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We investigate the effects of the electromagnetic vacuum field on a harmonically bound electron. We show that in the electric-dipole approximation the model atom couples only to an effective one-dimensional electric field. In a simplified form, in which the problem is reduced to a single spatial dimension, we determine, analytically, the form of the ground state and discuss the significance of this state.

We investigate the effects of the electromagnetic vacuum field on a harmonically bound electron. We show that in the electric-dipole approximation the model atom couples only to an effective one-dimensional electric field. In a simplified form, in which the problem is reduced to a single spatial dimension, we determine, analytically, the form of the ground state and discuss the significance of this state. [ABSTRACT FROM AUTHOR]

The credible solution of discretized Maxwell's equations in spaces occupied by Lorentz dispersive media is the main subject of this work. Specifically, we introduce a finite‐difference time‐domain (FDTD) algorithm with a typical (2,4) structure that features dispersion‐relation‐preserving characteristics and produces reduced numerical errors in two‐dimensional electromagnetic simulations, compared to the standard approach with similar computational requirements. We consider the case of dispersive media with non‐vanishing absorption coefficients and investigate different options for the suitable modification of the spatial approximations, so that the accomplished accuracy is optimized for a given computational overhead. The properties of the proposed FDTD technique are thoroughly examined, both theoretically and in numerical tests, and the performance upgrade compared with the conventional solution is assessed. [ABSTRACT FROM AUTHOR]

The possibility of the breaking of Lorentz symmetry has been discussed in many models of quantum gravity. In this paper we follow the Lorentz violation model in Ref. [14] (i.e., our previous work) to discuss the Doppler frequency shift of photons and the Compton scattering process between photons and electrons, pointing out that following the idea in Ref. [14] we have to modify the usual quantum relation of photons in the Doppler effect. But due to the current limited information and knowledge, we could not yet determine the specific expression for the correction coefficient in the modified quantum relation of photons. However, the phenomenon called spontaneous radiation in a cyclotron maser give us an opportunity to see what the expression for this correction coefficient might look like. Therefor, under some necessary constraints, we construct a very concise expression for this correction coefficient through the discussion of different cases. And then we use this expression to analyze the wavelength of radiation in the cyclotron maser, which tends to a limited value at v → c, rather than to 0 as predicted by the Lorentz model. And the inverse Compton scattering phenomenon is also discussed and we find that there is a limit to the maximum energy that can be obtained by photons in the collision between extremely relativistic particles and low-energy photons, which conclusion is also very different from that obtained from the Lorentz model, in which the energy that can be obtained by the photon tends to be infinite as the velocity of particle is close to c. This paper still follows the purpose in Ref. [14] that the energy and momentum of particles (i.e., any particles, including photons) cannot be infinite, otherwise it will make some physical scenarios invalid. When the parameter Q characterizing the degree of deviation from the Lorentz model is equal to 0, all the results and conclusions in this paper will return to the case as in the Lorentz model, so this paper also provides us with a possible experimental scheme to determine the value of Q in Ref. [14], although it still requires extremely high experimental energy.

Background. Interest in the study of microwave metamaterials is associated with the possibility of using them to achieve the required frequency and polarization selective properties of interaction with electromagnetic radiation, which cant be obtained for structures based on homogeneous media. Aim. The mathematical model of a chiral metamaterial based on a periodic matrix of arbitrarily oriented conducting thin-wire cylindrical helices located in a homogeneous isotropic container creation is considered. Unlike known models, it takes into account the explicit form of the dependence of the effective permittivity and the relative chirality parameter on the helices concentration. Methods. The heterogeneity of a chiral metamaterial based on the Maxwell Garnett formula, which makes it possible to determine the effective dielectric permittivity from the permeabilities of the container and the region occupied by conducting mirror asymmetric inclusions is taken into account when creating a mathematical model. The dispersion of permittivity using the quadratic Lorentz formula and the dispersion of the chirality parameter based on the Condon model are taken into account. Results. Analytical frequency-dependent expressions for the effective permittivity and the chirality parameter taking into account the concentration of helices and their geometric parameters, were obtained in the work. The expression for the relationship between the dimensionless volume concentration of inclusions and the distance between adjacent elements is obtained. The quasi-static approach is used to calculate the resonant frequency of conducting thin-wire cylindrical helices. Conclusion. The proposed method for constructing a mathematical model can be applied to chiral metamaterials based on periodic matrices of conductive elements of an arbitrary mirror asymmetric spatial configuration

