathematical model and the method of its linearization make it possible to determing the main components in the diffusion-drift process and to study their role. For example, it becomes possible to study (including by analytical methods) the behavior of plasma in the p-i-, n-i-contacts zones. The results of the study are aimed at developing methods for de-signing p-i-n-diode structures, used, in particular, as active ele-ments of the signals switches of a microwave data transmission systems and the corresponding protective devices.

Accurate energies of transition metal atoms, ions, and monoxides using selected configuration interaction and density-based basis-set corrections.

The semistochastic heat-bath configuration interaction method is a selected configuration interaction plus perturbation theory method that has provided near-full configuration interaction (FCI) levels of accuracy for many systems with both single- and multi-reference character. However, obtaining accurate energies in the complete basis-set limit is hindered by the slow convergence of the FCI energy with respect to basis size. Here, we show that the recently developed basis-set correction method based on range-separated density functional theory can be used to significantly speed up basis-set convergence in SHCI calculations. In particular, we study two such schemes that differ in the functional used and apply them to transition metal atoms and monoxides to obtain total, ionization, and dissociation energies well converged to the complete-basis-set limit within chemical accuracy.

New relativistic and nonrelativistic model of diatomic molecules and fermionic particles interacting with improved modified Mobius potential in the framework of noncommutative quantum mechanics symmetries

In this study, the deformed Klein–Gordon equation, Dirac equation, and Schrödinger equations were solved with the improved the modified Mobius square potential model (IMSPM, in short) using Bopp’s shift and standard perturbation theory methods in the symmetries of extended quantum mechanics. By employing the improved approximation to the centrifugal term, the relativistic and nonrelativistic bound state energies were obtained for some selected diatomic molecules (H2, I2, CO, NO, and HCl). The relativistic shift energy ΔEmsptot(n,α,A,B,V0,Θ,σ,χ,j,l,s,m) and the perturbative nonrelativistic corrections ΔEmspnr(n,α,A,B,V0,Θ,σ,χ,j,l,s,m) appeared as a function of the parameters (α,A,B,V0), the parameters of noncommutativity (Θ,σ,χ), in addition to the atomic quantum numbers (n,j,l,s,m). In both relativistic and nonrelativistic problems, we show that the corrections on the spectrum energy are smaller than the main energy in the ordinary cases of RQM and NRQM. A straightforward limit of our results to ordinary quantum mechanics shows that the present result under the improved modified Mobius square potential model is consistent with what is obtained in the literature. In the new symmetries of NCQM, is not possible to get the exact analytical solutions for l=0 and l≠0 can only be solved approximately. Through this research, we came to two noteworthy results, the first is related to the deformed Klein-Gordon equation under the influence of the improved modified Mobius square potential model becomes equivalent to the Duffin-Kemmer equation for a meson with spin-s, while the second result concerns the deformed Schrödinger equation, which can now describe the state of high-energy fermionic particles similar to the Dirac equation in the literature.

Ab initio calculations of the spectrum of lawrencium

Planned optical spectroscopy experiments in lawrencium (Lr, Z = 103) require accurate theoretical predictions of the location of spectral lines in order to narrow the experimental search window. We present ab initio calculations of the atomic energy levels, transition amplitudes and g-factors for lawrencium, as well as its lighter homologue lutetium (Lu, Z = 71). We use the configuration interaction with many-body perturbation-theory (CI+MBPT) method to calculate energy levels and transition properties, and benchmark the accuracy of our predicted energies using relativistic coupled-cluster codes. Our results are numerically converged and in close agreement with experimentally measured energy levels for Lu, and we expect a similar accuracy for Lr. These systematic calculations have identified multiple transitions of experimental utility and will serve to guide future experimental studies of Lr.

