Finite Systems Research Articles

Order-by-disorder and long-range interactions in the antiferromagnetic transverse-field Ising model on the triangular lattice—A perturbative point of view

We study the low-field ground-state (GS) properties of the antiferromagnetic transverse-field Ising model with long-range interactions (afLRTFIM) on the triangular lattice. We use the method of perturbative continuous unitary transformations (pCUT) to derive an effective model for the degenerate GS space of the antiferromagnetic nearest-neighbour (NN) Ising model on a finite system, by treating the transverse-field (TF) and the long-range interactions (LRI) as a perturbation. We determine a level-crossing between the gapped plain stripe phase at small TF and the gapped clock-ordered phase at intermediate TF at hc≅0.129 for α=6, N=36 spins in order three perturbation theory on the finite system. We discuss the qualitative layout of the quantum phase diagram of the afLRTFIM on the triangular lattice.

Relativistic Fully Self-Consistent GW for Molecules: Total Energies and Ionization Potentials.

The fully self-consistent GW (scGW) method with an iterative solution of the Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of scGW for molecules containing heavy elements using the exact two-component (X2C) Coulomb approximation. We benchmark SOC-81 data set containing closed shell heavy elements for the first ionization potential using the fully self-consistent GW as well as one-shot GW. The self-consistent GW provides superior results compared to G0W0 with PBE reference and comparable results to G0W0 with PBE0 while also removing the starting point dependence. The photoelectron spectra obtained at the X2C level demonstrate very good agreement with the experimental spectra. We also observe that scGW provides very good estimation of ionization potential for the inner d-shell orbitals. Additionally, using the well-conserved total energy, we investigate the equilibrium bond length and harmonic frequencies of a few halogen dimers using scGW. Overall, our findings demonstrate the applicability of the fully self-consistent GW method for accurate ionization potential, photoelectron spectra, and total energies in finite systems with heavy elements with a reasonable computational scaling.

Electron-photon exchange-correlation approximation for quantum-electrodynamical density-functional theory

Quantum-electrodynamical density-functional theory (QEDFT) provides a promising avenue for exploring complex light-matter interactions in optical cavities for real materials. Similar to conventional density-functional theory, the Kohn-Sham formulation of QEDFT needs approximations for the generally unknown exchange-correlation functional. In addition to the usual electron-electron exchange-correlation potential, an approximation for the electron-photon exchange-correlation potential is needed. A recent electron-photon exchange functional [C. Schäfer , ], derived from the equation of motion of the nonrelativistic Pauli-Fierz Hamiltonian, shows robust performance in one-dimensional systems across weak- and strong-coupling regimes. Yet, its performance in reproducing electron densities in higher dimensions remains unexplored. Here we consider this QEDFT functional approximation from one- to three-dimensional finite systems and across weak to strong light-matter couplings. The electron-photon exchange approximation provides excellent results in the ultrastrong-coupling regime. However, to ensure accuracy also in the weak-coupling regime across higher dimensions, we introduce a computationally efficient renormalization factor for the electron-photon exchange functional, which accounts for part of the electron-photon correlation contribution. These findings extend the applicability of photon-exchange-based functionals to realistic cavity-matter systems, fostering the field of cavity QED (quantum-electrodynamics) materials engineering. Published by the American Physical Society 2024

Detection of data tampering attack in FIR system identification with binary-valued observations

This paper addresses the security detection of data tampering attack in identification of finite impulse response systems with quantized observations. First, we designed a detection algorithm for data tampering attack based on the prior information of the system and gave its online detection form. Second, the introduction of the concepts of the false judgment rate and the missed judgment rate gave a specific evaluation index for the performance of the detection algorithm. Considering the high nonlinearity of binary quantized and the difficulty of obtaining distribution function, we provided calculation methods for two indexes and gave expressions under large samples. Then, the effects of the data length, the prior information of the system parameter, and the attack strategy on the detection algorithm are discussed in this paper. Finally, the theoretical results are verified by numerical simulation.

