High-order Perturbation Research Articles

An investigation of a series of layered Zn-1,4-diazabicyclo[2.2.2]octane metal–organic frameworks: local structure and adsorption properties of mixed-metal centre

The mixed-metal pillar-layered metal–organic frameworks of Zn(bdc)(DABCO)0.5, Zn0.5Cu0.5(bdc)(DABCO)0.5 and Cu(bdc)(DABCO)0.5 (bdc = 1,4-benzenedicarboxylate, DABCO = 1,4-diazabicyclo[2.2.2]octane) are investigated for their local structures and gas adsorption properties. According to the obtained electron paramagnetic resonance (EPR) spectra, the distorted structures around Cu2+ are proposed to be tetragonally and orthorhombically elongated [CuO4N] with the well fitted high-order perturbation formulae of the EPR parameters. Due to the doped Cu2+, the adsorption isotherms of industrially relevant gases (CO2, CO, CH4 and N2) and lower alkanes (CH4, C2H6, C3H8, C4H10 and C5H12) are different, especially at different temperatures. By combining the structural properties and adsorption isotherms, a comprehensive study suggests that the ZnDABCO series can be a controllable tool in gas storage and separation.

Running Coupling Constant from Position-Space Current-Current Correlation Functions in Three-Flavor Lattice QCD.

In this Letter, we provide a determination of the coupling constant in three-flavor quantum chromodynamics (QCD), α_{s}^{MS[over ¯]}(μ), for MS[over ¯] renormalization scales μ∈(1,2) GeV. The computation uses gauge field configuration ensembles with O(a)-improved Wilson-clover fermions generated by the Coordinated Lattice Simulations (CLS) consortium. Our approach is based on current-current correlation functions and has never been applied before in this context. We convert the results perturbatively to the QCD Λ parameter and obtain Λ_{MS[over ¯]}^{N_{f}=3}=342±17 MeV, which agrees with the world average published by the Particle Data Group and has competing precision. The latter was made possible by a unique combination of state-of-the-art CLS ensembles with very fine lattice spacings, further reduction of discretization effects from a dedicated numerical stochastic perturbation theory simulation, combining data from vector and axial-vector channels, and matching to high-order perturbation theory.

Hamiltonian formulations for perturbed dissipationless plasma equations

The Hamiltonian formulations for the perturbed Vlasov–Maxwell equations and the perturbed ideal magnetohydrodynamics (MHD) equations are expressed in terms of the perturbation derivative ∂F/∂ϵ≡[F,S] of an arbitrary functional F[ψ] of the Vlasov–Maxwell fields ψ=(f,E,B) or the ideal MHD fields ψ=(ρ,u,s,B), which are assumed to depend continuously on the (dimensionless) perturbation parameter ϵ. Here, [ , ] denotes the functional Poisson bracket for each set of plasma equations and the perturbation action functional S is said to generate dynamically accessible perturbations of the plasma fields. The new Hamiltonian perturbation formulation introduces a framework for functional perturbation methods in plasma physics and highlights the crucial roles played by polarization and magnetization in Vlasov–Maxwell and ideal MHD perturbation theories. One application considered in this paper is a formulation of plasma stability that guarantees dynamical accessibility and leads to a natural generalization to higher-order perturbation theory.

Application of Higher-Order Interpolation Perturbation Theory on Postprandial Plasma Glucose Waveform of a Single Lunch Based on GH-Method: Math-Physical Medicine (No. 426)

In this particular research note, the author arbitrarily selects the postprandial plasma glucose (PPG) data and waveforms from his lunch on 3/31/21 as the reference base. He then applies the higher-order, including first-order, second-order, and third-order interpolation perturbation theory to generate three approximated PPG waveforms to compare them against the measured nonlinear PPG waveform. The two major purposes of this study is to check the waveform shape similarity via correlation coefficients and the prediction accuracy via comparison of the averaged PPG values using the “higher order” interpolation perturbation theory. One obvious conclusion can be drawn from this article is that the higher-order perturbation equation provides a better approximate solution. However, in reality, there are very few patients who understand the perturbation theory of quantum mechanics, let alone to be able to conduct the complex mathematical calculations in order to achieve their desired glucose projection.

