Diagonalization Method Research Articles

Superdiffusive Energy Transport in Kinetically Constrained Models

Universal nonequilibrium properties of isolated quantum systems are typically probed by studying transport of conserved quantities, such as charge or spin, while transport of energy has received considerably less attention. Here, we study infinite-temperature energy transport in the kinetically-constrained PXP model describing Rydberg atom quantum simulators. Our state-of-the-art numerical simulations, including exact diagonalization and time-evolving block decimation methods, reveal the existence of two distinct transport regimes. At moderate times, the energy-energy correlation function displays periodic oscillations due to families of eigenstates forming different su(2) representations hidden within the spectrum. These families of eigenstates generalize the quantum many-body scarred states found in previous works and leave an imprint on the infinite-temperature energy transport. At later times, we observe a broad superdiffusive transport regime that we attribute to the proximity of a nearby integrable point. Intriguingly, strong deformations of the PXP model by the chemical potential do not restore diffusion, but instead lead to a stable superdiffusive exponent $z\approx3/2$. Our results suggest constrained models to be potential hosts of novel transport regimes and call for developing an analytic understanding of their energy transport.

Some finite temperature and ground state properties of high-Tc superconductivity within the planar t-J-U model

In high-Tc materials, considering pair hopping and on-site pairing of electrons, presence of two electrons at a site following Pauli exclusion principle (a t-J-U model) is relevant. Considering this novelty, within a two-dimensional (2D) t-J-U Hamiltonian, some thermodynamic and ground state properties of high-Tc cuprates at various hole doping concentrations (〈h〉) have been investigated. Any theory based on perturbation approximation is inapplicable in strongly correlated electron systems, therefore, Lanczos method of exact diagonalization on a square cluster (tilted) of 8-sites is followed. Results show that double occupancy (δ) is maximum for hole concentration 〈h〉 = 0.25 and increases at a particular temperature T = T(U). Local moment shows the opposite behavior. Spin-spin correlation is negative between nearest-neighbor sites, confirming antiferromagnetic nature of the system. It appears that on-site Coulomb repulsion (U/t ≥ 6.0) destabilizes the superconducting ground state. In the system, antiferromagnetism (AF) and superconductivity are seen to coexist. A uniform distribution of charges is seen with increasing on-site Coulomb repulsion (U), which results in constant electron–electron correlation.

Robust adaptive beamforming via covariance matrix reconstruction with diagonal loading on interference sources covariance matrix

The majority of the existing adaptive beamforming methods utilize the interference-plus-noise covariance matrix (INCM) to prevent the signal of interest (SOI) from being suppressed. However, the removal of the SOI component will lead to a decrease in the performance at low input signal-to-noise ratio (SNR). In this paper, a novel interference sources covariance matrix (ISCM) diagonal loading method is proposed to improve the robustness of the beamformer. First of all, we employ the peaks of the Capon spectrum to calculate the corresponding nominal steering vectors (SVs), and then accurate SVs of the SOI and interferences are obtained by subspace projection. Instead of utilizing the orthogonality, the proposed method preserves the non-orthogonality between SVs to estimate an accurate signal-plus-interference sources covariance matrix (SISCM), and then obtains a reconstructed array covariance matrix (RACM). Furthermore, we conduct diagonal loading on ISCM and construct a modified array covariance matrix (MACM) to keep the interference-to-signal ratio (ISR) after loading at a proper large value. Simulation results demonstrate the robustness of the proposed method, and indicate that the proposed method not only has the low computational complexity but also performs well at both low and high input SNR.

Harmonic-Gaussian Symmetric and Asymmetric Double Quantum Wells: Magnetic Field Effects

In this study, we considered the linear and non-linear optical properties of an electron in both symmetrical and asymmetrical double quantum wells, which consist of the sum of an internal Gaussian barrier and a harmonic potential under an applied magnetic field. Calculations are in the effective mass and parabolic band approximations. We have used the diagonalization method to find eigenvalues and eigenfunctions of the electron confined within the symmetric and asymmetric double well formed by the sum of a parabolic and Gaussian potential. A two-level approach is used in the density matrix expansion to calculate the linear and third-order non-linear optical absorption and refractive index coefficients. The potential model proposed in this study is useful for simulating and manipulating the optical and electronic properties of symmetric and asymmetric double quantum heterostructures, such as double quantum wells and double quantum dots, with controllable coupling and subjected to externally applied magnetic fields.