Exact closed forms for the transmittance of electromagnetic waves in one-dimensional anisotropic periodic media

In this work, we obtain closed expressions for the transfer matrix and the transmittance of electromagnetic waves propagating in finite one-dimensional anisotropic periodic stratified media with an arbitrary number of cells. By invoking the Cayley–Hamilton theorem on the transfer matrix for the electromagnetic field in a periodic stratified media formed by N cells, we obtain a fourth-order recursive relation for the matrix coefficients that defines the so-called Tetranacci polynomials (TPs). In the symmetric case, corresponding to a unit-cell transfer matrix with a characteristic polynomial where the coefficients of the linear and cubic terms are equal, closed expressions for the solutions to the recursive relation, known as symmetric TPs, have recently been derived, allowing us to write the transfer matrix and transmittance in a closed form. We show as sufficient conditions that the 4×4 differential propagation matrix of each layer in the binary unit cell, Δ , a) has eigenvalues of the form ±p1 , ±p2 , with p1≠p2 , and b) its off-diagonal 2×2 block matrices possess the same symmetric structure in both layers. Otherwise, the recursive relations are still solvable for any 4×4 matrix and provide an algorithm to compute the Nth power of the transfer matrix without carrying out explicitly the matrix multiplication of N matrices. We obtain analytical expressions for the dispersion relation and transmittance, in closed form, for two finite periodic systems: the first one consists of two birefringent uniaxial media with their optical axis perpendicular to the z-axis, and the second consists of two isotropic media subject to an external magnetic field oriented along the z-axis and exhibiting the Faraday effect. Our formalism applies also to lossy media, magnetic anisotropy or optical activity.

Linear-space-variant model for Fourier ptychographic microscopy.

Fourier ptychographic microscopy (FPM) needs to realize well-accepted reconstruction by image segmentation and discarding problematic data due to artifacts caused by vignetting. However, the imaging results have long suffered from uneven color blocks and the consequent digital stitching artifacts, failing to bring satisfying experiences to researchers and users over the past decade since the invention of FPM. In fact, the fundamental reason for vignetting artifacts lies in that the acquired data does not match the adopted linear-space-invariant (LSI) forward model, i.e., the actual object function is modulated by a quadratic phase factor during data acquisition, which has been neglected in the advancement of FPM. In this Letter, we rederive a linear-space-variant (LSV) model for FPM and design the corresponding loss function for FPM, termed LSV-FPM. Utilizing LSV-FPM for optimization enables the efficient removal of wrinkle artifacts caused by vignetting in the reconstruction results, without the need of segmenting or discarding images. The effectiveness of LSV-FPM is validated through data acquired in both 4f and finite conjugate single-lens systems.

Subhomogeneous Operator Systems and Classification of Operator Systems Generated by Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}-Commuting Unitaries

A unital C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebra is called N-subhomogeneous if its irreducible representations are finite dimensional with dimension at most N. We extend this notion to operator systems, replacing irreducible representations by boundary representations. This is done by considering UCP(S)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {UCP }(\\mathcal {S})$$\\end{document} which is the matrix state space associated with an operator system S\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {S}$$\\end{document} and identifying the boundary representations as absolute matrix extreme points. We show that two N-subhomogeneous operator systems are completely order equivalent if and only if they are N-order equivalent. Moreover, we show that a unital N-positive map into a finite dimensional N-subhomogeneous operator system is completely positive. We apply these tools to classify pairs of q-commuting unitaries up to ∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$*$$\\end{document}-isomorphism. Similar results are obtained for operator systems related to higher dimensional non-commutative tori.

Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions.

Long-range interactions are relevant for a large variety of quantum systems in quantum optics and condensed matter physics. In particular, the control of quantum-optical platforms promises to gain deep insights into quantum-critical properties induced by the long-range nature of interactions. From a theoretical perspective, long-range interactions are notoriously complicated to treat. Here, we give an overview of recent advancements to investigate quantum magnets with long-range interactions focusing on two techniques based on Monte Carlo integration. First, the method of perturbative continuous unitary transformations where classical Monte Carlo integration is applied within the embedding scheme of white graphs. This linked-cluster expansion allows extracting high-order series expansions of energies and observables in the thermodynamic limit. Second, stochastic series expansion quantum Monte Carlo integration enables calculations on large finite systems. Finite-size scaling can then be used to determine the physical properties of the infinite system. In recent years, both techniques have been applied successfully to one- and two-dimensional quantum magnets involving long-range Ising, XY, and Heisenberg interactions on various bipartite and non-bipartite lattices. Here, we summarise the obtained quantum-critical properties including critical exponents for all these systems in a coherent way. Further, we review how long-range interactions are used to study quantum phase transitions above the upper critical dimension and the scaling techniques to extract these quantum critical properties from the numerical calculations.