Application of the First, Second, and Third Order Equations of Interpolation Perturbation Theory from Quantum Mechanics to Predict a Synthesized 3-year Postprandial Plasma Glucose Wave Based on GH-Method: Math-Physical Medicine (No. 460)

In this research note, the author applies the higher-order interpolation perturbation equations from quantum mechanics. They include the first-order, second-order, and third-order, to generate three predicted PPG waveforms. He then utilizes his measured postprandial plasma glucose (PPG) data and a synthesized waveform generated from his 3,422 meals in 3+ years, from 5/5/2018 to 6/1/2021, as the comparison base against the three predicted PPG waveforms. There are two final yardsticks to check this study. The first target is to verify the prediction accuracies of the three perturbed PPG values. The second target is to examine the waveform shape similarity via correlation coefficients between the measured PPG dataset or waveform and the three perturbed PPG dataset or waveform.

Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms.

Connections between the Görling–Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew–Burke–Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.

Quantifying uncertainties and correlations in the nuclear-matter equation of state

We perform statistically rigorous uncertainty quantification (UQ) for chiral effective field theory ($\chi$EFT) applied to infinite nuclear matter up to twice nuclear saturation density. The equation of state (EOS) is based on high-order many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the $\chi$EFT expansion. From these calculations our newly developed Bayesian machine-learning approach extracts the size and smoothness properties of the correlated EFT truncation error. We then propose a novel extension that uses multitask machine learning to reveal correlations between the EOS at different proton fractions. The inferred in-medium $\chi$EFT breakdown scale in pure neutron matter and symmetric nuclear matter is consistent with that from free-space nucleon-nucleon scattering. These significant advances allow us to provide posterior distributions for the nuclear saturation point and propagate theoretical uncertainties to derived quantities: the pressure and incompressibility of symmetric nuclear matter, the nuclear symmetry energy, and its derivative. Our results, which are validated by statistical diagnostics, demonstrate that an understanding of truncation-error correlations between different densities and different observables is crucial for reliable UQ. The methods developed here are publicly available as annotated Jupyter notebooks.

Higher-order homotopy perturbation method for conservative nonlinear oscillators generally and microelectromechanical systems’ oscillators particularly

A modification of the homotopy perturbation method is proposed by taking advantage of the enhanced perturbation method and the parameter expanding technology. A generalized oscillatory equation and some nonlinear oscillators as the special cases of this equation are considered as examples to outline the basic properties of the modification, and the result is of high accuracy.

Uncharted Stable Peninsula for Multivariable Milling Tools by High-Order Homotopy Perturbation Method

In this work, a new method for solving a delay differential equation (DDE) with multiple delays is presented by using second- and third-order polynomials to approximate the delayed terms using the enhanced homotopy perturbation method (EMHPM). To study the proposed method performance in terms of convergency and computational cost in comparison with the first-order EMHPM, semi-discretization and full-discretization methods, a delay differential equation that model the cutting milling operation process was used. To further assess the accuracy of the proposed method, a milling process with a multivariable cutter is examined in order to find the stability boundaries. Then, theoretical predictions are computed from the corresponding DDE finding uncharted stable zones at high axial depths of cut. Time-domain simulations based on continuous wavelet transform (CWT) scalograms, power spectral density (PSD) charts and Poincaré maps (PM) were employed to validate the stability lobes found by using the third-order EMHPM for the multivariable tool.

Optimized geometric quantum computation with a mesoscopic ensemble of Rydberg atoms