Common canonical variate analysis (CCVA) based modeling and monitoring for multimode processes

Multiple operating modes are common in industrial processes due to feed stock alterations, product specifications, working environment changes and so on. Although different modes show different behaviors, some underlying process characteristics may stay invariable as mode changes, which reveal the essence information of the process. In this work, the issue of multimode process monitoring is studied with subspace separation, in which each mode is divided into the common subspace and specific subspace. A modified canonical variate analysis (CVA), termed as common CVA (CCVA), is put forward to extract the mode-common features based on joint approximate diagonalization method. The concatenation of all Hankel matrices is analyzed to find a common orthonormal set eigenvectors by minimization of joint diagonality criterion. Then, the remaining part of each mode is regarded as local specific subspace, which provides more representative information in each different mode. CVA algorithm is applied to build multiple local models based on mode-specific information. Two case studies, a numerical example and Tennessee Eastman (TE) process, are provided to validate the feasibility and effectiveness of the proposed method in monitoring abnormal operation for multimode processes.

Numerical study of resonant inelastic x-ray scattering at the oxygen K edge in insulating cuprates

We investigate resonant inelastic X-ray scattering (RIXS) at the O $K$-edge in insulating cuprates by means of three methods: cluster perturbation theory (CPT), Hartree--Fock approximation (HFA) and exact diagonalization (ED) method. We consider the three-band Hubbard model and show the overall momentum-dependence of the Zhang--Rice singlet (ZRS) excitation and charge-transfer excitation by the CPT combining with the perturbation scheme. A comparison of the RIXS spectra calculated using CPT and HFA reveals different momentum-dependencies through the changes in the properties of the upper Hubbard band and the ZRS band. These findings are supported by analyses using the ED method on the RIXS spectra and dynamical charge structure factor.

Mobile impurities interacting with a few one-dimensional lattice bosons

We report a comprehensive study of the ground-state properties of one and two bosonic impurities immersed in small one-dimensional optical lattices loaded with a few interacting bosons. We model the system with a two-component Bose–Hubbard model and solve the problem numerically by means of the exact diagonalization method. We report binding energies of one and two impurities across the superfluid (SF) to Mott-insulator transition and confirm the formation of two-body bound states of impurities induced by repulsive interactions. In particular, we found that an insulator bath induces tightly bound di-impurity dimers, whereas a SF bath induces shallower bound states.

Eigenvalue-Corrected Natural Gradient Based on a New Approximation

Using second-order optimization methods for training deep neural networks (DNNs) has attracted many researchers. A recently proposed method, Eigenvalue-corrected Kronecker Factorization (EKFAC), proposed an interpretation by viewing natural gradient update as a diagonal method and corrects the inaccurate re-scaling factor in the KFAC eigenbasis. What’s more, a new method to approximate the natural gradient called Trace-restricted Kronecker-factored Approximate Curvature (TKFAC) is also proposed, in which the Fisher information matrix (FIM) is approximated as a constant multiplied by the Kronecker product of two matrices and the traces can be kept equal before and after the approximation. In this work, we combine the ideas of these two methods and propose Trace-restricted Eigenvalue-corrected Kronecker Factorization (TEKFAC). The proposed method not only corrects the inexact re-scaling factor under the Kronecker-factored eigenbasis, but also considers the new approximation method and the effective damping technique adopted by TKFAC. We also discuss the differences and relationships among the related Kronecker-factored approximations. Empirically, our method outperforms SGD with momentum, Adam, EKFAC and TKFAC on several DNNs.

A new approach to training neural networks using natural gradient descent with momentum based on Dirichlet distributions

In this paper, we propose a natural gradient descent algorithm with momentum based on Dirichlet distributions to speed up the training of neural networks. This approach takes into account not only the direction of the gradients, but also the convexity of the minimized function, which significantly accelerates the process of searching for the extremes. Calculations of natural gradients based on Dirichlet distributions are presented, with the proposed approach introduced into an error backpropagation scheme. The results of image recognition and time series forecasting during the experiments show that the proposed approach gives higher accuracy and does not require a large number of iterations to minimize loss functions compared to the methods of stochastic gradient descent, adaptive moment estimation and adaptive parameter-wise diagonal quasi-Newton method for nonconvex stochastic optimization.