Constructing and analyzing mathematical model of plasma characteristics in the active region of integrated p-i-n-structures by the methods of perturbation theory and conformal mappings

The results of mathematical modeling of stationary physical processes in the electron-hole plasma of the active region (i-region) of integral p-i-n-structures are presented. The mathematical model is written in the framework of the hydrodynamic thermal approximation, taking into account the phenomenological data on the effect on the dynamic characteristics of charge carriers of heating of the electron-hole plasma as a result of the release of Joule heat in the volume of the i-th region and the release of recombination energy. The model is based on a nonlinear boundary value problem on a given spatial domain with curvilinear sections of the boundary for the system of equations for the continuity of the current of charge carriers, Poisson, and thermal conductivity. The statement of the problem contains a naturally formed small parameter, which made it possible to use asymptotic methods for its analytical-numerical solution. A model nonlinear boundary value problem with a small parameter is reduced to a sequence of linear boundary value problems by the methods of perturbation theory, and the physical domain of the problem with curvilinear sections of the boundary is reduced to the canonical form by the method of conformal mappings. Stationary distributions of charge carrier concentrations and the corresponding temperature field in the active region of p-i-n-structures are obtained in the form of asymptotic series in powers of a small parameter. The process of refining solutions is iterative, with the alternate fixation of unknown tasks at different stages of the iterative process. The asymptotic series describing the behavior of the plasma concentration and potential in the region under study, in contrast to the classical ones, contain boundary layer corrections. It was found that boundary functions play a key role in describing the electrostatic plasma field. The proposed approach to solving the corresponding nonlinear problem can significantly save computing resources

Theoretical electronic structure with rovibrational studies of the molecules YP, YP+ and YP-

Due to the absence of the electronic structure of the YP molecule and its ions in literature, this work is conducted via an ab initio Complete Active Space Self Consistent Field and the Multi-Reference Configuration Interaction with Davidson correction calculation (CASSCF/MRCI + Q) to investigate the low–lying electronic states of these molecules. Adiabatic potential energy curves (PECs) along with static dipole moment (DM) curves for 27, 24, and 21 low-lying electronic states in the representation of 2s+1Λ(+/−) for YP, YP+, and YP- molecules have been investigated, respectively. For the low-lying electronic states of the YP molecule and their anion and cation, the spectroscopic constants Re, Te, ωe, ωexe, Be, De are provided. The rovibrational constants Ev, Bv, Dv, and the abscissa of turning points Rmin and Rmax (up to vibrational level v = 37) are calculated using the canonical functions approach and referring to the calculated data from the PECs. Perturbation theory method is also used to compare our data's validity, as no results are presented in the literature for these molecules.

Inflation by variation of the strong coupling constant: Update for Planck 2018

We apply the “systematic” first-order cosmological perturbation theory method to re-derive the formulation of an inflationary model generated by variation of constants, then to study the case where it is nonminimally coupled to gravity within both the “Metric” and “Palatini” formulations. Accommodating Planck 2018 data with a length scale [Formula: see text] larger than Planck length [Formula: see text] requires amending the model. First, we assume [Formula: see text] gravity where we show that an [Formula: see text]-term within Palatini formulation is able to make the model viable. All along the discussions, we elucidate the origin of the difference between the “Metric” and “Palatini” formalisms, and also highlight the terms dropped when applying the shortcut “potential formulae method,” unlike the “systematic method,” for the observable parameters. Second, another variant of the model, represented by a two-exponentials potential, fits also the data with [Formula: see text].

Geometric singular perturbation analysis to Camassa-Holm Kuramoto-Sivashinsky equation

We analyze a singularly Kuramoto-Sivashinsky perturbed Camassa-Holm equation with methods of the geometric singular perturbation theory. Especially, we study the persistence of smooth and peaked solitons. Whether a solitary wave of the original Camassa-Holm equation is smooth or peaked depends on whether there is linear dispersion, i.e. whether 2k=0. If 2k>0, then a unique smooth solitary wave persists with selected wave speed under singular Kuramoto-Sivashinsky perturbation just as what happens in the KS-KdV equation. On the other hand, we show that if there is no linear dispersion, i.e. 2k=0, then any observable peaked soliton fails to persist. This case is non-typical since the related slow manifold blows up and the classical geometric singular perturbation theory is not available.

Waves in the gas centrifuge: asymptotic theory and similarities with the atmosphere

We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of around 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 revolutions per minute. Using gases of lower heat capacities at constant pressure, such as xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid.