Deep neural networks, often equipped with powerful auto-optimization tools, find widespread use in diverse domains like NLP and computer vision. However, traditional neural architectures come with specific inductive biases, designed to reduce parameter search space, cut computational costs, or introduce domain expertise into the network design. In contrast, multilayer perceptrons (MLPs) offer greater freedom and lower inductive bias than convolutional neural networks (CNNs), making them versatile for learning complex patterns. Despite their flexibility, most neural architectures operate in a flat Euclidean space, which may not be optimal for various data types, particularly those with hierarchical correlations. In this paper, we move one step further by introducing the hyperbolic Res-MLP (HR-MLP), an architecture extending the attention-free MLP to a non-Euclidean space. HR-MLP leverages fully hyperbolic layers for feature embeddings and end-to-end image classification. Our novel Lorentz cross-patch and cross-channel layers enable direct hyperbolic operations with fewer parameters, facilitating faster training and superior performance compared to Euclidean counterparts. Experimental results on CIFAR10, CIFAR100, and MiniImageNet confirm HR-MLP's competitive and improved performance. [ABSTRACT FROM AUTHOR]

A broadband absorber that utilizes a dispersive metamaterial and covers the entire microwave X-band (8–12 GHz) is proposed in the present study. An ideal absorber attached to the surface of a perfect electric conductor requires the permittivity of the absorbing layer to be anomalously dispersive in the targeted broad frequency band. We show that anomalous dispersion of the permittivity for the X-band can be fitted to a two-pole Lorentz oscillator model and realized with the use of a double-layered, square-loop metamaterial. We explain the connection between the two-pole oscillator model and the double-layered, square-loop metamaterial using an equivalent circuit model and present explicit design rules for the metamaterial. We fabricate a 4-mm-thick metamaterial absorber with flexible silicon rubber, a resistor element, and conductive wire using carbon and silver conductive ink. Our metamaterial absorber achieves a reflectance of less than −20 dB over the entire X-band region.

The authors have developed a mathematical model to determine the conditions whereby the rate of increase of greenhouse gas (GHG) concentrations in the atmosphere is minimized, and the given level of life quality of the population is maintained. The model combines in a holistic structure the economic sectors described in the same way. Each of them is considered in terms of the level of productivity, number of jobs, and the level of structural disturbances (the six-sector Lorenz model with variable coefficients that depend on the GHG level). The model makes it possible to investigate how changes in the GHG level and the relationships between different sectors of the economy affect the risks to sustainable development and the general level of the life quality of the population. The authors have determined conditions for the emergence of turbulent operating modes, which lead to an increase in the total number of structural disturbances and a decrease in the aggregate level of productivity. They also proposed an approach to assessing the level of threats to sustainable development under climate changes. [ABSTRACT FROM AUTHOR]

A mathematical model has been developed to determine the conditions whereby the growth rate of the concentration of greenhouse gases (GHG) in the atmosphere is minimized and the given standard of living of the population is maintained. The model combines in a single structure identically described sectors of the economy, each being considered in terms of productivity levels, number of jobs and structural violations (six-sector Lorenz model with variable coefficients that depend on the GHG level). The model makes it possible to investigate how changes in the level of GHG and the interrelationships between different sectors of the economy affect the risks of sustainable development and the general level of the quality of life of the population. The conditions for the emergence of turbulent modes of operation, which lead to an increase in the total number of structural violations and a decrease in the total level of productivity, have been determined. An approach to assessing the level of threats to sustainable development under climate change is proposed. [ABSTRACT FROM AUTHOR]

This work develops a finite-difference time-domain (FDTD) methodology with controllable accuracy within prescribed frequency bands, which is suitable for problems incorporating material dispersion described by the Lorentz model. An optimization technique is introduced, which is based on the one-dimensional (1D) numerical dispersion relation and modifies appropriately the form of the spatial operators. Through the implementation of a least-squares approach, the numerical wavenumber is forced to be close to the exact one within arbitrary parts of the frequency spectrum, located either below or above the medium's absorption band, according to the spectral content of the simulation. The formulation initially considers 1D problems and lossless materials. Yet, generalizations to multi-dimensional problems and the incorporation of at least low-loss materials are also discussed. • An optimized (2,4) FDTD scheme for problems with dispersive materials is developed. • The numerical dispersion relation is used for the extraction of modified spatial finite-difference operators. • The proposed method accomplishes minimized errors within a preselected range of frequencies. • The new technique features simple implementation and identical computational cost with the original algorithm. [ABSTRACT FROM AUTHOR]