Modeling and simulation of xenon storage and supply system for electric propulsion system based on fundamental equation of state

The electric propulsion system (EPS) xenon storage and supply system (SSS) is a complex pipeline network system, which involves the multi-physics coupled fields of transcritical flow, heat transfer, rigid body motion, electromagnetics, and control. Based on the fundamental equation of state, a one-dimensional finite volume model system is proposed for compressible transcritical transient pipe flow. Six typical components of the SSS are modularization modeled by using an object-oriented programming method in Fortran 2018. To evaluate the performance of the algorithm, a simulation model consisting of 77 components is developed for a proportional controlled EPS xenon SSS, and a system-level simulation is performed. Compared with the standard case constructed on the Amesim platform, the model has a pressure rise time error lower than 6%, and the restrictors mass-flow-rate errors of the anode, cathode, and neutralizer are less than 2.8% of the rated flow rate after stabilization. Moreover, the proposed model yields more accurate results at certain operating points. The model system provides an efficient reference for the design and optimization of EPS SSSs, and offers a new approach to simulate complex cryogenic pipe flow systems.

The method for design of combined electromagnetic shield for overhead power lines magnetic field

Aim. Development of the method of designing a combined electromagnetic shield, consisting of active and passive parts, to improve the effectiveness of reduction of industrial frequency magnetic field created by two-circuit overhead power lines in residential buildings. Methodology. The problem of design of combined electromagnetic shield including robust system of active shielding and electromagnetic passive shield of initial magnetic field solved based on of the multi-criteria two-player antagonistic game. The game payoff vector calculated based on the finite element calculations system COMSOL Muliphysics. The game solution calculated based on the particles multiswarm optimization algorithms. During the design of combined electromagnetic shields spatial location coordinates of shielding winding, the currents and phases in the shielding winding of active shielding, geometric dimensions and thickness of the electromagnetic passive shield are calculated. Results. The results of theoretical and experimental studies of combined electromagnetic passive and active shielding of magnetic field in residential building from power transmission line with a «Barrel» type arrangement of wires presented. Originality. For the first time the method of designing a combined electromagnetic shield, consisting of active and passive parts, for more effective reduction of the magnetic field of industrial frequency created by two-circuit overhead power lines in residential buildings is developed. Practical value. Based on results of calculated and experimental study the shielding efficiency of the initial magnetic field determined that shielding factors whith only electromagnetic passive shield is more 2 units, whith only active shield is more 4 units and with combined electromagnetic passive and active shield is more 10 units. It is shown the possibility to reduce the level of magnetic field induction in residential building from power transmission line with a «Barrel» type arrangement of wires by means of a combined electromagnetic passive and active shielding with single compensating winding to 0.5 μT level safe for the population. References 53, figures 15.

Bilateral Elimination Rule-Based Finite Class Bayesian Inference System for Circular and Linear Walking Prediction.

The prediction of upcoming circular walking during linear walking is important for the usability and safety of the interaction between a lower limb assistive device and the wearer. This study aims to build a bilateral elimination rule-based finite class Bayesian inference system (BER-FC-BesIS) with the ability to predict the transition between circular walking and linear walking using inertial measurement units. Bilateral motion data of the human body were used to improve the recognition and prediction accuracy of BER-FC-BesIS. The mean predicted time of BER-FC-BesIS in predicting the left and right lower limbs' upcoming steady walking activities is 119.32 ± 9.71 ms and 113.75 ± 11.83 ms, respectively. The mean time differences between the predicted time and the real time of BER-FC-BesIS in the left and right lower limbs' prediction are 14.22 ± 3.74 ms and 13.59 ± 4.92 ms, respectively. The prediction accuracy of BER-FC-BesIS is 93.98%. Upcoming steady walking activities (e.g., linear walking and circular walking) can be accurately predicted by BER-FC-BesIS innovatively. This study could be helpful and instructional to improve the lower limb assistive devices' capabilities of walking activity prediction with emphasis on non-linear walking activities in daily living.

On a Stokes hemivariational inequality for incompressible fluid flows with damping

In this paper, a Stokes hemivariational inequality is studied for incompressible fluid flows with the damping effect. The hemivariational inequality feature is caused by the presence of a nonsmooth slip boundary condition of friction type. Well-posedness of the Stokes hemivariational inequality is established through the consideration of a minimization problem. Mixed finite element methods are introduced to solve the Stokes hemivariational inequality and error estimates are derived for the mixed finite element solutions. The error estimates are of optimal order for low-order mixed element pairs under suitable solution regularity assumptions. An efficient iterative algorithm is introduced to solve the mixed finite element system. Numerical results are reported on the performance of the proposed algorithm and the numerical convergence orders of the finite element solutions.

