Real Part Research Articles

Responses of quark-antiquark interactions and heavy quark dynamics to magnetic fields

We investigate the impact of the magnetic field generated by colliding nuclei on heavy quark-antiquark interactions and heavy quark dynamics in the quark-gluon plasma (QGP). By means of the hard-thermal-loop resummation technique combined with dimension-two gluon condensates, the static heavy quark potential and heavy quark momentum diffusion coefficient, which incorporate both perturbative and nonperturbative interactions between heavy quarks and the QGP medium, are computed beyond the lowest Landau level approximation. We find that the imaginary part of the heavy quark potential in the magnetic field exhibits significant anisotropy. Specifically, the absolute value of the imaginary part is larger when the quark-antiquark separation is aligned perpendicular to the magnetic field direction, compared to when it is aligned parallel to the magnetic field direction. The heavy quark momentum diffusion coefficient in the magnetized QGP medium also becomes anisotropic. As the temperature rises, the influence of higher Landau levels becomes increasingly significant, resulting in a decrease in the anisotropy ratio of the heavy quark momentum diffusion coefficient to values even below 1. At sufficiently high temperatures, this ratio ultimately approaches 1. The nonperturbative interactions are indispensable for understanding heavy quark dynamics in the low-temperature region. We also study the response of viscous quark matter to the magnetic field and explore its implications for heavy quark potential, thermal decay widths of quarkonium states, as well as heavy quark momentum diffusion coefficient. Published by the American Physical Society 2024

Scalar field perturbation around a rotating hairy black hole: quasinormal modes, quasibound states and superradiant instability

We consider the quasinormal modes, quasibound states and superradiant instability of a rotating hairy black hole, which possesses a Horndeski hair as deviation from Kerr black hole, under the perturbation of massive scalar field. With the use of the matrix method, we mainly calculate the eigenfrequencies related to those modes of the perturbation. Under the perturbation of the massless scalar field, the Horndeski hair and spin parameter have significant influences on the quasinormal frequency, but its imaginary part is always finite negative and no unstable mode is found. Under the perturbation of the massive scalar field, we focus on the eigenfrequencies of quasibound states and find the modes of which the imaginary part of eigenfrequencies is positive, indicating that the black hole undergoes superradiant instability. Then we scan the parameters and figure out a diagram in the space of Horndeski hair and spin parameters to distinguish the rotating hairy black hole with superradiant instability from the stable one.

Tackling capacitive coupling in broad-band spectral electrical impedance tomography (sEIT) measurements by selecting electrode configurations

SUMMARY Electromagnetic (EM) coupling effects including both inductive and capacitive coupling have long been an essential problem in broad-band spectral electrical impedance tomography (sEIT) measurements at the field scale. Efforts have been made to remove EM coupling numerically or to suppress the effects by modified data acquisition strategies. For near-surface applications with relatively small survey layouts, inductive coupling can be well removed in the mHz to kHz frequency range. With the use of shielded coaxial cables and so-called active electrodes where the amplifiers are mounted at the electrodes, capacitive coupling in sEIT measurements can also be reduced. However, it remains challenging to cope with capacitive coupling between the cable shield and the ground, especially in resistive field conditions. The aim of this study is to deal with this type of capacitive coupling effect by identifying and filtering out sEIT measurements that are strongly affected by capacitive coupling. Based on a correction method for capacitive coupling proposed in a previous study, an approach to estimate measurement errors due to capacitive coupling is presented first. In the second step, a workflow was proposed to calculate the capacitive coupling strength (CCS) for each electrode configuration, which is defined as the ratio of the imaginary part of the impedance induced by capacitive coupling and the imaginary part of the impedance due to the subsurface electrical conductivity. In the final step, measurements with low CCS were selected for inversion and the results were compared with inversion results obtained using the previously developed correction approach. It was found that the filtering method based on CCS is more capable in tackling capacitive coupling compared to using model-based corrections. Spectrally consistent sEIT results up to kHz were obtained using the newly developed filtering method, which were not achieved in previous work using model-based correction.