Recently, hyperbolic deep neural networks (HDNNs) have been gaining momentum as the deep representations in the hyperbolic space provide high fidelity embeddings with few dimensions, especially for data possessing hierarchical structure. Such a hyperbolic neural architecture is quickly extended to different scientific fields, including natural language processing, single-cell RNA-sequence analysis, graph embedding, financial analysis, and computer vision. The promising results demonstrate its superior capability, significant compactness of the model, and a substantially better physical interpretability than its counterpart in the euclidean space. To stimulate future research, this paper presents a comprehensive review of the literature around the neural components in the construction of HDNN, as well as the generalization of the leading deep approaches to the hyperbolic space. It also presents current applications of various tasks, together with insightful observations and identifying open questions and promising future directions. [ABSTRACT FROM AUTHOR]

We studied terahertz (THz) optical and dielectric properties of stoichiometric lithium tantalate (sLT) from room down to liquid nitrogen temperature in the range of 0.15–1.8 THz using terahertz time-domain spectroscopy. Two-oscillator Lorentz models were fitted well to the crystal properties for both ordinary and extraordinary waves. We also studied changes in sLT ultraviolet (UV) absorption from room to liquid nitrogen temperature. The measurements showed a significant drop in absorption in both the THz and UV ranges with cooling. According to these results cooling should increase lithium tantalate potential in optical-to-terahertz conversion of high-power 800-nm radiation. The measured properties can be used in designing nonlinear optical conversion schemes and devices based on sLT. [ABSTRACT FROM AUTHOR]

• Light can also arise the phenomenon of shock wave in the context of a special Lorentz violation model, just like the shock wave in acoustic. • Making a correction to the quantum relation of photons so that the energy and momentum of photons are finite in any cases, such as the energy or momentum of spontaneous and synchrotron radiation in a cyclotron maser, and the energy and momentum obtained by photons in inverse Compton scattering, rather than be infinite as predicted by the Lorentz model. The possibility of the breaking of Lorentz symmetry has been discussed in many models of quantum gravity. In this paper we follow the Lorentz violation model in Ref. [14] (i.e., our previous work) to discuss the Doppler frequency shift of photons and the Compton scattering process between photons and electrons, pointing out that following the idea in Ref. [14] we have to modify the usual quantum relation of photons in the Doppler effect. But due to the current limited information and knowledge, we could not yet determine the specific expression for the correction coefficient in the modified quantum relation of photons. However, the phenomenon called spontaneous radiation in a cyclotron maser give us an opportunity to see what the expression for this correction coefficient might look like. Therefor, under some necessary constraints, we construct a very concise expression for this correction coefficient through the discussion of different cases. And then we use this expression to analyze the wavelength of radiation in the cyclotron maser, which tends to a limited value at v → c, rather than to 0 as predicted by the Lorentz model. And the inverse Compton scattering phenomenon is also discussed and we find that there is a limit to the maximum energy that can be obtained by photons in the collision between extremely relativistic particles and low-energy photons, which conclusion is also very different from that obtained from the Lorentz model, in which the energy that can be obtained by the photon tends to be infinite as the velocity of particle is close to c. This paper still follows the purpose in Ref. [14] that the energy and momentum of particles (i.e., any particles, including photons) cannot be infinite, otherwise it will make some physical scenarios invalid. When the parameter Q characterizing the degree of deviation from the Lorentz model is equal to 0, all the results and conclusions in this paper will return to the case as in the Lorentz model, so this paper also provides us with a possible experimental scheme to determine the value of Q in Ref. [14] , although it still requires extremely high experimental energy. [ABSTRACT FROM AUTHOR]