Mechanical response and damage evolution of CF/PEEK‐reinforced Al metal‐composite hybrid structure at high strain rate

AbstractA CF/PEEK‐reinforced Al metal‐composite hybrid structure (CF/PEEK/Al) and CF/PEEK bar were subjected to high strain rate compression tests with a split Hopkinson pressure bar (SHPB). With the increase in strain rates, both CF/PEEK and CF/PEEK/Al showed the strain rate strengthening effect, and the microscopic fracture surface of CF/PEEK changes from rough to smooth. In the plastic rheological stage of stress–strain curve, CF/PEEK shows a plateau effect, while CF/PEEK/Al shows the strain weakening effect. When the strain rate exceeds 3800 s−1, the stress–strain curve exhibits a secondary wave peak. The peak values of the secondary peak in CF/PEEK/Al are larger than CF/PEEK. In terms of peak stress, yield stress, and specific energy absorption, CF/PEEK/Al outperforms CF/PEEK. Compared with other structures, the CF/PEEK/Al metal‐composite hybrid structure has certain advantages in terms of yield strength and yield strain. The finite element method (FEM) and DIC system were applied to observe the dynamic damage process in the compression impact test. It was found that in CF/PEEK/A1, the Al thin‐walled tube was damaged and cracked at the contact interface, and the inner CF/PEEK began to be damaged at the contact center with the input bar. And at 335 μs after contact began, the shear band ran through to the side of the samples.Highlights A CF/PEEK‐reinforced Al metal‐composite hybrid structure (CF/PEEK/Al) was proposed, which is superior to CF/PEEK. When the strain rate exceeds 3800 s−1, the stress–strain curves of CF/PEEK and CF/PEEK/Al exhibit a secondary wave peak. The peak values of the secondary peak in CF/PEEK/Al are larger than CF/PEEK. With the increase in strain rates, both CF/PEEK and CF/PEEK/Al showed the strain rate strengthening effect, and the microscopic fracture surface of CF/PEEK changes from rough to smooth. In CF/PEEK/A1, the Al thin‐walled tube was damaged and cracked at the contact interface, and the inner CF/PEEK began to be damaged at the contact center with the input bar. And at 335 μs after contact began, the shear band ran through to the side of the samples.

Damping separation of finite open systems in gravity-related experiments in the free molecular flow regime

Damping separation of finite open systems in gravity-related experiments in the free molecular flow regime

On complementarity and distribution of imaginarity in finite dimensions

We investigate the complementarity relation among the l1 norm of imaginarity, linear entropy and the Brukner–Zeilinger invariant information in the presence of conjugate symmetry. By using an equality derived from the complementarity relation, we define a quantity named index of imaginarity distribution with respect to the imaginarity, linear entropy and invariant information in finite dimensional quantum systems. We show that the index of imaginarity distribution is nonnegative and upper bounded by the square of the l1 norm of imaginarity, and serves as an invaluable tool in characterizing effectively the imaginarity distribution. Detailed examples are presented to illustrate our theoretical analysis.

Fully Dynamic G3W2 Self-Energy for Finite Systems: Formulas and Benchmark.

Over the years, Hedin's GW self-energy has been proven to be a rather accurate and simple approximation to evaluate electronic quasiparticle energies in solids and in molecules. Attempts to improve over the simple GW approximation, the so-called vertex corrections, have been constantly proposed in the literature. Here, we derive, analyze, and benchmark the complete second-order term in the screened Coulomb interaction W for finite systems. This self-energy named G3W2 contains all the possible time orderings that combine 3 Green's functions G and 2 dynamic W. We present the analytic formula and its imaginary frequency counterpart, with the latter allowing us to treat larger molecules. The accuracy of the G3W2 self-energy is evaluated on well-established benchmarks (GW100, Acceptor 24, and Core 65) for valence and core quasiparticle energies. Its link with the simpler static approximation, named SOSEX for static screened second-order exchange, is analyzed, which leads us to propose a more consistent approximation named 2SOSEX. In the end, we find that neither the G3W2 self-energy nor any of the investigated approximations to it improve over one-shot G0W0 with a good starting point. Only quasi-particle self-consistent GW HOMO energies are slightly improved by addition of the G3W2 self-energy correction. We show that this is due to the self-consistent update of the screened Coulomb interaction, leading to an overall sign change of the vertex correction to the frontier quasiparticle energies.

