Phase Factor Research Articles

Quantum phases of two-component bosons in a non-Hermitian optical lattice system

In this paper, we investigate the quantum phases of two-component bosons in a non-Hermitian optical lattice system featuring a nonreciprocal hopping phase factor. Our analysis focuses on the Bose–Hubbard model in a two-dimensional (2D) square lattice, utilizing the inhomogeneous dynamical Gutzwiller mean-field theory (DGMFT) to examine the ground state. The impact on quantum phases of the inter component interaction varies in the weak-interaction (the inter-component interactions are smaller than intra-component interactions, i.e., [Formula: see text]) and in the strong-interaction (the inter-component interactions are bigger than intra-component interactions, i.e., [Formula: see text]) regime. In the weak regime, we observe a diverse range of quantum phases, including vortex-like liquid, MI islands (the Mott insulator (MI) islands periodically distributed in the superfluid (SF) background) and SF islands (the SF islands periodically distributed in the MI background), and the inter-component counterflow superfluid (CFSF) phases. In the strong regime, we observe phase separation of the two-component bosons.

Generation of periodic evolution patterns by the interaction of pearcey-gaussian beams carrying sidelobe in parabolic potential

Based on the fractional Schrödinger equation, the propagation properties of the Pearcey-Gaussian beam with the sidelobe in the parabolic potential are studied by using the split-step Fourier numerical simulation method. The focusing phenomenon appears without the parabolic potential when Pearcey-Gaussian beam carries the sidelobe. In the case of the parabolic potential, the beam forms the bound state in the propagation process. The period of the bound state decreases as the parabolic potential coefficient increases. In addition, the interaction of two Pearcey-Gaussian beams with the sidelobe in the potential is investigated. The effect of Lévy index, interval parameter, initial phase factor and parabolic potential coefficient on the interaction of two Pearcey-Gaussian beams with sidelobe is considered.

Propagating analysis of Airy beams via complex phase space and ray method.

A complex phase space and ray method is proposed to present intuitive interpretation of unique intensity profiles, parabolic accelerating trajectories, and distinctive phase shifts of Airy beam and its exponentially decaying version (i.e., finite-energy Airy beam). In the complex phase space, finite-energy Airy beam manifests itself as a complex parabolic phase space curve (PSC) which represents a cluster of light rays with complex wave vectors. The complex ray cluster converges to a complex parabolic caustic curve in complex coordinate space. For infinite-energy Airy beam, phase space, PSC, light ray and caustic curve change to real values. In the paraxial condition, Airy beams can maintain parabolic form of PSC and keep constant ray density, which guarantees the non-diffraction property of Airy beam and approximate non-diffraction property of finite-energy Airy beam. From the evolution of vertexes of parabolic PSC along a parabolic trajectory in phase space, one can also give the parabolic caustic curve for Airy beam and the complex parabolic caustic curve for exponentially decaying Airy beam. Further, the special phase and decay factors in the propagating solution of complex amplitude of Airy beams can be directly derived from the phase shifts of light ray cluster along transverse and longitudinal directions. The proposed phase space and ray method can present intuitive comprehension to distinctive propagating characteristics of Airy beams including intensity and phase, without resort to solving wave equation or diffracting integral formula.

Electron Beams on the Brillouin Zone: A Cohomological Approach via Sheaves of Fourier Algebras