In order to characterize the common feature of the general Lorentz violation models that the local speed of light is variable at ultrahigh energy scale, we introduced a parameter n to characterize the variation of the speed of light between inertial systems. And in order not to violate some fundamental principles and experiments’ results, some constraints were imposed on n. Then a coordinate transformation with the parameter n, which meets the symmetry of inertial systems, was naturally obtained.But just to satisfy the symmetry of inertial systems, the expression for n cannot be determined. Inspired by the idea of DSR model, we then discussed a specific expression for n that makes the particle’s energy have a limit rather than be infinite derived from the Lorentz model. We found that the modified dispersion relation corresponding to the specific expression for n is deeply associated with the general formula of dispersion relation from the DSR. The motivation of introducing such a parameter n was also discussed.Finally, we discussed the possible LIV effects from astrophysical observations in GRB events and photon annihilation events. Using the data from GRB 190114C we investigated the special dispersion relation obtained in this paper and found that it appears to fit these data better than the two models corresponding to the first or second order approximation of the general formula of dispersion relation. And similar to the other Lorentz violation models corresponding to the subluminal case, the modified dispersion relation obtained in this paper can also result in increasing the energy threshold of photon annihilation reaction, which is expected to be verified by the future energetic photons events.

An approach to the estimation of distribution parameters with a priori specified constraints is developed. The Lorentz six-sector model is generated and used to analyze on the relationships between food, energy, and water resources, supply systems, epidemic and social situation. It is investigated how the successive transition of interconnected sectors into the mode of deterministic chaos affects the mode of system’s operation as a whole. A method of risk assessment for food safety and their management was created. [ABSTRACT FROM AUTHOR]

The approach to estimating distribution parameters with a priori constraints has been developed. The Lorentz six-sector model has been constructed. Based on this model, the authors have studied the relationships between food, energy, water resources, supply systems, epidemic, and social situations. They also have investigated the impact of the successive transitions of interconnected sectors to the deterministic chaos regime on the operation mode of the whole system. The method of risk assessment for food security and risk management has been elaborated. [ABSTRACT FROM AUTHOR]

Groundwater tables and soil salinity can greatly affect the biogeochemical cycles of carbon and nitrogen by altering soil physicochemical properties. Coastal wetlands with different plant cover types (including bare land, Phragmites australis, and Suaeda salsa wetlands) and groundwater table wetlands (including low groundwater table, medium groundwater table, and high groundwater table wetlands) were investigated in 2012–2013 to characterize the spatial and temporal changes and the effects of groundwater tables on soil organic carbon (SOC) and total nitrogen (TN) in the Yellow River Estuary, China. The results showed that SOCs in 2012 was higher than that in 2013 regardless of the groundwater tables, while TNs was higher in 2013 than in 2012 except in the BL soil with low groundwater tables and the PA wetlands with middle groundwater tables. The SOCs and TNs were mainly concentrated in the top 20 cm soils. SOCc and TNc were fitted very well with soil depth by the general linear fit (p

The resonant detection of terahertz radiation using a dispersive AlN/GaN multichannel high-electron-mobility transistor (HEMT) is analyzed and modeled in this paper. The proposed full-wave model is based on the concurrent solution of the complete hydrodynamic model (CHM) and Maxwell's equations. The CHM is derived from the first three moments of the Boltzmann transport equation (BTE). Considering the variations of the electron temperature and transport parameters along the HEMT channel, this model well characterizes the electron–wave interaction in the device for both low- and high-field conditions. Moreover, the effect of the optical phonon modes of the GaN buffer, which cannot be ignored in the target terahertz frequency band, is described using the Lorentz dispersive model. Employing the developed model, the transmission spectrum of the device is extracted numerically using the finite-difference time-domain (FDTD) method for grating-gate single-, double-, and three-channel HEMT structures. The results show that, at a lattice temperature of 300 K for a GaN grating-gate HEMT with gate periodicity of 680 nm and gate width of 520 nm, at given resonance frequency and overall electron concentration, the resonance depth improves by about 2.7 dB in the three- compared with the single-channel structure. Moreover, it is shown that the detection performance of such a structure at 300 K is similar to the single-channel HEMT at a reduced temperature of 120 K. Therefore, the multichannel HEMTs can show notably improved resonant detection performance, enabling the design of resonant detectors with enhanced sensitivity at room temperature. [ABSTRACT FROM AUTHOR]