Electron Propagator Theory of Vertical Electron Detachment Energies of Anions: Benchmarks and Applications to Nucleotides

A new generation of ab initio electron-propagator self-energy approximations that are free of adjustable parameters is tested on a benchmark set of 55 vertical electron detachment energies of closed-shell anions. Comparisons with older self-energy approximations indicate that several new methods that make the diagonal self-energy approximation in the canonical Hartree-Fock orbital basis provide superior accuracy and computational efficiency. These methods and their acronyms, mean absolute errors (in eV), and arithmetic bottlenecks expressed in terms of occupied (O) and virtual (V) orbitals are the opposite-spin, non-Dyson, diagonal second-order method (os-nD-D2, 0.2, OV2), the approximately renormalized quasiparticle third-order method (Q3+, 0.15, O2V3) and the approximately renormalized, non-Dyson, linear, third-order method (nD-L3+, 0.1, OV4). The Brueckner doubles with triple field operators (BD-T1) nondiagonal electron-propagator method provides such close agreement with coupled-cluster single, double, and perturbative triple replacement total energy differences that it may be used as an alternative means of obtaining standard data. The new methods with diagonal self-energy matrices are the foundation of a composite procedure for estimating basis-set effects. This model produces accurate predictions and clear interpretations based on Dyson orbitals for the photoelectron spectra of the nucleotides found in DNA.

On tropical intersection theory

We develop a tropical intersection formalism of forms and currents that extends classical tropical intersection theory in two ways. First, it allows to work with arbitrary polyhedra, also non-rational ones. Second, it allows for smooth differential forms as coefficients. The intersection product in our formalism can be defined through the diagonal intersection method of Allermann–Rau or the fan displacement rule. We prove with a limiting argument that both definitions agree.

Angular Super-Resolution of Multi-Channel APAR in Interference Environments

Aiming to resolve azimuth-dense targets in interference environments, the radar needs to have the ability of single snap echo angular super-resolution with anti-interference. To solve the problem, the angular super-resolution algorithm based on single snap echo while anti-interference with blocking matrix method is studied for active phased array radar (APAR) in this paper. Since the super-resolution ability of the conventional MUSIC algorithm and iterative adaptive algorithm (IAA) algorithm are limited in single snap echo, the iterative re-weighted least squares (IRLS) algorithm under p-norm constraint is proposed. Further, the near main lobe interference suppression ability is enhanced by the adaptive diagonal loading method. The performance differences of IAA and IRLS algorithms for single-target detection and double-target angular super-resolution are analyzed in detail by numerical simulation on three scenes of no interference, side-lobe interference, and near-main-lobe interference. The simulation results show that the proposed algorithm can effectively solve the problem of target angle estimation and super-resolution based on single sample echo in an interference environment, including near main-lobe interference.

Study of Soil Erodibility in Various Agroforestry Systems Based on Elephant Foot Yam (Amorphophallus oncophyllus) in Bayan District, North Lombok Regency

Bayan District has a wavy to mountainous topography. The type of soil in the area is classified as Inceptisol, so it is very susceptible to erosion. An agroforestry system, with various stands of perennial crops, has been developed in the area, as a conservative measure to support the sustainability of land resources. This study aims to assess the value of soil erodibility in Elephant foot yam-based agroforestry systems in five types of stands, namely: Teak (A1), Cashew (A2), “Gamal” and Banana (A3), Cocoa (A4), and Coffee (A5). The method used is descriptive method with survey technique. Determination of the research location was carried out by purposive sampling with the criteria of land having a rather steep slope (15-17%), the soil order Inceptisol, located in the upper slope, and a high level of stand vegetation homogeneity. Soil samples (undisturbed and disturbed) were collected using the diagonal method on 10 x 10 m plots randomly placed in each agroforestry system with a depth of 0-20 cm. Parameters observed were soil texture (pipette method), soil permeability (constant head), soil structure (qualitative in the field), and soil organic matter (Walkley and Black). The result showed that the value of soil erodibility, in agroforestry systems with different stands, was significantly difference, with the lowest value was found in the Coffee agroforestry system (A5) of 0,416 and the highest was found in the Cashew system (A2) of 0,661. The effectiveness of improvement soil erodibility in the agroforestry system of A5 was 37% better than A2.

A Modification to the Enhanced Correction Factor Technique for the Subsonic Wing–Body Interference Model

In this work, the enhanced correction factor technique (ECFT) is modified for a subsonic wing–body interference model, which can consider the forces on both the lifting boxes and the body elements of an idealized airplane, termed the advanced ECFT method. A passenger aircraft model is chosen as the simulation model, and the longitudinal static aeroelasticity at the transonic situation for two-degree freedom, including the α (angle of attack) degree and ϕ (angle of horizontal tail) degree, is simulated in this paper. The corresponding CFD results are used to correct the aerodynamic influence coefficients (AIC) matrix, which is then simulated by MSC.NASTRAN. The pressure distribution results of different aircraft components received by the advanced ECFT method indicate that it is suitable for the subsonic wing–body interference model. Compared with the uncorrected linear method and the diagonal corrected method, it is generally more consistent with the CFD/CSD coupling method, not only for the lifting boxes, but also for the body elements. In addition, the aerodynamic derivative results also show good agreement with the flight test data, which solidly verifies the advance ECFT method.