We propose a nonadiabatic non-Abelian geometric quantum operation scheme to realize universal quantum computation with mesoscopic Rydberg atoms. A single control atom entangles a mesoscopic ensemble of target atoms through long-range interactions between Rydberg states. We demonstrate theoretically that both the single qubit and two-qubit quantum gates can achieve high fidelities around or above 99.9% in ideal situations. Besides, to address the experimental issue of Rabi frequency fluctuation (Rabi error) in Rydberg atom and ensemble, we apply the dynamical-invariant-based zero systematic-error sensitivity (ZSS) optimal control theory to the proposed scheme. Our numerical simulations show that the average fidelity could be 99.98% for single ensemble qubit gate and 99.94% for two-qubit gate even when the Rabi frequency of the gate laser acquires 10% fluctuations. We also find that the optimized scheme can also reduce errors caused by higher-order perturbation terms in deriving the Hamiltonian of the ensemble atoms. To address the experimental issue of decoherence error between the ground state and Rydberg levels in Rydberg ensemble, we introduce a dispersive coupling regime between Rydberg and ground levels, based on which the Rydberg state is adiabatically discarded. The numerical simulation demonstrate that the quantum gate is enhanced. By combining strong Rydberg atom interactions, nonadiabatic geometric quantum computation, dynamical invariant and optimal control theory together, our scheme shows a new route to construct fast and robust quantum gates with mesoscopic atomic ensembles. Our study contributes to the ongoing effort in developing quantum information processing with Rydberg atoms trapped in optical lattices or tweezer arrays.

Degenerate perturbation theory in thermoacoustics: high-order sensitivities and exceptional points

Abstract

Transients from initial conditions based on Lagrangian perturbation theory in N-body simulations III: The case of Gadget-2 code

In modern cosmology, the precision of the theoretical prediction is increasingly required. In cosmological [Formula: see text]-body simulations, the effect of higher-order Lagrangian perturbation on the initial conditions appears in terms of statistical quantities of matter density field. We have considered the effect of third-order Lagrangian perturbation theory (3LPT) on the initial conditions, which can be applied to Gadget-2 code. Then, as statistical quantities, non-Gaussianity of matter density field has been compared between cases of different order perturbations for the initial conditions. Then, we demonstrate the validity of the initial conditions with second-order Lagrangian perturbation theory (2LPT).

Investigation on the EPR Parameters for Tetragonal VO2+ Centers in LiHSO4 Single Crystals

In this work, the electron paramagnetic resonance (EPR) parameters (g-factors and A-constants) of the tetragonal VO2+ centers in LiHSO4 single crystals are theoretically investigated by the high-order perturbation formulae for these parameters based on two-spin–orbit-parameter model. Since the spin–orbit coupling coefficient of the ligand O2− is close to that of the central ion V4+ for the present system with strong covalence, the contributions to the EPR parameters from the ligand p- and s-orbitals as well as the spin–orbit coupling coefficient of the O2− ligand should be considered. The requirements of the crystal-field parameters are determined from the optical spectrum. The calculated results show good agreement with the experimental values. The signs of A-constants are ascertained in the discussion.

A Sixth-Order Numerical Method Based on Shishkin Mesh for Singularly Perturbed Boundary Value Problems

Recently, Lodhi and Mishra (J Comput Appl Math 319:170–187, 2017) presented the standard B-spline method based on quintic B-spline basis functions to solve a type of singularly perturbed boundary value problems (SPBVP). We note that their method provides only fourth-order convergence approximation to the solution of such problem. In this paper, we present a novel optimal B-spline technique, based on same quintic B-spline basis function as used in Lodhi and Mishra (2017), for solving linear and nonlinear SPBVP. The advantage of the suggested method over the method in Lodhi and Mishra (2017) is that our method has sixth-order rate of convergence. To obtain higher order of convergence, a high-order perturbation of the SPBVP is generated. The method is tested for its efficiency by applying it on five test problems.

Quantum Quasi-Monte Carlo Technique for Many-Body Perturbative Expansions.

High order perturbation theory has seen an unexpected recent revival for controlled calculations of quantum many-body systems, even at strong coupling. We adapt integration methods using low-discrepancy sequences to this problem. They greatly outperform state-of-the-art diagrammatic MonteCarlo simulations. In practical applications, we show speed-ups of several orders of magnitude with scaling as fast as 1/N in sample number N; parametrically faster than 1/sqrt[N] in MonteCarlo simulations. We illustrate our technique with a solution of the Kondo ridge in quantum dots, where it allows large parameter sweeps.