Elastic-Plastic Problem for a Stringer Plate with a Circular Hole

When calculating the strength of machines, structures and buildings with technological holes, it is important to take into account the plastic zones that emerge around the holes. However, the unknown shape and size of the plastic zone complicate the solution of elastic-plastic problems. This paper gives an approximate method and solution of the plane elastic-plastic problem of the distribution of stresses in a thin plate, reinforced with a regular system of stiffeners (stringers). The stringer plate under consideration has a circular hole, which is completely surrounded by the zone of plastic deformation. At infinity, the plate is subjected to a uniform tension along the stiffeners. A constant normal load is applied to the contour of the hole. The plate and stringer materials are assumed to be isotropic. The loading conditions are assumed to be quasi-static. It is assumed that the plate is in the plane-stressed state. Taken as the plasticity condition in the plastic zone is the Tresca-Saint-Venant plasticity condition. Methods of perturbation theory, analytic function theory, and the least squares method are used. The solution to the stated elastic-plastic problem consists of two stages. At the first stage, the stress-strain state for the elastic zone is found, and then the unknown interface between the elastic and plastic zones is determined using the least squares method. A closed system of algebraic equations has been constructed in each approximation, the numerical solution of which makes it possible to study the stress-strain state of a stringer plate, with the hole entirely surrounded by the plastic zone, as well as to determine the magnitudes of the concentrated forces that replace the action of the stringers. The interface between the elastic and plastic deformations has been found. The presented solution technique can be developed to solve other elastic-plastic problems. The solution obtained in this paper makes it possible to consider elastic-plastic problems for a stringer plate with other plasticity criteria.

Internal Conversion between Bright (11Bu+) and Dark (21Ag-) States in s-trans-Butadiene and s-trans-Hexatriene.

Internal conversion (IC) between the two lowest singlet excited states, 11Bu+ and 21Ag-, of s-trans-butadiene and s-trans-hexatriene is investigated using a series of single- and multi- reference wave function and density functional theory (DFT) methodologies. Three independent types of the equation-of-motion coupled-cluster (EOMCC) theory capable of providing an accurate and balanced description of one- as well as two-electron transitions, abbreviated as δ-CR-EOMCC(2,3), DIP-EOMCC(4h2p){No}, and DEA-EOMCC(4p2h){Nu} or DEA-EOMCC(3p1h,4p2h){Nu}, consistently predict that the 11Bu+/21Ag- crossing in both molecules occurs along the bond length alternation coordinate. However, the analogous 11Bu+ and 21Ag- potentials obtained with some multireference approaches, such as CASSCF and MRCIS(D), as well as with the linear-response formulation of time-dependent DFT (TDDFT), do not cross. Hence, caution needs to be exercised when studying the low-lying singlet excited states of polyenes with conventional multiconfigurational methods and TDDFT. The multistate many-body perturbation theory methods, such as XMCQDPT2, do correctly reproduce the curve crossing. Among the simplest and least expensive computational methodologies, the DFT approaches that incorporate the contributions of doubly excited configurations, abbreviated as MRSF (mixed reference spin-flip) TDDFT and SSR(4,4), accurately reproduce our best EOMCC results. This is highly promising for nonadiabatic molecular dynamics simulations in larger systems.

Evolution equations of the multi-planetary problem with variable masses

AbstractWe investigated the influence of the variability of the masses of planets and the parent star on the dynamic evolution of n planetary systems, considering that the masses of bodies change isotropically with different rates. The methods of canonical perturbation theory, which developed on the basis of aperiodic motion over a quasi-conical cross section and methods of computer algebra were used. 4n evolutionary equations were obtained in analogues of Poincare elements. As an example, the evolutionary equations of the three-planet exosystem K2 − 3 were obtained explicitly, which is a system of 12 linear non-autonomous differential equations. Further, the evolutionary equations will be investigated numerically.