Topological properties and skin effects modulated by different-density nonreciprocal couplings in the Su-Schrieffer-Heeger structure

We pay attention to the topological properties and skin effects in the one-dimensional Su-Schrieffer-Heeger (SSH) structure, by considering the presence of different-density non-reciprocal couplings. We find that when only one single non-reciprocal coupling term is introduced, e.g., in the middle of the SSH structure, edge states can be induced around the sites suffering from the non-reciprocal coupling. As one non-reciprocal coupling term is introduced in each two cells, the topological phase transition is modified. Besides, new topological edge states and skin effects appear at the ends of the SSH structure, and the edge states can be differentiated by their localities, localization degrees, and the imaginary part of energy. Furthermore, if two neighboring cells of the SSH structure are coupled by the non-reciprocal coupling, the topological edge states and skin effect more well-defined, accompanied by the further change of the topological phase transition condition. These results suggest that the non-reciprocal coupling plays a unique and important role in modulating the topological properties and the skin effects of the one-dimensional SSH structure.

Structural, phonon, optical, electronic, and thermodynamic properties of NpX (X = S, Se, Te) chalcogenides: A DFT study

Binary chalcogenides with small Reststrahlen bands in the far infrared and microwave region make them intriguing for IR sensors and radar communication purposes. In this study, we have theoretically investigated the structural, phonon, electronic, optical, IR optical and thermodynamic properties of NpX, where X = S, Se, and Te chalcogenides. The face-centered cubic structure is relaxed to determine the optimized lattice parameters which increased with an increase in the size of involving chalcogen atom. Band structure reveals their metallic nature. The significant contribution of d and f-states of Np and p-states of chalcogens in band formation is evident from the density of state plots. The detailed analysis of optical parameters including real and imaginary parts of dielectric constant and refractive index, optical conductivity, and optical loss exhibit high absorption in the IR region.

Directional growth of 2-ethylimidazolium d-tartrate crystal along (001) and investigation of optical properties for optical limiting applications

A single crystal of 2-Ethylimidazolium d-Tartrate (2EIMDT) was grown along the preferred direction of (001) by the Sankaranarayanan-Ramasamy method. The growth direction was confirmed by X-ray Diffraction analysis. The optical homogeneity and the defect analysis of the grown crystal were carried out using birefringence interferometry, Williamson-Hall plot, and chemical etching. They revealed that the grown crystal possesses good optical and crystalline quality. Using the optical transmission spectrum, the optical band gap and Urbach energy were estimated to be 5.1 eV and 140 meV, respectively. The temperature dependence of the refractive index and thermo-optic coefficient were measured using the prism coupling technique for different wavelengths. The thermo-optic coefficient was found to be negative with values ∼10−5/°C. The laser damage threshold was estimated to be 6.5 GW/cm2 for a 1064 nm laser. Vickers micro-hardness study revealed that the (001) plane of the crystal is characterized by Meyer's index of 1.93. From the Z-scan measurement, it was found that the grown crystal exhibits two-photon absorption characteristics and the obtained imaginary parts of the third-order nonlinear optical (TONLO) susceptibility is 1.95 × 10−14 esu. Additionally, the onset optical limiting threshold was estimated to be 3.89 × 1012 W/m2 which indicates the potential of 2EIMDT for optical limiting applications.

Vortex Identification Method Based on Topological Analysis and Velocity Gradient Invariance

Abstract Analysis on eddy motion is the essential method for understanding viscous flows. Compared with the current methods to identify the vortex, the study presents a method to investigate vortex structures based on topological analysis and nonlinear dynamics, and establishes a connection between the direction of the vortex and the real eigenvalue of the velocity gradient tensor. The study highlights the significance of the real and imaginary parts of complex eigenvalues in vortex development, wherein the real part indicates topological stability and the imaginary part represents swirling strength, contributing to get the characters of the viscous flows.