Topological states of matter can be classified only in terms of global topological invariants. These global topological invariants are encoded in terms of global observable topological phase factors in the state vectors of electrons. In condensed matter, the energy spectrum of the Hamiltonian operator has a band structure, meaning that it is piecewise continuous. The energy in each continuous piece depends on the quasi-momentum which varies in the Brillouin zone. Thus, the Brillouin zone of quasi-momentum variables constitutes the base localization space of the energy eigenstates of electrons. This is a continuous topological parameter space bearing the homotopy of a torus. Since the base localization space has the homotopy of a torus, if we vary the quasi-momentum in a direction, when the edge of the zone is reached, we obtain a closed path. Then, if we lift this loop from the base space to the sections of the sheaf-theoretic fibration induced by the localization of the energy eigenfunctions, we obtain a global topological phase factor which encodes the topological structure of the Brillouin zone. Because it is homotopically equivalent to a torus, the global phase factor turns out to be quantized, taking integer values. The experimental significance of this model stems from the recent discovery that there are observable global topological phase factors in fairly ordinary materials. In this communication, we show that it is the unitary representation theory of the discrete Heisenberg group in terms of commutative modular symplectic variables, giving rise to a joint commutative representation space endowed with an integral and Z2-invariant symplectic form that articulates the specific form of the topological conditions characterizing both the quantum Hall effect and the spin quantum Hall effect under a unified sheaf-theoretic cohomological framework.

Hom-Lie-Virasoro symmetries in Bloch electron systems and quantum plane in tight binding models

We discuss the Curtright-Zachos (CZ) deformation of the Virasoro algebra and its extensions in terms of magnetic translation (MT) group in a discrete Bloch electron system, so-called the tight binding model (TBM), as well as in its continuous system. We verify that the CZ generators are essentially composed of a specific combination of MT operators representing deformed and undeformed U(1) translational groups, which determine phase factors for a ⁎-bracket commutator. The phase factors can be formulated as a ⁎-ordered product of the commutable U(1) operators by interpreting the AB phase factor of discrete MT action as fluctuation parameter q of a quantum plane. We also show that some sequences of TBM Hamiltonians are described by the CZ generators.

Designing dual ontological products for human factors: a machine learning and harmonistic knowledge-based computational support tool

The physical construct of a dual ontological product is essential for those products which physically interact directly with humans, whereas the product's emotional construct interconnects with human cognition. Multitude of human factor aspects must be considered when designing dual ontological products. To increase the product's impact and reach, designers should also understand the requirements of potential users. Designers find it difficult to achieve the right compromise between these constructions. This research therefore contributes a novel harmonistic knowledge-based computational support tool which makes designers aware of design stage conflicts and consequences of commitments made on human factors in the use phase of the artefact. This paper describes in detail the machine learning and harmonistic knowledge-based system which exploits information collected directly from potential users to proactively assist, guide, and motivate product designers. The paper takes the motorcycle artefact as a case of dual ontological product. The prototype support tool has been evaluated with 28 motorcycle design engineers. The results obtained from this evaluation have shown that the approach and design computational-based tool meet their goals, are beneficial, and are required in design engineering practice.

The propagation of Hermite–Gauss wave packets in optics and quantum mechanics

AbstractThe two‐dimensional paraxial equation of optics and the two‐dimensional time‐dependent Schrödinger equation, derived as approximations of the three‐dimensional Helmholtz equation and the three‐dimensional time‐independent Schrödinger equation, respectively, are identical. Here the free propagation in space and time of Hermite–Gauss wave packets (optics) or harmonic oscillator eigenfunctions (quantum mechanics) is examined in detail. The Gouy phase is shown to be a dynamic phase, appearing as the integral of the adiabatic eigenfrequency or eigenenergy. The wave packets propagate adiabatically in that at each space or time point they are solutions of the instantaneous harmonic problem. In both cases, it is shown that the form of the wave function is unchanged along the loci of the normals to wave fronts. This invariance along such trajectories is connected to the propagation of the invariant amplitude of the corresponding free wave number (optics) or momentum (quantum mechanics) wave packets. It is shown that the van Vleck classical density of trajectories function appears in the wave function amplitude over the complete trajectory. A transformation to the co‐moving frame along a trajectory gives a constant wave function multiplied by a simple energy or frequency phase factor. The Gouy phase becomes the proper time in this frame.Key PointsThis paper builds a bridge between quantum mechanics (QM) and classical optics in that the identity of the paraxial equation of optics and the Schrödinger equation of QM is shown, the Bohmian trajectories of QM are defined in optics, the Gouy phase of optics is defined in QM and given a new interpretation and The space and momentum wave functions are equivalent along a trajectory.

