The major goal of this work is to find solutions of Einstein-Maxwell field equations for anisotropic, expansion-free, non-static, spherically distributed matter content. The analytical models that highlight the major benefit of simplicity are shown and this makes it possible to use them as a toy model to illustrate how cavities evolve. Furthermore, the transport equations, quasi-homologous constraints and the junction conditions are also evaluated along with their useful implications. Eventually, the consequences of electric force on this system are summed up in the last section.

We derive the hyperbolic orbit of binary black holes with electric and magnetic charges. In the low-velocity and weak-field regime, by using the Newtonian method, we calculate the total emission rate of energy due to gravitational and electromagnetic radiation from binary black holes with electric and magnetic charges in hyperbolic orbits. Moreover, we develop a formalism to derive the merger rate of binary black holes with electric and magnetic charges from the two-body dynamical capture. We apply the formalism to investigate the effects of the charges on the merger rate for the near-extremal case and find that the effects cannot be ignored.

Using the Monte Carlo method, the compensation temperature and hysteresis loops of a ferrimagnetic mixed spin-3/2 and spin-5/2 Ising-type graphene-like bilayer are investigated induced by different physical parameters such as crystal field, exchange coupling, external magnetic field, and temperature. The variations of magnetization, magnetic susceptibility, specific heat, and internal energy with the change of temperature are discussed. In addition, we also plot the phase diagrams including transition temperature and compensation temperature. Finally, multiple hysteresis loops under certain parameters are given.

In this paper, an active tunable terahertz bandwidth absorber based on single-layer graphene is proposed, which consists of a graphene layer, a photo crystal plate, and a gold substrate. When the Fermi energy (E_f) of graphene is 1.5 eV, the absorber shows high absorption in the range of 3.7 THz–8 THz, and the total absorption rate is 96.8%. By exploring the absorption mechanism of the absorber, the absorber shows excellent physical regulation. The absorber also shows good adjustability by changing the E_f of graphene. This means that the absorber exhibits excellent tunability by adjusting the physical parameters and E_f of the absorber. Meanwhile, the absorber is polarization independent and insensitive to the incident angle. The fine characteristics of the absorber mean that the absorber has superior application value in many fields such as biotechnology and space exploration.

The relativistic transformation rule for temperature is a debated topic for more than 110 years. Several incompatible proposals exist in the literature but a final resolution is still missing. In this work, we reconsider the problem of relativistic transformation rules for a number of thermodynamic parameters including temperature, chemical potential, pressure, entropy and enthalpy densities for a relativistic perfect fluid using relativistic kinetic theory. The analysis is carried out in a fully relativistic covariant manner, and the explicit transformation rules for the above quantities are obtained in both Minkowski and Rindler spacetimes. Our results suggest that the temperature of a moving fluid appears to be colder, supporting the proposal by de Broglie, Einstein, and Planck, in contrast to other proposals. Moreover, in the case of a Rindler fluid, our findings suggest that the total number of particles and the total entropy of a perfect fluid in a box whose bottom is parallel to the Rindler horizon are proportional to the area of the bottom, but are independent of the height of the box, provided the bottom of the box is sufficiently close to the Rindler horizon. The area dependence of the particle number implies that the particles tend to be gathered toward the bottom of the box, and hence implicitly determines the distribution of the chemical potential of the system, whereas the area dependence of the entropy indicates that the entropy is still additive and may have potential applications in explaining the area law of black hole entropy. As a by-product, we also obtain a relativistically refined version of the famous Saha equation which holds in both Minkowski and Rindler spacetimes.

Pronounced changes of nuclear charge radii provide a stringent benchmark on the theoretical models and play a vital role in recognizing various nuclear phenomena. In this work, the systematic evolutions of nuclear charge radii along even Z = 84-120 isotopic chains are first investigated by the recently developed new ansatz under the covariant density functional. The calculated results show that the shell closure effects of nuclear charge radii appear remarkably at the neutron numbers N = 126 and 184. Interestingly, the arch-like shapes of charge radii between these two strong neutron-closed shells are naturally observed. Across the N = 184 shell closure, the abrupt increase in charge radii is still evidently emerged. In addition, the rapid raise of nuclear charge radii from the neutron numbers N = 138 to N = 144 is disclosed clearly in superheavy regions due to the enhanced shape deformation.