Analytic solutions of alpha-beta -time- derivatives complex finance chaotic dynamical system: synchronization and extended center manifold. An explicit approach

The present study focuses on a real finance nonlinear dynamic system (FNLDS), which has been shown to exhibit chaotic behavior. The solutions for such nonlinear dynamical systems (NLDSs) have typically been derived using numerical techniques. The objective of this study aims to; firstly, derive approximate analytical solutions for the complex FNLDS (CFNLDS) by constructing the Picard iterative scheme. The convergence of this scheme is proven, and the error analysis shows good tolerance, indicating the efficiency of the technique. Second, a novel criterion for synchronizing the real and imaginary parts of the system is presented, based on a necessary condition. Thirdly, a new method for constructing the extended center manifold is introduced. The 3D portrait reveals a feedback scroll pattern, while the 2D portrait, representing the mutual components, shows multiple pools. The synchronization of the real and imaginary parts of the system is demonstrated graphically. The FNLDS is tested for sensitivity dependence against tiny variations in the initial conditions, and it is found that the system components are moderately sensitive. Furthermore, the Hamiltonian and the extended center manifold establish a two-fold structure. It is observed that the effect of the α-β derivative leads to a delay in the behavior of the solutions.

Computational Study of the Effect of the Size-Dependent Dielectric Functions of Gold Nanomaterials on Optical Properties

The effect of size on the optical properties of gold nanomaterials has been studied using the theoretical Drude–Sommerfield model. The real and imaginary parts of the dielectric function of bulk as a function of wavelength due to free electron contribution and the real and imaginary parts of the dielectric function of nanogold materials as a function of wavelength due to free electron and bond electron contribution are calculated. The real and imaginary parts of the dielectric function of bulk as a function of wavelength due to the free electron contribution graph and The real and imaginary parts of the dielectric function of nanogold materials as a function of wavelength due to free electron and bond electron contributions are plotted. As we observed from the graphs, the real dielectric functions of both bulk and nanogold materials are inversely proportional to wavelength. The imaginary part of the dielectric function of bulk gold materials is independent of wavelength. At high wavelengths, the size of the gold nanomaterial is highly influenced by both real and imagined dielectric functions at high waves. As the wavelength increases, the effect of the size on the dielectric function also increases. The size-dependent dielectric function of nanomaterials is highly influenced by their optical properties and electrical structure.

Operator Bohr-type inequalities

Abstract The classical Bohr inequality for scalars was extended to the non-commutative case of Hilbert space operators in the literature. The sole goal of this article is to discuss the operator Bohr inequality and present some of its new variants. This includes fresh reverses and refinements of this inequality with applications towards an operator’s real and imaginary parts, not to forget the new discussion of different domains of the parameters. One further application towards the operator Dunkl-Williams inequality will be presented too. While the new results are interesting, we emphasize that the approach used to explore these inequalities differs from the existing literature methods for this context.

The numerical analysis of low diffraction efficiency phenomenon at the blaze wavelength for echelle gratings

In this paper, we explain and unify the low diffraction efficiency behavior of echelle gratings at blaze wavelengths under Littrow mount in terms of the metal refractive index (RI). The similarity in the diffraction efficiency (DE) behavior (e.g., efficiency decline and valley-like diffraction curves for low-efficiency orders) of echelle gratings with different metals at TM polarization points the research line of sight to the RIs. Further, the numerical calculations based on the rigorous vector diffraction theory show that the efficiency behavior of the echelle grating at TM polarization is extremely sensitive to the imaginary part of the RI. This is because there is a series of low light-collecting ability (LCA) regions as the imaginary part of the RI changes in the echelle grating, resulting in several disturbed DE zones. In addition, the increase in groove depth improves the LCA at both polarizations, which moves away from the low LCA region at the TM polarization. This leads to low polarization sensitivity and higher DE for echelle gratings, further revealing the essence of the efficiency improvement by increasing the groove depth. From the RI to the LCA, these results will give new concepts to designing and fabricating broadband high-efficiency echelle gratings.

Exploring Motor Network Connectivity in State-Dependent Transcranial Magnetic Stimulation: A Proof-of-Concept Study.