Injectivity of sampled Gabor phase retrieval in spaces with general integrability conditions

It was recently shown that functions in L4([−B,B]) can be uniquely recovered up to a global phase factor from the absolute values of their Gabor transforms sampled on a rectangular lattice. We prove that this remains true if one replaces L4([−B,B]) by Lp([−B,B]) with p∈[1,∞]. To do so, we adapt the original proof by Grohs and Liehr and use a classical sampling result due to Beurling. Furthermore, we present a minor modification of a result of Müntz–Szász type by Zalik. Finally, we consider the implications of our results for more general function spaces obtained by applying the fractional Fourier transform to Lp([−B,B]) and for more general nonuniform sampling sets.

Study on the buffeting response of a long-span truss arch bridge during construction based on a large-scale full bridge model wind tunnel test

The buffeting response of long-span truss arch bridges has become a key factor in the cantilever construction phase. It is essential to study the wind-resistant performance of arch bridges in typical construction stages. In this study, the buffeting displacements and buffeting forces were investigated based on a 1:40 scaled full bridge model wind tunnel test. Three wind attack angles and seven wind yaw angles were considered in the test. The test results show that the maximum lateral buffeting displacements of the cantilever end and the buckle tower top occur at a wind yaw angle between −15 and 15°. Finite-element analysis was performed to investigate the vibration mitigation measures of the arch bridge during the maximum cantilever construction stage. Finally, we propose some recommendations to alleviate the buffeting response of the buckle tower. The results of our study reveal that setting two symmetric wind resistance cables with an angle >20° between the cable direction and the vertical direction is useful in reducing the transverse buffeting displacement of the buckle tower. This study provides new insights into the buffeting response and vibration reduction of long-span truss arch bridges during cantilever construction.

Thermal analysis of the influence of harmonics on the current capacity of medium‐voltage underground power cables

AbstractIn this article, an algorithm is proposed and used to study the influence of harmonics on the behavior of medium‐voltage underground cables in flat formation. The proposed algorithm is a thermal model based on the heat equilibrium of the thermal circuit nodes of the medium‐voltage cable system. The impact of harmonics on the temperature rise of the cable elements and the cable capacity is evaluated in this article. Also, the impact of harmonics on the derating factors of cable for different soil types is presented. Finally, the measurement of temperatures of cable cores is carried out experimentally and compared with the calculated results to validate the proposed algorithm. One of the algorithm merits is that several harmonic percentages can be taken into account for each cable phase individually, and the heat exchange between the cable phases and their sheath is also taken into consideration. From the obtained results, it is illustrated that the presence of harmonics has a remarkable influence on the cable core temperature; mainly, harmonics of the third and fifth orders may lead to dry zone formation around the cable. It is also observed that the presence of harmonics has an important influence on the cable current, especially when it is buried in soil that has high thermal resistivity during the summer season (suction tension = ∞). In summer, the cable core temperature reached 152.162°C, 139.053°C, and 133.375°C when lime, sand, and silty sand, respectively, are used as backfill materials, rather than 90°C in the normal operating condition of the 11 kV three‐phase single‐core cable. It is observed also that with the increase of the soil thermal resistivity, the ratio of /) reached about 1.2 times at 2.5 K m/W soil thermal resistivity. In addition, it is also observed that the impact of harmonics leads to a percentage reduction in the derating factor of the cable center phase by 11.88%–12.37% depending on the composition of the backfill materials.

Thiazolidinediones: Recent Development in Analytical Methodologies.

The instrumental analytical methods that have been developed and utilized for the determination of thiazolidinedione in bulk medications, formulations and biological fluids have been reviewed after an in-depth analysis of the literature published in a variety of analytical and pharmaceutical chemistry-related journals. The approaches covered by this research, which covers the years 2001-2022, include complex methods for analysis, chromatographic techniques and spectrometric analytical procedures. The mobile phase, flow rate, sample matrix, wavelength and other factors identified in the literature were just a few of the parameters used to evaluate thiazolidinediones. The present review focuses on the published analytical techniques for thiazolidinedione analysis that have been previously identified in the literature. The specified outcomes followed extensive learning, and the most recent advances in analytical methods for the identification of pioglitazone, pioglitazone HCl, rosiglitazone, rosiglitazone maleate and lobeglitazone were reviewed. Additionally, this article briefly discusses features of analytical discovery on thiazolidinediones, which will enable readers to access all discoveries in one place with precise outcomes.

