First-order Perturbation Theory Research Articles

Generic low-density corrections to the equation of state of chain molecules with repulsive intermolecular forces.

Molecular-based equations of state for describing the thermodynamics of chain molecules are often based on mean-field like arguments that reduce the problem of describing the interactions between chains to a simpler one involving only nonbonded monomers. While for dense liquids such arguments are known to work well, at low density they are typically less appropriate due to an incomplete description of the effect of chain connectivity on the local environment of the chains' monomer segments. To address this issue, we develop three semi-empirical approaches that significantly improve the thermodynamic description of chain molecules at low density. The approaches are developed for chain molecules with repulsive intermolecular forces; therefore, they could be used as reference models for developing equations of the state of real fluids based on perturbation theory. All three approaches are extensions of Wertheim's first-order thermodynamic perturbation theory (TPT1) for polymerization. The first model, referred to as TPT1-v, incorporates a second-virial correction that is scaled to zero at liquid-like densities. The second model, referred to as TPT1-y, introduces a Helmholtz-energy contribution to account for correlations between next-nearest-neighbor segments within chain molecules. The third approach, called TPT-E, directly modifies TPT1 without utilizing an additional Helmholtz energy contribution. By employing TPT1 at the core of these approaches, we ensure an accurate description of mixtures and enable a seamless extension from chains of tangentially bonded hard-sphere segments of equal size to hetero-segmented chains, fused chains, and chains of soft repulsive segments (which are influenced by temperature). The low-density corrections implemented in TPT1 are designed to preserve these good characteristics, as confirmed through comparisons with novel molecular simulation results for the pressure of various chain fluids. TPT1-v exhibits excellent transferability across different chain types, but it relies on knowing the second virial coefficient of the chain molecules, which is non-trivial to obtain and determined here using Monte Carlo simulation. The TPT1-y model, on the other hand, achieves comparable accuracy to TPT1-v while being fully predictive, requiring no input besides the geometry of the chain molecules.

Analytical Gaussian process cosmography: unveiling insights into matter-energy density parameter at present

In this study, we introduce a novel analytical Gaussian Process (GP) cosmography methodology, leveraging the differentiable properties of GPs to derive key cosmological quantities analytically. Our approach combines cosmic chronometer (CC) Hubble parameter data with growth rate (f) observations to constrain the Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document} parameter, offering insights into the underlying dynamics of the Universe. By formulating a consistency relation independent of specific cosmological models, we analyze under a flat FLRW metric and first-order Newtonian perturbation theory framework. Our analytical approach simplifies the process of Gaussian Process regression (GPR), providing a more efficient means of handling large datasets while offering deeper interpretability of results. We demonstrate the effectiveness of our methodology by deriving precise constraints on Ωm0h2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}h^2$$\\end{document}, revealing Ωm0h2=0.139±0.017\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _\ extrm{m0}h^2=0.139\\pm 0.017$$\\end{document}. Moreover, leveraging H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} observations, we further constrain Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document}, uncovering an inverse correlation between mean H0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$H_0$$\\end{document} and Ωm0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Omega _{\ extrm{m0}}$$\\end{document}. Our investigation offers a proof of concept for analytical GP cosmography, highlighting the advantages of analytical methods in cosmological parameter estimation.

Computer Simulation of the Total Energy and Shielding Function of a Carbon Molecule Using the First-Order Perturbation Theory

Computer Simulation of the Total Energy and Shielding Function of a Carbon Molecule Using the First-Order Perturbation Theory

Computer Simulation of the Total Energy and the Screening Function of a Nitrogen Molecule in First-Order Perturbation Theory

Computer Simulation of the Total Energy and the Screening Function of a Nitrogen Molecule in First-Order Perturbation Theory

Dynamical theory of topological defects II: universal aspects of defect motion

We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework (Romano et al 2023 J. Stat. Mech. 083211). We show how the equation of motion of point defects, domain walls, disclination lines and any other singularity can be understood with one unifying mathematical framework. For disclination lines, this also allows us to study the interplay between the internal line tension and the interaction with other lines. This interplay is non-trivial, allowing defect loops to expand, instead of contracting, due to external interaction. We also use this framework to obtain an analytical description of two long-lasting problems in point defect motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. For the former, we show that the effective defect mobility is strongly problem-dependent, but it can be computed with high accuracy for a pair of annihilating defects. For the latter, we show that at the first order in perturbation theory, anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. At higher orders, it also induces a correction in the mobility, which becomes non-isotropic for the +1/2 defect. We argue that, due to its generality, our method can help to shed light on the motion of singularities in many different systems, including driven and active non-equilibrium theories.