High–order perturbation of surfaces algorithms for the simulation of localized surface plasmon resonances in graphene nanotubes

The plasmonics of two–dimensional materials, such as graphene, has become an important field over the past decade. The active tunability of graphene via electrical gating or chemical doping has generated a great deal of excitement among engineers seeking sensing devices. Consequently there is significant demand for robust and highly accurate computational capabilities which can simulate such materials. The class of High–Order Perturbation of Surfaces methods have proven to be particularly appropriate for this purpose. In this contribution we describe our recent efforts to utilize both Dirichlet–Neumann Operators and Impedance–Impedance Operators in these schemes. In addition, we present detailed numerical results which not only validate our simulations using the Method of Manufactured Solutions, but we also describe Localized Surface Plasmon Resonances in graphene nanotubes enclosing rod–shaped dielectric materials.

Investigation of the Optical Spectra and Spin-Hamiltonian Parameters for Vanadyl in Zinc Phosphate Glass

The optical absorption spectra and spin-Hamiltonian parameters (g factors g||, g⊥, and hyperfine structure constants A||, A⊥ ) of vanadyl in zinc phosphate glass are investigated, using the high-order perturbation formulas for a 3d1 ion in tetragonally compressed octahedra. In the calculations, the required crystal-field parameters are estimated from the superposition model, and the optical absorption bands and spin-Hamiltonian parameters are linked with the tetragonal distortion (characterized by ΔR = R⊥ – R||, where R⊥ and R|| denote the bond lengths perpendicular and parallel to the C4 axis). Based on the calculations, the tetragonal distortion ΔR (≈1.795 A) was obtained, and negative signs of the hyperfine structure constants A|| and A⊥ are suggested.

Spatiotemporal dynamics of immunogenic tumors

A mathematical model, consisting of a system of two coupled reaction-diffusion partial differential equations describing the interaction between solid tumor and immune system (termed as effector cells), is proposed here. The main focus is on the analysis of the spatiotemporal dynamics of tumor cells and immune cells. The resulting system is analyzed and numerical simulations are presented. Different types of spatial patterns with respect to different initial conditions, and time are observed. Their analysis and mechanism of spatiotemporal pattern formation in immunogenic tumor are studied. Spatiotemporal perturbation around non-spatial steady state beyond the linear regime is obtained based on the analysis of higher-order perturbation terms.

Multiparton webs beyond three loops

Correlators of Wilson-line operators are fundamental ingredients for the study of the infrared properties of non-abelian gauge theories. In perturbation theory, they are known to exponentiate, and their logarithm can be organised in terms of collections of Feynman diagrams called webs. We study the classification of webs to high perturbative orders, proposing a set of tools to generate them recursively: in particular, we introduce the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, instead of individual Feynman diagrams. As an application, we enumerate all Cwebs entering the soft anomalous dimension matrix for multi-parton scattering amplitudes at four loops, and we compute the mixing matrices for all Cwebs connecting four or five Wilson lines at that loop order, verifying that they obey sum rules that were derived or conjectured in the literature. Our results provide the colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

Perturbative approach to tunneling and quantum interferences in spin clusters

Collective tunneling is a ubiquitous phenomenon in finite-size spin clusters that shows up in systems as diverse as molecular magnets or spin clusters adsorbed at surfaces. The problem we explore is to understand how small flipping terms can cooperate to flip a large spin to the opposite direction or a cluster of interacting elementary Ising spins into the time-reversed state. These high order processes will involve at least two channels, a single spin-flip channel due to a transverse field and a two-spin flip channel due to exchange or due to single-ion anisotropies. In the present paper, we show that high-order perturbation theory can be formulated and evaluated with the help of simple recurrence relations, leading to a compact theory of tunnelling in macroscopic spins, in one-dimensional clusters, as well as in small higher-dimensional clusters. This is demonstrated explicitly in the case of the Ising model with a transverse field and transverse exchange, and in the case of macroscopic spins with uniaxial anisotropy. Our approach provides a transparent theory of level crossings, where the tunneling between time reversed configurations vanishes as a function of the external field. The crossings result from destructive quantum interferences between competing flipping channels. Our theory consistently predicts N crossings in chains of N Ising spins, 2S crossings in single spins of magnitude S, and yields explicit analytical formulae for the level crossings of open chains and macroscopic spins. Disorder can be easily implemented in this perturbative formalism. Leading disorder effects can be treated analytically for spin rings. At the smallest transverse field crossing, the suppression of tunneling is most robust with respect to disorder. We briefly discuss the implications of our findings for the use of realistic spin clusters on surfaces to store information.