Atmospheric attenuation of electromagnetic signals at the 60 GHz frequency band is dominated by oxygen absorption which represents a major obstacle to 5G communications using this band. So far, only empirical equations that fit the experimental absorption data have been reported. These empirical models are not suitable to employ in standard full-wave electromagnetic simulators based on the numerical solution of Maxwell's equations. In this paper, a frequency-dependent material model for atmospheric absorption at the 60 GHz band is presented. Further, a numerical simulator that incorporates this multi-pole material dispersion model and uses the rotating boundary conditions to allow for long propagation distances is developed. The simulation algorithm is based on the auxiliary differential equation finite-difference time-domain (ADE-FDTD) technique which implements the general electric polarization formulation. The results are useful in the prediction of propagation power loss between line-of-sight communication links and in the planning and positioning of ground and air-borne facilities. [ABSTRACT FROM AUTHOR]

In this paper, we consider Maxwell's equations in linear dispersive media described by a single-pole Lorentz model for electronic polarization. We study two classes of commonly used spatial discretizations: finite difference methods (FD) with arbitrary even order accuracy in space and high spatial order discontinuous Galerkin (DG) finite element methods. Both types of spatial discretizations are coupled with second order semi-implicit leap-frog and implicit trapezoidal temporal schemes. By performing detailed dispersion analysis for the semi-discrete and fully discrete schemes, we obtain rigorous quantification of the dispersion error for Lorentz dispersive dielectrics. In particular, comparisons of dispersion error can be made taking into account the model parameters, and mesh sizes in the design of the two types of schemes. This work is a continuation of our previous research on energy-stable numerical schemes for nonlinear dispersive optical media [6,7]. The results for the numerical dispersion analysis of the reduced linear model, considered in the present paper, can guide us in the optimal choice of discretization parameters for the more complicated and nonlinear models. The numerical dispersion analysis of the fully discrete FD and DG schemes, for the dispersive Maxwell model considered in this paper, clearly indicate the dependence of the numerical dispersion errors on spatial and temporal discretizations, their order of accuracy, mesh discretization parameters and model parameters. The results obtained here cannot be arrived at by considering discretizations of Maxwell's equations in free space. In particular, our results contrast the advantages and disadvantages of using high order FD or DG schemes and leap-frog or trapezoidal time integrators over different frequency ranges using a variety of measures of numerical dispersion errors. Finally, we highlight the limitations of the second order accurate temporal discretizations considered. • Maxwell's equations. • Lorentz model. • Numerical dispersion. • Finite differences. • Discontinuous Galerkin finite elements. [ABSTRACT FROM AUTHOR]

Abstract This work deals with the generalization of the Lorentz model. It is made using the Caputo fractional derivative of order 0 < γ ≤ 1 in the frequency domain. The fractional complex dielectric function, index of refraction, reflectance, electric susceptibility were obtained. It is shown that all of them depend not only on the frequency of applied field, but also on the fractional order of the differential equation 0 < γ ≤ 1. This opens the possibility to describe more accurately the experimental results in complex systems. The ordinary results are obtained when γ = 1. [ABSTRACT FROM AUTHOR]

A helical slow-wave structure consisting of a metallic helix supported by double-negative metamaterial (DNG-MTM) rods, symmetrically arranged around the helix, in a metal envelope was analyzed, considering the frequency-dependent permeability and the permittivity of the DNG-MTM following Lorentz and Drude models. The analysis was validated against the 3-D electromagnetic simulation using CST Studio and was extended for studying the effects of the DNG-MTM parameters on the dispersion and interaction impedance of the structure. Tunability of the structure over multiple-frequency bands was also demonstrated. The possible means of metal MTM layering of the radial faces of the discrete support rods were suggested in a more realistic structure configuration. The structure exhibited a high value of interaction impedance as compared to its traditional counterpart, promising enhanced device efficiency and miniaturization. The structure has potential applications in backward-wave amplifiers and backward-wave oscillators. [ABSTRACT FROM AUTHOR]