Anti-Vascular Endothelial Growth Factor Therapy with or Without Initial Steroid Therapy for Macular Edema in Branch Retinal Vein Occlusion.

In branch retinal vein occlusion (BRVO), administering steroid injections to inhibit expression of inflammatory factors in the first phase of macular edema may reduce recurrence of the edema. The purpose of our study was to investigate the functional and morphological prognosis and frequency of recurrence after injection of an anti-vascular endothelial growth factor (VEGF) with and without initial steroid therapy to treat macular edema with BRVO. Patients with BRVO and macular edema (41 eyes) received intravitreal ranibizumab injection (IRI) alone (IRI group, 21 eyes) or subtenon triamcinolone (STTA) injection and IRI (combination group, 20 eyes). Patients in both groups with recurrent macular edema received further IRI as appropriate. A laser flare meter was used to assess aqueous flare values, and an optical coherence tomography device was used to measure central macular thickness (CMT). Before the first treatment, we obtained samples of aqueous humor and analyzed them by the suspension array method to evaluate VEGF, placental growth factor (PlGF), platelet-derived growth factor (PDGF)-AA, soluble intercellular adhesion molecule (sICAM)-1, monocyte chemoattractant protein 1 (MCP-1), interleukin (IL)-6, IL-8, and interferon-inducible 10-kDa protein (IP-10). The two groups were not significantly different with regard to levels of VEGF, PlGF, PDGF-AA, sICAM-1, MCP-1, IL-6, IL-8, or IP-10. Best-corrected visual acuity, CMT, and aqueous flare value (IRI group, baseline 8.69 ± 4.55 photon counts/ms; combination group, baseline 9.21 ± 3.72 photon counts/ms) improved significantly in both groups without significant intergroup differences. Analyses showed no significant intergroup differences in the mean number of IRIs during the 12-month follow-up, but the proportion of patients without recurrence (ie, who received only one IRI) was significantly higher in the combination group than in the IRI group (P = 0.032). Furthermore, the time to initial recurrence was significantly longer in the combination group than in the IRI group (P = 0.003). These findings suggest that initial STTA injection and IRI may have a synergistic effect in patients with BRVO and macular edema in that they increase the time between anti-VEGF treatments.

Exactly solvable complex PT symmetry potential A[sech(λx) + i tanh(λx)

We obtained the exact solutions of the PT symmetric potential V(x) = A[sech(λx) + i tanh(λx)] and found that this system has no bound-state. The PT symmetric potential was first studied in this article, and the handedness effect is shown from reflection coefficients. As the asymptotically non-vanishing imaginary potential component, when the direction of the incident wave is opposite, the transmission coefficient will emerge a complex phase factor.

Modeling of the Sintered Density in Cu-Al Alloy Using Machine Learning Approaches.

In powder metallurgy materials, sintered density in Cu-Al alloy plays a critical role in detecting mechanical properties. Experimental measurement of this property is costly and time-consuming. In this study, adaptive boosting decision tree, support vector regression, k-nearest neighbors, extreme gradient boosting, and four multilayer perceptron (MLP) models tuned by resilient backpropagation, Levenberg-Marquardt (LM), scaled conjugate gradient, and Bayesian regularization were employed for predicting powder densification through sintering. Yield strength, Young's modulus, volume variation caused by the phase transformation, hardness, liquid volume, liquidus temperature, the solubility ratio among the liquid phase and the solid phase, sintered temperature, solidus temperature, sintered atmosphere, holding time, compaction pressure, particle size, and specific shape factor were regarded as the input parameters of the suggested models. The cross plot, error distribution curve, and cumulative frequency diagram as graphical tools and average percent relative error (APRE), average absolute percent relative error (AAPRE), root mean square error (RMSE), standard deviation (SD), and coefficient of correlation (R) as the statistical evaluations were utilized to estimate the models' accuracy. All of the developed models were compared with preexisting approaches, and the results exhibited that the developed models in the present work are more precise and valid than the existing ones. The designed MLP-LM model was found to be the most precise approach with AAPRE = 1.292%, APRE = -0.032%, SD = 0.020, RMSE = 0.016, and R = 0.989. Lately, outlier detection was applied performing the leverage technique to detect the suspected data points. The outlier detection discovered that few points are located out of the applicability domain of the proposed MLP-LM model.