To the dynamics of the two-body problem with variable masses in the presence of reactive forces

AbstractWe studied the problem of two spherical celestial bodies in the general case when the masses of the bodies change non-isotropically at different rates in the presence of reactive forces. The problem was investigated by methods of perturbation theory based on aperiodic motion along a quasi-conic section, using the equation of perturbed motion in the form of Newton’s equations. The problem is described by the variables a, e, i, π, ω, λ, which are analogs of the corresponding Keplerian elements and the equations of motion in these variables are obtained. Averaging over the mean longitude, we obtained the evolution equations of the two-body problem with variable masses in the presence of reactive forces. The obtained evolution equations have the exact analytic integral ${a^3 e^4 = a^3_0 e^4_0} = {const}$.

Metal Hydride Technologies for Separation of Hydrogen Isotopes

The paper considers the issue of theoretical prediction of characteristics at which separation of hydrogen isotopes occurs in the “gas-metal” system. Mathematical modeling of sorption is based on the use of the lattice gas model often used for metal hydrides. In contrast to the Leicher ideal solution model, it is taken into account that the dissolution of hydrogen in the metal increases the volume of the crystal lattice. This leads to additional contributions to potential energy. The model also takes into account the interaction between the atoms of the incorporated (absorbed) hydrogen isotopes. These phenomena are described by the methods of thermodynamic perturbation theory. The different composition of the gas (protium and deuterium) in contact with the metal leads to the fact that sorption, accompanied by the formation of hydride, proceeds for the same temperature at different equilibrium pressures. This phenomenon characterizes the isotope effect. The temperature dependences of the pressure on the "plateau" for palladium hydride and deuteride are obtained. The differences in these pressures can be used for the practical use of metal hydrides in the separation of hydrogen isotopes.

Prediction of the charge carriers stationary distribution in the active region of the p-i-n structures by the perturbation theory methods

The p-i-n diode is an electronic device that is widely used for switching a microwave signals. The theory of the p-i-n diode is based on linear mathematical models that satisfactorily explain the diodes switching properties at low microwave power levels. The developed methods for modeling the corresponding devices on p-i-n diodes turned out to be untenable when studying the properties of diodes and diode structures under the with high-power microwave signals (typical for high-power switches and protective devices). Here are faced with the need to take into account the mutual influence of diffusion-drift, wave, thermal processes, in which the nonlinear components of the mathematical models will dominate. The development of the computer technology and the corresponding mathematical methods (for example, the perturbation theory methods) determines the possibility of improving the existing p-i-n diodes mathematical models and the possibility of the new approaches developing to the analysis of the nonlinear processes in p-i-n diodes and similar electronic devices. The goal of this paper is to improve the mathematical model and methods for predicting the electron-hole plasma stationary distribution in the active region of surface-oriented p-i-n structures based on the use of the boundary functions method. The mathematical model of the electron-hole plasma stationary distribution in the integrated surface-oriented p-i-n structures active region is constructed in the form of the nonlinear singularly perturbed boundary value problem for the system of equations of the charge carriers current continuity and Poisson. An approximate solution of the corresponding boundary value problem is found in the form of the asymptotic series leading terms in powers of a small parameter. A scheme for finding the problem solution is proposed, which automatically includes the classical formulations of problems for modeling the p-i-n structures characteristics and allows you to make significant amendments to the solution. This ensures an increase in the level of adequacy of modeling and understanding of the features of a number of physical processes (diffusion-drift, recombinant, injection) in the p-i-n diodes active region. We consider the proposed approach a promising tool for studying nonlinear thermal, diffusion-drift, generation-recombination stationary and non-stationary processes occurring in the p-i-n structures elements under the action of the external microwave radiation, and predicting new physical effects in the studied systems, for example, due to the influence of local surface and bulk defects on the p-i-n structures characteristics.

Orbital Optimization in Selected Configuration Interaction Methods.

We study several approaches to orbital optimization in selected configuration interaction (SCI) plus perturbation theory methods and test them on the ground and excited states of three molecules using the semistochastic heat-bath configuration interaction method. We discuss the ways in which the orbital optimization problem in SCI resembles and differs from that in complete active space self-consistent field. Starting from natural orbitals, these approaches divide into three classes of optimization methods according to how they treat coupling between configuration interaction coefficients and orbital parameters, namely uncoupled, fully coupled, and quasi-fully coupled methods. We demonstrate that taking the coupling into account is crucial for fast convergence and recommend two quasi-fully coupled methods for such applications: accelerated diagonal Newton and Broyden-Fletcher-Goldfarb-Shanno.