State-dependent non-invasive brain stimulation (NIBS) informed by electroencephalography (EEG) has contributed to the understanding of NIBS inter-subject and inter-session variability. While these approaches focus on local EEG characteristics, it is acknowledged that the brain exhibits an intrinsic long-range dynamic organization in networks. This proof-of-concept study explores whether EEG connectivity of the primary motor cortex (M1) in the pre-stimulation period aligns with the Motor Network (MN) and how the MN state affects responses to the transcranial magnetic stimulation (TMS) of M1. One thousand suprathreshold TMS pulses were delivered to the left M1 in eight subjects at rest, with simultaneous EEG. Motor-evoked potentials (MEPs) were measured from the right hand. The source space functional connectivity of the left M1 to the whole brain was assessed using the imaginary part of the phase locking value at the frequency of the sensorimotor μ-rhythm in a 1 s window before the pulse. Group-level connectivity revealed functional links between the left M1, left supplementary motor area, and right M1. Also, pulses delivered at high MN connectivity states result in a greater MEP amplitude compared to low connectivity states. At the single-subject level, this relation is more highly expressed in subjects that feature an overall high cortico-spinal excitability. In conclusion, this study paves the way for MN connectivity-based NIBS.

Dual rectangular fuzzy complex matrix equations: extended solution, algebraic solution, solution and their calculating1

In this paper, we focus on generalized fuzzy complex numbers and propose a straightforward matrix method to solve the dual rectangular fuzzy complex matrix equations C · Z ˜ + L ˜ = R · Z ˜ + W ˜ , in which C and R are crisp complex matrices and Z ˜ , L ˜ and M ˜ are fuzzy complex number matrices. The existing methods for solving fuzzy complex matrix equations involve separately calculating the extended solution and the corresponding parameters of the real and imaginary parts, whereby we obtain the algebraic solution of the equations. By means of the interval arithmetic and embedding approach, the n × n dual rectangular fuzzy complex linear systems could be converted into 2n × 2n fuzzy linear systems, which are also equivalent to the 4n × 4n real linear systems. By directly solving the 4n × 4n real linear systems, the algebraic solutions can be obtained. The general dual rectangular fuzzy complex matrix equations and dual rectangular fuzzy complex linear systems are investigated by the generalized inverses of matrices. Finally, some examples are given to illustrate the effectiveness of method.

The Kerr–Bumblebee exact massive and massless scalar quasibound states and Hawking radiation

In this letter, we will focus on the Klein–Gordon equation with rotating axially symmetric black hole solution of the Einstein–Bumblebee theory, so called the Kerr–Bumblebee black hole, as its 3 + 1 background space-time. We start with constructing the covariant Klein–Gordon equation component by component and with the help of the ansatz of separation of variables, we successfully separate the polar part and found the exact solution in terms of Spheroidal Harmonics while the radial exact solution is discovered in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that is resulted in a complex-valued energy levels expression for a massive scalar field, where the real part is the scalar particle’s energy while the imaginary part represents the quasibound stats’s decay. And for a massless scalar, a pure imaginary energy levels is obtained. The quasibound states, thus, describe the decaying nature of the relativistic scalar field bound in the curved Kerr–Bumblebee space-time. We also investigate the Hawking radiation of the Kerr–Bumblebee black hole’s apparent horizon via the Damour–Ruffini method by making use the obtained exact scalar’s wave functions. The radiation distribution function and the Hawking temperature are successfully obtained.

Equalization of RGB coupling efficiencies of metasurface waveguide coupler by adjusting imaginary part of refractive index

Optical metasurfaces offer high-efficiency and flexible wavefront shaping for near-eye displays, especially in wideband waveguide couplers accommodating RGB primary colors. By leveraging the resonance characteristics of sub-wavelength periodic nanostructures, metasurfaces surpass the limitations of traditional optics that rely on multiple components and mediums. In this study, we propose adjustment of the imaginary parts of the material refractive indices as a new method to achieve balanced first-order diffraction efficiencies among RGB colors over a wide field of view (FOV) in an in-coupling metasurface waveguide coupler. Physical mechanism is investigated deeply and systematically in theory. It is found that nanostructure resonances deflect the wavefront and Poynting vector, significantly enhancing first-order diffraction efficiency, while resonance-enhanced absorption plays a crucial role in balancing the diffraction efficiency of RGB primary colors. First experimental demonstration well confirms the practical feasibility of this method and a uniform first-order diffraction efficiency of approximately 20% is achieved among RGB colors across a FOV as large as ∼30° over a single-piece glass substrate. This research provides insights into the design and mechanisms of metasurface waveguide couplers, advancing our understanding of metasurface-based RGB displays and facilitating further advancements in this field.