Analysing the contributions of lower limb muscles to eccentric cycling using musculoskeletal modeling and simulation.

Eccentric (ECC) cycling, compared to traditional concentric cycling, has been shown to improve muscle strength and neuromuscular control at a lower metabolic cost. Despite the popularity of this exercise in the sports and rehabilitation contexts, there is a gap in our knowledge of which muscles are behaving eccentrically during ECC cycling. To this end, we used a musculoskeletal model and computer simulations to calculate joint kinematics and muscle lengths during ECC cycling. Movements were recorded using 3D motion capture technology while cycling eccentrically on a custom-built semi-recumbent ergometer. The software Opensim was used to calculate joint kinematics and muscle lengths from recorded movements. We found that among the primary knee extensors, it was predominantly the Vastii muscles that acted eccentrically in the ECC cycling phase, with other lower limb muscles showing mixed eccentric/concentric activation. Additionally, the muscle force-length and force-velocity factors in the ECC phase suggest that changes to the participant's pose and pedaling speed may elicit larger active muscle forces. Our work provides an interesting application of musculoskeletal modeling to ECC cycling, and an alternative way to help understand in-vivo muscle mechanics during this activity.

A Comprehensive Analysis of PAPR Reduction in Scrambled UFMC and OFDM Using Artificial Bee Colony Algorithm for 5G Communications

ABSTRACT With the advent of 5G communications, the demand for high data rates and improved spectral efficiency has necessitated the exploration of advanced modulation techniques. Orthogonal Frequency Division Multiplexing (OFDM) and Universal Filtered Multi-Carrier (UFMC) are two prominent modulation schemes for 5G systems. However, both OFDM and UFMC suffer from a high Peak-to-Average Power Ratio (PAPR), leading to signal distortion and inefficient power amplification. The Partial Transmit Sequence (PTS) approach is a promising strategy to minimize PAPR in OFDM and is applied to UFMC to minimize PAPR in UFMC and is known as scrambled UFMC (S-UFMC). PTS, however, involves an extensive search to identify the best phase factors that increase computational complexity. The artificial bee colony algorithm is proposed to reduce the computational complexity S-UFMC and OFDM. A novel modulation scheme, amplitude phase shift keying (APSK), is used instead of quadrature phase shift keying (QPSK) and quadrature amplitude modulation (QAM) in S-UFMC and OFDM, which has better performance than conventional modulation schemes. In this research, OFDM, PTS OFDM, UFMC and S-UFMC are compared and it is found that the proposed scrambled UFMC with APSK modulation using ABC algorithm performs better than OFDM and UFMC in terms of PAPR, spectral efficiency and computational complexity.

Concentric triangular mapping with iterative substitution method for PAPR reduction in OCDM system without SI