Analytic Error Analysis of the Partial Derivatives Cross-Section Model—II: Numerical Results

Accurately predicting errors incurred in a cross-section model for two-step reactor analysis enables the development of optimal case matrices and more efficient cross-section models. In a companion paper, we developed a systematic methodology for the partial derivatives cross-section model through rigorous analytic error analysis. In this paper, we verify our methodology against the conventional “brute force” numerical approach using a typical pressurized water reactor (PWR) lattice. By successfully reproducing known results, we gain confidence in our methodology’s application to advanced reactor environments, where optimal case matrices are generally not known. Our error methodology relies on accurately estimating bounds on the derivatives of the cross-section functions, a task we achieve through an order of convergence study. We use these derivative bounds in derived error expressions to obtain pointwise and setwise cross-section error bounds and verify these results with reference solutions of various two-group cross sections. We then propagate the cross-section error bounds to reactivity error using first-order perturbation theory and analyze their combined effect. Application of this approach to our test problem corroborates our prior qualitative findings with quantitative evidence and reveals the relative magnitudes of interpolation and model form error sources across diverse PWR cross-section functionalizations. Our results suggest systematic pathways for improving case matrix construction to minimize the overall error. These findings also confirm what is well known to the light water reactor design community, which is that interpolation error of cross sections for standard interpolation procedures and case matrix structures is on the order of 10 pcm or less. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multi-lattice problems, and investigating historical effects within the macroscopic depletion model.

Theoretical study of double oscillating fields induced electron-positron pairs creation process

<sec>We investigate an important aspect of electron-positron pair creation from vacuum in the presence of a strong background field, where the combined field plays a key role in the pair creation process. By utilizing computational quantum field theory, we explore electron-positron pair creation induced by double-located oscillating electric fields by numerically solving the Dirac equation in full spacetime dimensions. We demonstrate theoretically that computational quantum field theory is equivalent to the first-order time-dependent perturbation theory for single-photon transition pair creation in a spatially inhomogeneous and time-dependent electric field, and verify their equivalence through numerical simulations of pair creation in double-located oscillating fields. We show some interesting results about the periodic oscillation of the momentum spectrum structure of the created particle and the asymmetric multi-photon pair creation process due to the interference between two fields. By using first-order time-dependent perturbation theory, we find that the periodic oscillation in the momentum distribution of the created particle is affected by the field width, the field frequency and the distance between two fields. The period of the oscillation of momentum spectrum structure is changed by the distance between two fields, while the field width has an influence on both the difference between the peak and valley of the momentum spectra and the width of the momentum space available to the created particle. Increasing the frequency of the electric field results in larger momentum for the created particle pairs, while correspondingly reducing the coupling matrix element <inline-formula><tex-math id="M1">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M1.png"/></alternatives></inline-formula> and diminishing the probability of electron-positron pair creation.</sec><sec>The interference between two fields significantly enhances the yield of pair numbers for small distances between two fields. When the distance is too large, the number of pairs created by double oscillating fields is twice that created by a single field, and the enhancement is vanished. When the distance between two fields increases, the period of oscillation decreases. In turn, the creation of electron-positron pairs can become more monochromatic in momentum (energy), while the number of pairs created remains almost constant. As the electric field broadens, the yield of the created pairs decreases for constant potential height. Increasing the field width will reduce the number of particles for each momentum and narrow the momentum space of the created particle. Increasing the field frequency leads to the reduction of the coupling matrix element <inline-formula><tex-math id="M2">\begin{document}$ \langle p|V|n \rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20230432_M2.png"/></alternatives></inline-formula> and subsequently reduces the total number of electron-positron pairs created. The field profile parameters such as frequency, width, and distance between two fields can be utilized to select a specific momentum (energy) of particles in future electron-positron pair creation experiments.</sec>