Combining mBJ exchange potential and bootstrap kernel of TDDFT to compute optical spectra of solids

One of the fundamental challenges in calculating the optical properties of crystalline materials is the accurate description of exciton effects so as to make it computationally viable for studying large systems. We combine the modified Becke-Johnson (mBJ) exchange potential and bootstrap kernel (BSK) of time-dependent density functional theory (TDDFT) to compute the imaginary part of the dielectric function of a variety of semiconductors and insulators (Si, GaAs, NiO, TiO2, LiF, LiCl, SrTiO3 and NaMgF3). The results are compared with the experimental data available in the literature. We also compute their dielectric functions using the random phase approximations (RPA) to verify the effect of the BSK method on the optical spectra of these compounds. We conclude that TDDFT+BSK+mBJ calculations can determine the optical spectra of the solids in good agreement with the experimental data (except for small-energy gap materials such as Si and GaAs) with low computational cost, and using a fully ab initio procedure.

Graphene-Tuned, Tightly Coupled Hybrid Plasmonic Meta-Atoms.

Tightly coupled meta-atoms (TCMAs) are densely packed metamaterials with unnatural refractive indexes. Actively modulated TCMAs with tunable optical properties have found many applications in beam shaping, holography, and enhanced light-matter interactions. Typically, TCMAs are studied in the classic Bloch theory. Here, tightly coupled H-shaped meta-atoms are proposed with an ultra-high permittivity of ~6000, and their active modulation with graphene is designed by using the tightly coupled dipole array (TCDA) theory. The H-shaped meta-atoms are used as dipole arms, and the graphene strips function as the dipole loads. By tuning the chemical potential of graphene, the resonant amplitude, frequency, and permittivity are dynamically modulated. The simulations indicate that the real and imaginary parts of permittivity change from 6854 to 1522 and from 7356 to 2870, respectively. The experimental validation demonstrates a modulation depth of 11.6% in the resonant frequency, i.e., from 219.4 to 195 GHz, and a substantial 52.5% modulation depth in transmittance under a bias voltage of less than 1.5 V.

Transport and dielectric properties of MIS structure with embedded Si QDs (AuPd/SiO2:Si QDs/n-Si) grown by MBE

This study focuses on the growth of silicon quantum dots (Si QDs) on insulator substrates via solid-state dewetting of ultrathin silicon films deposited by molecular beam epitaxy (MBE). The resulting Si QDs exhibit well-defined spherical shapes, low size dispersion with an average diameter of 6 nm, and a high density (1012/cm2), making them ideal for microelectronic applications. Current-voltage spectroscopy and impedance spectroscopy were employed to investigate the electrical transport and dielectric properties of Si QDs integrated into a metal-insulator-semiconductor (MIS) structure (AuPd/SiO2: Si QDs/n-Si). Current-voltage measurements reveal that the insertion of Si QDs into the MIS structure improves the electrical transport by introducing new conduction mechanisms. Impedance measurements demonstrate the influence of Si QDs on the frequency dependence of the real part of the dielectric constant (ε′) and the loss tangent (tan δ). Furthermore, Si QDs impact both the real (M′) and imaginary (M″) parts of the electric modulus. Despite slight deviations in dielectric properties, the MIS structure retains its fundamental nature. These investigations affirm the high electrical quality of Si QDs grown via solid-state dewetting and offer valuable insights for researchers engaged in the development of Si QD-based devices, such as non-volatile memories and MIS photodetectors.