ЭВОЛЮЦИОННЫЕ УРАВНЕНИЯ ОГРАНИЧЕННОЙ ЗАДАЧИ ТРЕХ ТЕЛ С ПЕРЕМЕННЫМИ МАССАМИ

In classical celestial mechanics, the theory of perturbation based on Keplerian motion is well developed. Various kinds of perturbed motion equations are described by canonical equations, Lagrange equations and Newton's equations. The masses of bodies are assumed constant and the bodies are point or spherical. Classical perturbation theory is a basic tool in the study of many astronomical problems. Observational astronomy shows that the masses of real cosmic bodies change over time. Real celestial bodies are neither spherical nor solid. Celestial bodies are non-stationary and their masses, sizes, shapes and structures change over time as they evolve. There are now a number of studies with a community bibliography of papers on the celestial mechanics of bodies of variable mass. However, the perturbation theory for unsteady space systems is not sufficiently developed. Therefore, we considered a gravitational system consisting of three spherical celestial bodies, with spherical density distributions, with variable masses in the restricted formulation. We have considered the general case where the masses of the bodies change non-isotropically at different rates, in the presence of reactive forces. We will assume that a body with infinitesimal mass has no effect on the motions of the two main bodies. The problem was investigated by methods of perturbation theory based on aperiodic motion along the quasi-conic section developed for nonstationary gravitating systems. Evolution motion equations of a less massive body and a small body in oscillating elements, in the relative coordinate system, have been obtained.

Optical and electronic properties of SiTex (x = 1, 2) from first-principles

The optical and electronic properties of α-SiTe, β-SiTe, and RX-SiTe2 are investigated. A detailed analysis of electronic properties is done using standard density functional theory (DFT) and hybrid functional methods. The static dielectric properties are investigated using the density functional perturbation theory method. The optical properties are studied under three different methods: standard DFT, many-body Green's functions, and the Bethe–Salpeter equation. Our calculations show that the SiTe compounds possess extremely high static dielectric constants in their bulk forms [ε0(⊥) = 68.58 and ε0(‖) = 127.29 for α-SiTe, and ε0(⊥) = 76.23 and ε0(‖) = 74.61 for β-SiTe]. The frequency-dependent dielectric functions Im(ε) have very large values (>100) in the optical regime, which are among the highest of layered materials, suggesting them as excellent light absorbents in the corresponding frequencies. α-SiTe exhibits a high degree of optical anisotropy as compared to the other two compounds, consistent with their structural configurations. A strong interlayer excitonic effect is observed in bulk RX-SiTe2. In addition, an analysis of Raman intensity is also performed.

Strong quadratic acousto-optic coupling in 1D multilayer phoxonic crystal cavity

Abstract Four methods are applied to calculate the acousto-optic (AO) coupling in one-dimensional (1D) phoxonic crystal (PXC) cavity: transfer matrix method (TMM), finite element method (FEM), perturbation theory, and Born approximation. Two types of mechanisms, the photoelastic effect (PE) and the moving interface effect (MI), are investigated. Whether the AO coupling belongs to linear or quadratic, the results obtained by the perturbation theory are in good agreement with the numerical results. We show that the combination method of FEM and perturbation theory has some advantages over Born approximation. The dependence of linear and quadratic couplings on the symmetry of acoustic and optical modes has been discussed in detail. The linear coupling will vanish if the defect acoustic mode is even symmetry, but the quadratic effect may be enhanced. Based on second-order perturbation theory, the contribution of each optical eigenfrequency to quadratic coupling is clarified. Finally, the quadratic coupling is greatly enhanced by tuning the thickness of the defect layer, which is an order of magnitude larger than that of normal defect thickness. The enhancement mechanism of quadratic coupling is illustrated. The symmetry of the acoustic defect mode is transformed from odd to even, and two optical defect modes are modulated to be quasi-degenerated modes. This study opens up a possibility to achieve tunable phoxonic crystals on the basis of nonlinear AO effects.