A Closed-Form Model for 2-DEG Charge and Surface Potential in N-Polar Gallium Nitride Heterostructures

A closed-form model to calculate the 2-D electron gas (2-DEG) charge density and surface potential in an N-polar GaN/AlGaN heterostructure is presented. The proposed model is developed from the solution of Schrödinger’s equation for a finite triangular potential well. Asymptotic expressions of Airy functions are used to compute an initial value of subband energy. A new, unified expression to update the surface potential due to Poisson’s equation is presented. The modified Fang–Howard (M.F.H.) function is then employed to develop a closed-form correction to the subband energy using first-order perturbation theory. No fitting parameters are used. The results from our model are validated with numerical data for a wide range of bias conditions, channel layer thickness, and spacer layer mole fraction. Finally, the gate capacitance of the heterostructure is evaluated using automatic differentiation and validated against experimental data.

Thermalization of radiation-induced electrons in wide-bandgap materials: A first-principles approach

The present study is concerned with simulating the thermalization of high-energy charge carriers (electrons and/or electron–hole pairs), generated by ionizing radiation, in diamond and β-Ga2O3. Computational tools developed by the nuclear/particle physics and electronic device communities allow for accurate simulation of charge-carrier transport and thermalization in the high-energy (exceeding ∼100 eV) and low-energy (below ∼10 eV) regimes, respectively. Between these energy regimes, there is an intermediate energy range of about 10–100 eV, which we call the “10–100 eV gap,” in which the energy-loss processes are historically not well studied or understood. To close this “gap,” we use a first-principles approach (density functional theory) to calculate the band structure of diamond and β-Ga2O3 up to ∼100 eV along with the phonon dispersion, carrier-phonon matrix elements, and dynamic dielectric function. Additionally, using the first-order perturbation theory (Fermi's golden rule/first Born approximation), we calculate the carrier-phonon scattering rates and the carrier energy-loss rates (impact ionization and plasmon scattering). With these data, we simulate the thermalization of 100-eV electrons and the generated electron–hole pairs by solving the semiclassical Boltzmann transport equation using Monte Carlo techniques. We find that electron thermalization is complete within ∼0.4 and ∼1.0 ps for diamond and β-Ga2O3, respectively, while holes thermalize within ∼0.5 ps for both. We also calculate electron–hole pair creation energies of 12.87 and 11.24 eV, respectively.

Nonlinear Ringdown at the Black Hole Horizon.

The gravitational waves emitted by a perturbed black hole ringing down are well described by damped sinusoids, whose frequencies are those of quasinormal modes. Typically, first-order black hole perturbation theory is used to calculate these frequencies. Recently, it was shown that second-order effects are necessary in binary black hole merger simulations to model the gravitational-wave signal observed by a distant observer. Here, we show that the horizon of a newly formed black hole after the head-on collision of two black holes also shows evidence of nonlinear modes. Specifically, we identify one quadratic mode for the l=2 shear data, and two quadratic ones for the l=4, 6 data in simulations with varying mass ratio and boost parameter. The quadratic mode amplitudes display a quadratic relationship with the amplitudes of the linear modes that generate them.

Zeeman Splitting of Torsional Oscillation Frequencies of Magnetars

Magnetars form a special class of neutron stars possessing superstrong magnetic fields and demonstrating power flares triggered by these fields. Observations of such flares reveal the presence of quasi-periodic oscillations (QPOs) at certain frequencies; they are thought to be excited in the flares. QPOs carry potentially important information on magnetar structure, magnetic field, and mechanisms of magnetar activity. We calculate frequencies of torsional (magneto-elastic) oscillations of the magnetar crust treating the magnetic field effects in the first order of perturbation theory. The theory predicts the splitting of non-magnetic oscillation frequencies into Zeeman components. Zeeman splitting of the torsional oscillation spectrum of magnetars was suggested, clearly described and estimated by Shaisultanov and Eichler (2009), but their work has not been given considerable attention. To extend it, we suggest the technique of calculating oscillation frequencies, including Zeeman splitting at not too strong magnetic fields for arbitrary magnetic field configuration. Zeeman splitting enriches the oscillation spectrum and simplifies the theoretical interpretation of observations. We calculate several low-frequency oscillations of magnetars with a pure dipole magnetic field in the crust. The results qualitatively agree with the low-frequency QPOs detected in the hyperflare of SGR 1806–20 and in the giant flare of SGR 1900+14.