In this paper, we develop the teleportation scheme in [Zheng in Phys Rev A 69, 064302, 2004], in the sense that, we work in the strong atom-field coupling regime wherein the rotating wave approximation (RWA) is no longer valid. To achieve the purpose, a scheme consisting of a qubit interacting with a single-mode quantized field is described via the Rabi model (counter rotation terms are taken into account). Our first aim is to teleport an unknown atomic state of a qubit (which interacts with the quantized field in a cavity) to a second qubit (exists in another distant cavity field), beyond the RWA and without the Bell-state measurement method. In the continuation, in a similar way, we teleport an unknown state of a single-mode field too. In fact, it is shown that, in this regime, after applying some particular conditions, containing the interaction time of atom-field in the cavities, adjusting the involved frequencies, as well as the atom-field coupling in the model, if a proper measurement is performed on the state of the first qubit (the related field in the cavity), the unknown states of the qubit (field) can be teleported from the first qubit (cavity field) to the second qubit (cavity field), appropriately. We show that in both considered cases, the teleportation protocol is successfully performed with the maximum possible fidelity, 1, and the acceptable success probability, 0.25.

This work studies the dynamical transmission of chirped optical solitons in a spatially inhomogeneous nonlinear fiber with cubic-quintic-septic nonlinearity, weak nonlocal nonlinearity, self-frequency shift and parity-time (${ \mathcal P }{ \mathcal T }$) symmetry potential. A generalized variable-coefficient nonlinear Schrödinger equation that models the dynamical evolution of solitons has been investigated by the analytical method of similarity transformation and the numerical mixed method of split-step Fourier method and Runge–Kutta method. The analytical self-similar bright and kink solitons, as well as their associated frequency chirps, are derived for the first time. We found that the amplitude of the bright and kink solitons can be controlled by adjusting the imaginary part of the ${ \mathcal P }{ \mathcal T }$-symmetric potential. Moreover, the influence of the initial chirp parameter on the soliton pulse widths is quantitatively analyzed. It is worth emphasizing that we could control the chirp whether it is linear or nonlinear by adjusting optical fiber parameters. The simulation results of bright and kink solitons fit perfectly with the analytical ones, and the stabilities of these soliton solutions against noises are checked by numerical simulation.

It is demonstrated that for the isospin I = 1/2 πN scattering amplitude, T^I=1/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ and $s={m}_{N}^{2}+2{m}_{\pi }^{2}$ are two accumulation points of poles on the second sheet of complex s plane, and are hence accumulation of singularities of T^I=1/2(s, t). For T^I=3/2(s, t), $s={\left({m}_{N}^{2}-{m}_{\pi }^{2}\right)}^{2}/{m}_{N}^{2}$ is the accumulation point of poles on the second sheet of the complex s plane. The proof is valid up to all orders of chiral expansions.

In recent several years, the tensor force, one of the most important components of the nucleon–nucleon force, has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions, such as dissipation dynamics, sub-barrier fusions, and low-lying vibration states of colliding partners. Especially, the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion crosssections systematically. In this work, we present a mini review on the recent progress on this topic. Considering the recent progress of low-energy reaction theories, we will also mention more possible effects of the tensor force on reaction dynamics.

We give a brief review on the formation and the calculation of black hole shadows. Firstly, we introduce the concept of a black hole shadow and the current works on a variety of black hole shadows. Secondly, we present the main methods of calculating photon sphere radius and shadow radius, and then explain how the photon sphere affects the boundary of black hole shadows. We review the analytical calculation for black hole shadows which have analytic expressions for shadow boundary due to the integrable photon motion system. And we introduce the fundamental photon orbits which can explain the patterns of black hole shadow shape. Finally, we review the numerical calculation of black hole shadows with the backward ray-tracing method and introduce some chaotic black hole shadows with self-similar fractal structures. Since the gravitational waves from the merger of binary black holes have been detected, we introduce a couple of shadows of binary black holes, which all have eyebrowlike shadows around the main shadows with the fractal structures. We discuss the invariant phase space structures of the photon motion system in black hole space-time, and explain the formation of black hole shadow is dominated by the invariant manifolds of certain Lyapunov orbits near the fixed points.