Joint Transmissive and Reflective RIS-Aided Secure MIMO Systems Design Under Spatially-Correlated Angular Uncertainty and Coupled PSEs

This paper investigates a joint transmissive and reflective reconfigurable intelligent surfaces (RIS) -aided secure multiple-input multiple-output (MIMO) system, where both a RIS-assisted transmitter and a RIS-based reflector are deployed to defend against the simultaneous jamming attack and wiretapping threat. Our design focuses on maximizing the sum rate under the unknown jammer’s beamforming, joint RISs’ coupled phase shift errors (PSEs), and spatially-correlated angular channel uncertainties. Besides, we take into account the various quality-of-service (QoS) requirement constraints for guaranteeing the secure performance. Since the problem is non-convex and mathematically intractable, a new optimization framework is established to facilitate the solution development to the formulated problem. Specifically, armed with the Akaike information criterion, a novel diagonalization method is first proposed to estimate the unknown jamming covariance matrix. Then, a series of fractional-eliminated rate expressions is derived that facilitates the application of the proposed Double Deterministic Transformation (DDT) to tackle the coupled stochastic PSEs. Besides, regardless of the spatial correlation matrix, a general discretization method is proposed to convert the e spatially-correlatd angular uncertainties into a worst-case robust one. Subsequently, building upon the above transformations which transform the original problem into tractable one, a two-layer iterative Lagrange multiplier algorithm capitalizing a low-complexity dual method is proposed to obtain the globally optimal solution of the digital precoder, where the multiple QoS constraints are handled without iteration. Meanwhile, we develop a novel polyblock-based multiple penalty method to obtain the globally optimal solutions to RISs’ phase shifts which can simultaneously satisfy the multiple QoS constraints. Moreover, to address the narrow feasibility region induced by the multiple QoS constraints, a heuristic initial optimization method is proposed, which strengthens the existing result. Finally, theoretical analysis and numerical results demonstrate the optimality and the excellent performance of our proposed optimization framework.

Exact Decomposition of Optimal Control Problems via Simultaneous Block Diagonalization of Matrices.

In this paper, we consider optimal control problems (OCPs) applied to large-scale linear dynamical systems with a large number of states and inputs. We attempt to reduce such problems into a set of independent OCPs of lower dimensions. Our decomposition is 'exact' in the sense that it preserves all the information about the original system and the objective function. Previous work in this area has focused on strategies that exploit symmetries of the underlying system and of the objective function. Here, instead, we implement the algebraic method of simultaneous block diagonalization of matrices (SBD), which we show provides advantages both in terms of the dimension of the subproblems that are obtained and of the computation time. We provide practical examples with networked systems that demonstrate the benefits of applying the SBD decomposition over the decomposition method based on group symmetries.

Tensor Singular Spectrum Decomposition: Multisensor Denoising Algorithm and Application

Realising multi-sensor signal fusion and weak feature adaptive extraction is a challenging task. Therefore, a new algorithm called tensor singular spectrum decomposition is proposed in this study for the adaptive decomposition of multi-sensor time series. Traditional tensor decomposition algorithms, such as CP, HOSVD and Tucker decomposition, are derived from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -mode product. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -mode product essentially uses the idea of matrices to deal with tensors given that it defines the multiplication between matrix and higher-order tensor, thereby creating problems of non-pseudodiagonal core tensor and nonunique decomposition results in traditional tensor decomposition algorithms. To this end, decomposition of the original tensor signal and reconstruction of multi-sensor component signals are realised in this study by combining the trajectory tensor construction, superposition of the Gaussian function spectral model, adaptive iterative optimisation of embedding dimension and diagonal average method on the basis of the principle of tensor–tensor order-preserving multiplication. The proposed algorithm inherits the perfect mathematical theory and excellent properties of matrix singular value decomposition in processing single-sensor signals whilst retaining the inherent structure and coupling relationship between multi-sensor data and realising the organic fusion and adaptive decomposition of multi-sensor signals. The analysis results of simulation, experimental and engineering signals showed that the proposed method can effectively extract weak fault quantification features hidden in original multi-sensor signals compared with existing methods.