The effects of gravitational waves on a hydrogen atom

We investigate the influence of gravitational waves on a freely falling hydrogen atom by analyzing the dynamics of the bound electron described by the Dirac equation in the curved spacetime of a gravitational wave. From this, we derive the corresponding Dirac Hamiltonian in the local inertial frame of the atom, assuming gravitational waves are described by the linearized theory of general relativity. To maintain meaningful physical interpretations while obtaining a non-relativistic description, we employ the Foldy–Wouthuysen transformation. Through the analysis of resulting interaction terms and comparison with flat spacetime counterparts, valuable insights into the effects of gravitational waves (GWs) on the hydrogen atom are gained. Additionally, we explore selection rules governing the coupling between GWs and the atom and utilize first-order perturbation theory to quantify the induced energy shifts and spectral line splitting. This investigation contributes to our understanding of the interplay between quantum systems and gravitational waves, which could lead to alternative method of GWs indirect detection. However, measuring such tiny energy shifts would require a telescope with very high spectral resolution.

Valley polarization in a two-dimensional high-temperature semiconducting TiInTe[formula omitted] honeycomb ferromagnet

Exploring valley-contrasting physics in scarce intrinsic high-temperature ferromagnetic semiconductors with feasible synthesis route is of great significance for ever-evolving moden information technology. By first-principles calculations, the TiInTe3 monolayer is predicted to demonstrate excellent structural stability and easy-plane semiconducting ferromagnetism arising from indirect superexchange mechanism. Monte Carlo simulations based on the Heisenberg model reveal a magnetic phase transition at 583 K well above room temperature. Due to the inversion and time-reversal asymmetries, tunable valley polarization in the conduction band up to 110 meV can be achieved by varying the magnetization orientation, which is further validated by a first-order perturbation theory. More excitingly, electron doping for realizing the anomalous valley Hall effect gives rise to an out-of-plane preference for magnetization in the TiInTe3 monolayer and thus generates spontaneous and larger valley polarizations. After doping, the ferromagnetism above room temperature remains robust in the experimentally attainable electron density regime. Our findings highlight that the TiInTe3 monolayer is a promising ferrovalley material for developing high-performance spintronic and valleytronic nanodevices.

Second-order adiabatic connection: The theory and application to two electrons in a parabolic confinement.

The adiabatic connection formalism, usually based on the first-order perturbation theory, has been generalized to an arbitrary order. The generalization stems from the observation that the formalism can be derived from a properly arranged Taylor expansion. The second-order theory is developed in detail and applied to the description of two electrons in a parabolic confinement (harmonium). A significant improvement relative to the first-order theory has been obtained.

A perturbative production of massive Z bosons and fermion–antifermion pairs from the vacuum in the de Sitter Universe

In this paper we study the problem of neutral electro-weak interactions in a de Sitter geometry. We develop the formalism of reduction for the Proca field with the help of the solutions for the interacting fields and by using perturbative methods we obtain the definition of the transition amplitudes in the first order of perturbation theory. As an application to our formalism we study the generation of massive fermions and Z bosons from vacuum in the expanding de Sitter universe. Our results are the generalization to the curved geometry of the Weinberg–Salam electro-weak theory for the case of Z boson interaction with leptons. The probability is found to be a quantity that depends on the Hubble parameter and we prove that such perturbative processes are possible only for large expansion regime of the early Universe. The total probability and rate of transition are obtained for the case of large expansion and we use the dimensional regularization for extract finite results from the momenta integrals. In the Minkowski limit we obtain that the probability of particle generation from vacuum is vanishing recovering the well known result that forbids particle production in flat space-time due to the momentum-energy conservation.