In this work, we study the dynamical behaviors of the electromagnetic fields and material responses in the hyperbolic metamaterial consisting of periodically arranged metallic and dielectric layers. The thickness of each unit cell is assumed to be much smaller than the wavelength of the electromagnetic waves, so the effective medium concept can be applied. When electromagnetic (EM) fields are present, the responses of the medium in the directions parallel to and perpendicular to the layers are similar to those of Drude and Lorentz media, respectively. We derive the time-dependent energy density of the EM fields and the power loss in the effective medium based on Poynting theorem and the dynamical equations of the polarization field. The time-averaged energy density for harmonic fields was obtained by averaging the energy density in one period, and it reduces to the standard result for the lossless dispersive medium when we turn off the loss. A numerical example is given to reveal the general characteristics of the direction-dependent energy storage capacity of the medium. We also show that the Lagrangian density of the system can be constructed. The Euler–Lagrange equations yield the correct dynamical equations of the electromagnetic fields and the polarization field in the medium. The canonical momentum conjugates to every dynamical field can be derived from the Lagrangian density via differentiation or variation with respect to that field. We apply Legendre transformation to this system and find that the resultant Hamiltonian density is identical to the energy density up to an irrelevant divergence term. This coincidence implies the correctness of the energy density formula we obtained before. We also give a brief discussion about the Hamiltonian dynamics description of the system. The Lagrangian description and Hamiltonian formulation presented in this paper can be further developed for studying the elementary excitations or quasiparticles in other hyperbolic metamaterials.

Reflections from boundaries of the FDTD computational domain lead to inaccurate, even unstable codes when dealing with problems involving double negative (DNG) materials. Here, an efficient and simple algorithm is presented for terminating FDTD in DNG medium which is based on first and second order Mur's absorbing boundary conditions (ABC). FDTD update equations for Mur's ABC formulations are obtained from frequency domain one-way wave equations using piecewise linear recursive convolution (PLRC) method. Numerical examples are given both for 1D and 2D scenarios to demonstrate the validity and stability of the proposed Mur formulations, and its advantages over uniaxial perfectly matched layer (UPML) in reducing computational time and memory requirements. [ABSTRACT FROM AUTHOR]

We construct and study the stochastic force field generated by a Poisson distribution of sources at finite density, x1, x2, . . . , in R3 each of them yielding a long range potential QiΦ(x-xi) with possibly different charges Qi ε R. The potential Φ is assumed to behave typically as ∣x∣-s for large ∣x∣, with s > 1/2. We will denote the resulting random field as "generalized Holtsmark field". We then consider the dynamics of one tagged particle in such random force fields, in several scaling limits where the mean free path is much larger than the average distance between the scatterers. We estimate the diffusive time scale and identify conditions for the vanishing of correlations. These results are used to obtain appropriate kinetic descriptions in terms of a linear Boltzmann or Landau evolution equation depending on the specific choices of the interaction potential. [ABSTRACT FROM AUTHOR]

We investigate a random flight process approximation to a random scatterer Lorentz gas with variable scatterer density in a gravitational field. For power function densities we show how the parameters of the model determine recurrence or transience of the vertical component of the trajectory. Finally, our methods show that, with appropriate scaling of space, time and the density of obstacles, the trajectory of the particle converges to a diffusion with explicitly given parameters. [ABSTRACT FROM AUTHOR]

The aim of this study is to introduce a precise approach for the determination of the optical parameters of mechanically exfoliated gallium selenide (ε–GaSe) thin films from both the measurements of transmittance (T meas) and reflectance (R meas). Specifically, the absorption α(λ) and the reflection R(λ) coefficients can be accurately calculated at any wavelength. Our approach takes into consideration the multiple reflections and transmissions occurring on both sides of the film, providing a comprehensive analysis of the optical behavior. Then, the fundamental optical constants that are the complex refractive index N(λ) and the complex dielectric constant ε(λ) can be accurately determined. The modeling of the imaginary part of this last parameter allows a precise determination of the position of each resonance observed in the transmission and reflectance spectra. The modeling, based on the Lorentz model of interband oscillators, allows us to investigate up to five resonances, at and above the band gap, associated with the critical points of the Brillouin zone. Simultaneously, we consider the splitting on the valence band and the closeness of the indirect-direct minima of the configuration in the conduction band in our analysis. Our investigation reveals that the refractive index of GaSe material varies from 2.8 to 3.3 with strong peaks observed above the band gap at the resonances of 3.2 eV and 3.7 eV. Through the analysis of the oscillator strengths and lifetimes of the observed transitions, we were able to clearly identify the indirect nature of the fundamental band gap of GaSe. Its value of 1.97 eV is largely separated from the direct band gap of about 230 meV. Furthermore, the modeling allows us to estimate the transitions lifetimes. Their values are ranging between 0.6 fs and 24 fs. • Optical transmittance and reflectance measurements at T = 300K of GaSe. • Accurate determination of optical constants of ε–GaSe material. • Modeling the imaginary part of the complex dielectric constant - Lorentz model. • Energies, oscillator strengths, lifetimes of transitions above the band gap. • Large indirect-direct band gaps separation due to strain. [ABSTRACT FROM AUTHOR]