Abstract OCDM, a new MCM scheme, has been proposed in the literature. Like widely used OFDM, OCDM also has a drawback of high PAPR. PAPR reduction schemes like SLM and PTS require information about phase factors i.e. SI used at the transmitting end for PAPR reduction for recovery of original data signal at the receiver. Transmission and recovery of SI is always a concern. In this paper a new CTM-IS method has been proposed for PAPR reduction of OCDM signal without SI. Main objective of the proposed scheme is to improve the error performance of SI free SLM and PTS based schemes without any degradation in PAPR reduction. PAPR performance and SER performance, over AWGN as well as multipath Rayleigh fading channels, of OCDM signal with proposed CTM-IS scheme is evaluated. Analytical expression for SER of the proposed CTM-IS scheme over AWGN channel is also derived. The computational complexity of the proposed CTM-IS scheme is also presented. Performance of the proposed CTM-IS scheme is compared with the existing MSM combined with SLM (MSM-SLM), CCM combined with SLM (CCM-SLM) and OM combined with SLM (OM-SLM) schemes. The proposed CTM-IS scheme has demonstrated to offer a theoretical power gain of about 3.01 dB, 2.55 dB, and 14.23 dB over MSM-SLM, CCM-SLM and OM-SLM schemes, respectively. Proposed CTM-IS scheme provides better SER performance with respect to MSM-SLM, CCM-SLM and OM-SLM without any loss in the PAPR performance. Moreover, computational complexity of CTM-IS scheme is less than that of MSM-SLM and CCM-SLM schemes.

Compact and high gain slotted patch antenna with moderate bandwidth for 60 GHz applications

A compact and high gain dual semi-circular slotted patch antenna with moderate bandwidth for 60 GHz applications is presented in this article. A rectangular-shaped patch inspires this design. The slotted antenna provides an impedance bandwidth of 1.75 GHz (58.87–60.62 GHz) and a gain of 7.55 dB. The overall size of the proposed antenna is 12 × 9.5 mm2. A dielectric superstrate is used to improve the antenna bandwidth and gain. The proposed antenna with superstrate exhibits an improved bandwidth of 2.48 GHz (58.22–60.70 GHz), an enhanced gain of 11.8 dB, and an efficiency of 95%, respectively. The antenna provides stable time-domain performance (isolation, isolation phase, group delay, and fidelity factor) over the operating band. The design prototype is fabricated and tested experimentally. Measured results exhibit a good agreement with the simulated results. The proposed antenna is suitable for high data-rate radio access and high gain 60 GHz applications.

Condensation phases in a non-Hermitian optical lattices system

We explore the condensate phase of single-species bosons in an optical lattice through the use of dissipative Bose–Hubbard models. The ground state of system possesses a real-energy, which corresponds to non-Hermitian Hamiltonians with non-reciprocal hopping phase factors. Through the application of inhomogeneous dynamical Gutzwiller mean-field theory (DGMFT), we predict a fascinating phenomenon: the ground state displays a periodic arrangement of superfluid islands amidst a Mott insulator sea. Additionally, the number of superfluid islands is proportional to the spatial period squared.

Dynamics of tidal parameters depending on the landslide hazard condition of the salt mine roof

The dynamics of tidal parameters were studied based on the results of tilt observations in 4 points of the landslide hazard zone, which was formed over the exhausted field of a salt mine in the city of Soledar, Donetsk region. The reduction in the thickness of the supporting walls of the salt mine led to the loss of their supporting stability, which led to the lowering of the ground, the destruction of the foundations and walls of residential and administrative buildings in a plot 1.3 km long and 0.5 km wide. To eliminate the risk of collapse, the used underground galleries were filled with salt in order to strengthen their retaining walls.Thus, the landslide hazard zone has become a unique training ground for studying the change in tidal parameters γ and Δϕ depending on the state of the mine roof. In total, 256 continuous hourly monthly series were processed using modern methods of excluding their linear drift and anomalous meteorological disturbances from the initial data at short observation intervals, which made it possible to significantly increase the accuracy of determining tidal parameters based on the results of harmonic analysis. For the first time in the global earth tide practice, the normalization of the tilt parameters during and after strengthening the collapsing roof of the mine was revealed. If before the strengthening of the supporting walls of the underground galleries, the tidal parameters assumed abnormal values (the amplitude factor γ by 30 %, and the phase factor Δϕ by 10—15 degrees differed from the regional analogues), then in the process of backfilling they began to approach their regional values, which they reached a year after the backfilling. The real possibility of using the earth tide method for monitoring and forecasting the landslide hazard and related phenomena of the ground has been proven.