Recursive ensemble canonical variate analysis for online incipient fault detection in dynamic processes

Data-driven fault detection has made significant advancements. However, detecting incipient faults is still a challenging problem for traditional data-driven methods, because it has low amplitude and is easily masked by measurement noise. In this paper, we propose an approach for detecting incipient faults named recursive ensemble canonical variate analysis (RECVA) for dynamic processes. First, inspired by ensemble learning, multiple CVA-based incipient fault models are obtained based on sampling from the training data set using bootstrap. It generates two matrices based on the principal component and the residual subspace. Then, two sensitive detection metrics are created using the maximum eigenvalue of a one-step sliding window over each row of the two aforementioned matrices. Based on the first-order perturbation (FOP) theory, the eigenvalue can be recursively updated. Utilizing the two detection metrics, RECVA can effectively detect incipient faults, which cannot be detected by conventional statistics. The effectiveness of RECVA is fully validated with the incipient fault data collected from the continuous stirred tank heater (CSTH) and the Tennessee Eastman process (TEP) simulation benchmark. Compared with traditional PCA, CVA, and other incipient fault detection methods based on divergence, simulation demonstrated that incipient faults can be effectively detected at an early stage, which is very important for avoiding serious failures in the industrial processes, resulting in economic losses and casualties.

Revisiting leading quantum corrections to near extremal black hole thermodynamics

Computing the 4D Euclidean path integral to one-loop order we find the large quantum corrections that govern the behavior of a spherically symmetric non-supersymmetric near-extremal black hole at very low temperature. These corrections appear from the near-horizon geometry of the near-extremal black hole. Using first-order perturbation theory we find that such corrections arise from the zero modes of the extremal background. In the logarithm of the partition function, these correspond to terms involving logarithm of temperature. Part of our result matches with the existing one in literature derived from an effective Schwarzian theory.

Inelastic N_2+H_2 collisions and quantum-classical rate coefficients: large datasets and machine learning predictions

Rate coefficients for vibrational energy transfer are calculated for collisions between molecular nitrogen and hydrogen in a wide range of temperature and of initial vibrational states (vle 40 for N_2 and wle 10 for H_2). These data are needed for the modelling of discharges in N_2/H_2 plasma or of atmospheric and interstellar medium chemistry in different temperature ranges. The calculations were performed by a mixed quantum-classical method, to recover quantum effects associated with the vibrational motion, on a refined potential energy surface. The obtained rates present striking discrepancies with those evaluated by first-order perturbation theories, like the SSH (Schwartz, Slavsky, Herzfeld) theory, which are often adopted in kinetic modelling. In addition, we present a detailed, though preliminary, analysis on the performance of different Machine Learning models based on the Gaussian Process or Neural Network techniques to produce complete datasets of inelastic scattering rate coefficients. Eventually, by using the selected models, we give the complete dataset (i.e., covering the whole vibrational ladder) of rate coefficients for the textrm{N}_2(v)+textrm{H}_2(0) longrightarrow textrm{N}_2(v-Delta v)+textrm{H}_2(0), Delta v=1,2,3 processes.Graphical abstract

Modeling of polymer-enzyme conjugates formation: Thermodynamic perturbation theory and computer simulations

A simple model for the formation of the polymer-enzyme conjugates has been proposed and described using corresponding modification of the Wertheim's first-order thermodynamic perturbation theory (TPT) for the system of associating chain molecules. A set of computer simulation data for the polymer chains containing various number of functional groups was generated and used to testify the accuracy of the theoretical results. Predictions of the present theoretical approach are more accurate than that of the conventional TPT and are in a very good agreement with the computer simulation data. In particular, the theory is able to account for the difference in the position of the polymer functional groups along its backbone.

Scattering from an electric–magnetic anisotropic rough interface

Scattering from a rough interface between a simple isotropic medium and a uniaxial lossy medium is analyzed using the first-order perturbation theory (PT) and the small slope approximation (SSA). We consider a more generic uniaxial lossy medium exhibiting electric and magnetic anisotropy and an arbitrarily oriented optic axis. Scattering from the rough interface of such a medium is analyzed by assuming both deterministic sinusoidal function and a Gaussian distribution for the surface roughness. We also study the coherent and incoherent intensities employing both the PT and the SSA. The impact of surface roughness, anisotropy and material losses on scattering characteristics is examined. We show that the parameters describing the surface roughness, i.e., height, period, and slope may add significant contribution to the electromagnetic scattering from the anisotropic interface.