Comparison of the imaginary parts of the atmospheric refractive index structure parameter and aerosol flux based on different measurement methods

Abstract. The complexity of aerosol particle properties and the diversity of characterizations make aerosol vertical transport flux measurements and analysis difficult. Although there are different methods, such as aerosol particle number concentration flux and aerosol mass flux based on the eddy covariance principle as well as aerosol mass flux measurements based on the light-propagated large-aperture scintillation principle, there is a lack of mutual validation among the different methods. In this paper, a comparison of aerosol mass flux measurements based on the eddy covariance principle and aerosol mass flux measurements based on the light-propagated large-aperture scintillation principle is carried out. The key idea of aerosol mass flux measurements based on the light-propagated large-aperture scintillation principle is the determination of the imaginary part of the atmospheric equivalent refractive index structure parameter (AERISP). In this paper, we first compare the AERISPs measured by two different methods and then compare the aerosol mass vertical transport fluxes obtained by different methods. The experiments were conducted on the campus of the University of Science and Technology of China (USTC). A light propagation experiment was carried out between two tall buildings to obtain the imaginary and real parts of the AERISPs for the whole path, which in turn can be used to obtain the aerosol vertical transport flux. An updated visibility meter is installed on the meteorological tower in the middle of the light path, which is utilized to obtain the single-point visibility, which is then converted to the imaginary part of the atmospheric equivalent refractive index (AERI). The imaginary parts of the AERISP were obtained via spectral analysis with visibility data. The results show that the imaginary parts of the AERISPs obtained by different methods are in good agreement. The imaginary part of the AERI measured by the visibility meter and the vertical wind speed obtained by the ultrasonic anemometer were used for covariance calculations to obtain the aerosol vertical transport flux. The trends in aerosol vertical transport fluxes obtained by the different methods are consistent, and there are differences in some details, which may be caused by the inhomogeneity in the vertical transport of aerosol fluxes. The experimental results also showed that urban green land is a sink area for aerosol particles.

A photonic crystal waveguide intersection using phase change material for optical neuromorphic synapses

This paper introduces an innovative photonic crystal device that amalgamates a low cross-talk GaAs waveguide intersection with a ring employing phase change material (PCM) for application in all-optical neuromorphic synapses. The device uses a degenerate optical cavity housing Germanium–Antimony-Telluride (GST) phase-change material whose optical properties can be manipulated via a control signal. The proposed design facilitates the development of a non-volatile synapse for photonic neural networks and optical neuromorphic circuits. Numerical simulations using the finite difference time domain method (FDTD) exhibit a notably high-quality factor of 900 and a minimal cross-talk level of −60 dB at the intersection of two waveguides. To validate the FDTD results, the structure undergoes further simulations using the finite element method (FEM), confirming the accuracy of the initial calculations. The resultant structure achieves transmissions of 81 % and 13 % in the amorphous and fully crystalline states of PCM, respectively, enabling low output power in the crystalline state and high output power in the amorphous state. Moreover, modulation of the transmission coefficient between 13 % and 81 % is feasible by manipulating the crystallization coefficient of GST materials. To reduce the effect of the imaginary part of the refractive index of the GST material, the evaluation of the output transmission results for the GSST material (Ge2Sb2Se4Te1) has been performed. The results revealed that, despite having a lower imaginary part of the refractive index compared to GST, GSST exhibits lower absorption in both amorphous and crystalline states. However, the use of GSST materials shows a 27 % reduction in the figure of merit (FOM), indicating a lower effective range and fewer degrees of freedom in the different crystallization levels of the PCM ring. To investigate the effect of fabrication defects and structural sensitivity, the radius of photonic crystal rods and the rings of GaAs and GST have been changed, and the results indicate that the radius of the photonic crystal rods and the GST ring have negligible effects on the output transmission and resonant wavelength. However, the thickness of the GaAs ring shows a high sensitivity, which leads to a change in the resonance wavelength that is utilized as an effective tool for tuning the pass wavelength through the structure within the 171 nm bandgap range. The transmission loss in the amorphous state is −0.6 dB and in the fully crystalline state −7.5 dB, which is attributed to the absorption of GST material. This proposed photonic crystal synapse structure with an area of less than 30 μm2 significantly minimizes the required space compared to similar silicon photonic structures and increases the prospects for integration and scalability. The compatibility of the materials employed with optical fibre communications at the 1310 nm wavelength further bolsters the practical feasibility of this design. In summary, this paper presents a significant advancement in the domain of neuromorphic photonics by introducing a promising structure with substantial potential for neural network synapses.