Arthropods, Pests, and Diseases of Jack Bean (Canavalia Ensiformis) in Upland and Dry Climate Areas

Jack bean (Canavalia ensiformis) is one of the potential crops in tropical areas. Arthropods, plant pests, and microorganisms were observed in Jack bean crop ecosystems. The aims of this study were to observe the presence of arthropods in Jack bean plants in dry land and dry climate area, and disease symptoms caused by microorganisms. This research was conducted at Muneng experimental station Probolinggo, using a diagonal sampling method, with yellow trap, pitfall trap, and swapping net. Symptom variation, arthropod diversity, pest attack intensity, and disease incidence were recorded. The results showed that the types of arthropods, pests, and diseases that infect and the incidence of pest and disease attack on each accession do not differ between accessions. The highest number was recorded in the sweeping net with 12 families, followed by the pitfall trap with 4 families, while in yellow traps there were 3 families. Two insects as plant pest organisms were Liriomyza sp and Maruca sp with attack rates up to 70% and 80% respectively, while jack bean diseases were wilting and mosaic with 25% and 40%. It is necessary to identify the pathogens that caused the diseases in more detail and to study the proper management of pests to reduce yield loss.

Effects of long-range inter-particle interactions and isolated defect on quantum walks of two hard-core bosons in one-dimensional lattices

The quantum walk of two hard-core bosons in one-dimensional lattice under the effect of long-range inter-particle interaction is studied in detail. We also simulate the influence of an isolated defect that may exist in the lattice on the quantum walk of two particles by adding an additional potential energy to a certain lattice site. Using exact diagonalization method, the continuous-time quantum walk is directly simulated. The numerical simulations show that the range of interaction (long-range or short-range), the strength of the inter-particle interaction, the initial state of the two particles and the presence of the isolated defect have great influences on the quantum walk. Under the effect of strong long-range interaction, the particles initially located on the non-adjacent lattice sites have a co-walking behavior, while under the short-range interactions (nearest-neighbor interactions) only two particles initially located on the neighboring lattice sites can exhibit co-walking. After introducing the isolated defect into the system with strong interaction, two particles residing on the same side of the isolated defect keep co-walking, while two particles located on either sides of the isolated defect or one particle located on the isolated defect and the other particle staying on the side of the isolated defect, the two particles keep stationary or co-walking near the defect, displaying the characteristics of localization. By using the second-order perturbation theory of degenerate quantum system, a comprehensive theoretical analysis of the above numerical results is given. The theoretical analysis reveals the underlying physical law of quantum walks of two particles in one-dimensional lattice under the effects of strong long-range interaction and isolated defect in the lattice.

Electronic structure and terahertz intersubband absorption spectra of phosphorus donor in silicon using a variationally optimized diagonalization method

The electronic structure and terahertz (THz) intersubband absorption spectra of phosphorus (P) donor in silicon (Si) are theoretically investigated using a variationally optimized diagonalization method based on the three-dimensional (3D) nonorthogonal associated Laguerre basis set, the basis set of eigenfunctions of 3D hydrogen atom and the basis set of eigenfunctions of 3D isotropic harmonic oscillator. A fully analytical expression of the matrix elements of the Hamiltonian is derived. Due to the large band anisotropy of Si, the donor electron series appear in an anomalous energy-level order and interval of the orbital angular momentum. The donor electron energy levels with even a small number of basis functions are in excellent agreement with those reported in the previous literature. Compared to two different basis sets of eigenfunctions of 3D hydrogen atom and isotropic harmonic oscillator, my proposed variationally optimized diagonalization method based on the 3D nonorthogonal associated Laguerre basis set is proven to be more efficient and reliable in calculating highly accurate impurity states of anisotropic 3D materials. The intersubband absorption spectra of P donor electron involving transitions from the 1s to excited states are strongly dependent on the orientations of the valley and the polarization vector of the incident light, which results from the fact that the large band anisotropy of Si induces strong mixing of the donor electron states. Their absorption frequencies are found to fall into the THz part of the electromagnetic spectrum. These results show that P donor in Si provides a material platform that enables intersubband devices operating in the THz frequency domain. • A fully analytical expression of the matrix elements of the donor Hamiltonian is derived. • The donor electron energy levels are in excellent agreement with those reported in the previous literature. • The intersubband absorption spectra of P donor electron are strongly dependent on the orientations of the incident light polarization. • P donor in Si provides a material platform that enables optoelectronic devices operating in the THz frequency domain. • The 3D nonorthogonal Laguerre basis is more efficient and reliable in calculating impurity states of anisotropic 3D materials.