[Display omitted] • Attempt to overcome sensitivity calculation issues in THz metamaterials. • Fabrication of THz metamaterial based on asymmetric double split-ring resonator. • Investigation of optimized dispersion model of the refractive index of the analyte. • Thorough comparison of several models to identify issues. • Modified Lorentz model proposed based on comparisons and investigations. Resonant structures, such as metamaterials, which can focus electromagnetic fields on a localized spot, are essential to perform label-free detection with high sensitivity in the terahertz (THz) range. Moreover, the refractive index (RI) of a sensing analyte is the most important aspect in the optimization of the characteristics of a highly sensitive resonant structure. However, in previous studies, the sensitivity of metamaterials was calculated while considering the RI of an analyte as a constant value. Consequently, the result for a sensing material with a specific absorption spectrum was inaccurate. To solve this problem, this study developed a modified Lorentz model. Split-ring resonator-based metamaterials were fabricated to verify the model, and the glucose-sensing range from 0 to 500 mg/dL was measured using a commercial THz time-domain spectroscopy system. In addition, a finite-difference time-domain simulation was implemented based on the modified Lorentz model and fabrication design of the metamaterials. The calculation results were compared with the measurement results and were found to be consistent. [ABSTRACT FROM AUTHOR]

• Introducing a new parameter to characterize the violation of Lorentz invariance. • Presenting a new modified dispersion relation, which can be regard as a special case of the general rainbow model. • Discussed the upper bound of the given parameter based on the current experiments. • Comparing the special rainbow function with the other two models in the analysis of GRB event. In order to characterize the common feature of the general Lorentz violation models that the local speed of light is variable at ultrahigh energy scale, we introduced a parameter n to characterize the variation of the speed of light between inertial systems. And in order not to violate some fundamental principles and experiments' results, some constraints were imposed on n. Then a coordinate transformation with the parameter n , which meets the symmetry of inertial systems, was naturally obtained. But just to satisfy the symmetry of inertial systems, the expression for n cannot be determined. Inspired by the idea of DSR model, we then discussed a specific expression for n that makes the particle's energy have a limit rather than be infinite derived from the Lorentz model. We found that the modified dispersion relation corresponding to the specific expression for n is deeply associated with the general formula of dispersion relation from the DSR. The motivation of introducing such a parameter n was also discussed. Finally, we discussed the possible LIV effects from astrophysical observations in GRB events and photon annihilation events. Using the data from GRB 190114C we investigated the special dispersion relation obtained in this paper and found that it appears to fit these data better than the two models corresponding to the first or second order approximation of the general formula of dispersion relation. And similar to the other Lorentz violation models corresponding to the subluminal case, the modified dispersion relation obtained in this paper can also result in increasing the energy threshold of photon annihilation reaction, which is expected to be verified by the future energetic photons events. [ABSTRACT FROM AUTHOR]

A nonlinear optimization algorithm based on the Nelder Mead method is used to characterize the frequency dependent permittivity of 15 materials based on Lorentz, modified Lorentz, Drude and Lorentz-Drude models. The optimized model parameters are used to calculate the complex relative permittivity of each material and compare it with experimental data. In each case, a very good match is found between the optimized and experimental data over a long wavelength range. Comparative study of the models used for each material is performed based on accuracy, wavelength range of applicability and computational efficiency. The parameters presented can be used for computer simulation of electromagnetic wave phenomena involving these materials. [ABSTRACT FROM AUTHOR]

We consider the motion of a particle along the geodesic lines of the Poincaré half-plane. The particle is specularly reflected when it hits randomly-distributed obstacles that are assumed to be motionless. This is the hyperbolic version of the well-known Lorentz Process studied in the Euclidean context. We analyse the limit in which the density of the obstacles increases to infinity and the size of each obstacle vanishes: under a suitable scaling, we prove that our process converges to a Markovian process, namely a random flight on the hyperbolic manifold. [ABSTRACT FROM AUTHOR]