Asymptotic performance of reconfigurable intelligent surface assisted MIMO communication for large systems using random matrix theory

AbstractReconfigurable intelligent surface (RIS) can provide unprecedented spectral efficiency gains and excellent ability to manipulate electromagnetic waves. This article considered a RIS‐assisted multiuser multiple‐input multiple‐output (MIMO) downlink system, where the beamforming at the base station and RIS are jointly designed to maximize the sum‐rate. For the large dimension scenario and high‐rank beamforming matrix, the accurate deterministic approximations from random matrix theory are then utilized to simplify the RIS‐assisted MIMO systems. The asymptotical signal‐to‐interference‐plus‐noise ratio values obtained through random matrix theory is infinitely close to the theoretical limits calculated by accurately iteration. And the performance of the proposed algorithm computed via the sharing second‐order channel statistics matches that of the RIS algorithm with sharing full channel state information asymptotically. The deterministic approximations are instrumental to get improvement into the structure of the optimal beamforming and to reduce the implementation complexity in large‐scale MIMO system. Numerical simulations results are provided to evaluate and verify the accuracy of the asymptotic results obtained from the proposed algorithm in the finite system regime. With the complex operation process of large dimension matrix reducing to the deterministic approximations, a lower computational complexity can be obtained compared with other methods.

Fast Two-Grid Finite Element Algorithm for a Fractional Klein- Gordon Equation

In this article, we propose a spatial two-grid finite element algorithm combined with a shifted convolution quadrature (SCQ) formula for solving the fractional Klein-Gordon equation. The time direction at tn − θ is approximated utilizing a second-order SCQ formula, where θ is an arbitrary constant. The spatial discretization is performed using a two-grid finite element method involving three steps: calculating the numerical solution by solving a nonlinear system iteratively on the coarse grid, obtaining the interpolation solution based on the computed solutions in the first step, and solving a linear finite element system on the fine grid. We present a numerical algorithm, validate the two-grid finite element method’s effectiveness, and demonstrate the computational efficiency for our method by the comparison of the computing results between the two-grid finite element method and the standard finite element method.

Optimal work extraction from quantum batteries based on the expected utility hypothesis.

Work extraction in quantum finite systems is an important issue in quantum thermodynamics. The optimal work extracted is called ergotropy, and it is achieved by maximizing the average work extracted over all the unitary cycles. However, an agent that is non-neutral to risk is affected by fluctuations and should extract work by following the expected utility hypothesis. Thus, we investigate the optimal work extraction performed by a risk non-neutral agent by maximizing the average utility function over all the unitary cycles. We mainly focus on initial states that are incoherent with respect to the energy basis, achieving a probability distribution of work. In this case we show how the optimal work extraction will be performed with an incoherent unitary transformation, namely a permutation of the energy basis, which depends on the risk aversion of the agent. We give several examples, in particular also the work extraction from an ensemble of quantum batteries is examined. Furthermore, we also investigate how work extraction is affected by the presence of initial quantum coherence in the energy basis by considering a quasiprobability distribution of work.

Transmission of Polarized Electrons through Multilayered Spintronics

Objectives: We study transmission of polarized electrons through multilayered spintronics of the form of n-cell periodic (L/R)n and symmetric (L/R)nL multilayers. L and R are layers of ferromagnetic semiconductors or insulators. The multilayers are of arbitrary sizes with layer L of width a and layer R of width b. The number of cells n is arbitrary positive integer. For specific examples, we use ferromagnetic semiconductors Ga0.73Mn0.27N, In0.92Fe0.08As and Ga0.8Fe0.2N which have different sd-exchange energies. For the insulators, we use non-ferromagnetic insulator Al0.3Ga0.7As, and ferromagnetic insulator Al0.9Fe0.1Sb. Methods: For the purpose of the study, we will calculate transmission coefficients of polarized electrons through each multilayer by using the method of transfer matrix for finite periodic systems. Energy dependencies are analytically derived and generalize the transmission through several types of multilayered spintronics, accommodating an arbitrary number of cells and layer widths embedded between ferromagnetic semiconductors. Results will be derived for multilayers with ferromagnetic layers that are the same as or different from the ferromagnetic semiconductors embedded in the multilayer. Results: Various characteristics of transmissions are obtained from low transmissions to high transmissions with sharp peaks about certain energies, depending on the ferromagnetic semiconducting layers and the insulating layers being used for the multilayers. By varying the materials and sizes of the layers one can arrange desired transmissions such as those with high transmissions at resonances.