We investigate theoretically valley-resolved lateral shift of electrons traversing an n–p–n junction bulit on a typical tilted Dirac system (8-Pmmn borophene). A gauge-invariant formula on Goos–Hänchen (GH) shift of transmitted beams is derived, which holds for any anisotropic isoenergy surface. The tilt term brings valley dependence of relative position between the isoenergy surface in n region and that in the p region. Consequently, valley double refraction can occur at the n–p interface. The exiting positions of two valley-polarized beams depend on the incident angle and energy of incident beam and barrier parameters. Their spatial distance D can be enhanced to be ten to a hundred times larger than the barrier width. Due to tilting-induced high anisotropy of the isoenergy surface, D depends strongly on the barrier orientation. It is always zero when the junction is along the tilt direction of Dirac cones. Thus GH effect of transmitted beams in tilted Dirac systems can be utilized to design anisotropic and valley-resolved beam-splitter.

We conduct two group reductions of the Ablowitz–Kaup–Newell–Segur matrix spectral problems to present a class of novel reduced nonlocal reverse-spacetime integrable modified Korteweg–de Vries equations. One reduction is local, replacing the spectral parameter with its negative and the other is nonlocal, replacing the spectral parameter with itself. Then by taking advantage of distribution of eigenvalues, we generate soliton solutions from the reflectionless Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues.

In this work, a new superhard material named Pm BN is proposed. The structural properties, stability, mechanical properties, mechanical anisotropy properties, and electronic properties of Pm BN are studied in this work. Pm BN is dynamically and mechanically stable, the relative enthalpy of Pm BN is greater than that of c-BN, and in this respect, and it is more favorable than that of T-B₃N₃, T-B₇N₇, tP24 BN, Imm2 BN, NiAs BN, and rocksalt BN. The Young's modulus, bulk modulus, and shear modulus of Pm BN are 327 GPa, 331 GPa, and 738 GPa, respectively, and according to Chen's model, Pm BN is a novel superhard material. Compared with its original structure, the mechanical anisotropy of Young's modulus of Pm BN is larger than that of C14 carbon. Finally, the calculations of the electronic energy band structure show that Pm BN is a semiconductor material with not only a wide band gap but also an indirect band gap.

How to accurately probe chemically reactive flows with essential thermodynamic nonequilibrium effects is an open issue. Via the Chapman–Enskog analysis, the local nonequilibrium particle velocity distribution function is derived from the gas kinetic theory. It is demonstrated theoretically and numerically that the distribution function depends on the physical quantities and derivatives, and is independent of the chemical reactions directly as the chemical time scale is longer than the molecular relaxation time. Based on the simulation results of the discrete Boltzmann model, the departure between equilibrium and nonequilibrium distribution functions is obtained and analyzed around the detonation wave. In addition, it has been verified for the first time that the kinetic moments calculated by summations of the discrete distribution functions are close to those calculated by integrals of their original forms.

The entangled orbital angular momentum (OAM) photons propagating across a weakly turbulent atmosphere are investigated. Here, the paper uses the single-phase screen model based on the Kolmogorov theory of turbulence, and focuses on the influence of the backward scattering on OAM evolution. The results indicate that backward scattering plays an important role in the analysis of OAM entanglement evolution in the turbulent atmosphere. It cannot be negligible especially for higher-order OAM mode. Moreover, when OAM mode is greater than 4, entangled photon pairs composed of higher OAM modes are not more robust in turbulence within the weak scintillation regime. These results will be useful in future investigations of OAM-based optical wave propagation through turbulent atmosphere.

The spectrum of hadronic molecules composed of heavy–antiheavy charmed hadrons has been obtained in our previous work. The potentials are constants at the leading order, which are estimated from resonance saturation. The experimental candidates of hadronic molecules, say X(3872), Y(4260), three P_c states and P_cs(4459), fit the spectrum well. The success in describing the pattern of heavy–antiheavy hadronic molecules stimulates us to give more predictions for the heavy–heavy cases, which are less discussed in literature than the heavy–antiheavy ones. Given that the heavy–antiheavy hadronic molecules, several of which have strong experimental evidence, emerge from the dominant constant interaction from resonance saturation, we find that the existence of many heavy–heavy hadronic molecules is natural. Among these predicted heavy–heavy states we highlight the DD^* molecule and the ${D}^{(* )}{{\rm{\Sigma }}}_{c}^{(* )}$ molecules, which are the partners of the famous X(3872) and P_c states. Quite recently, LHCb collaboration reported a doubly charmed tetraquark state, T_cc, which is in line with our results for the DD^* molecule. With the first experimental signal of this new kind of exotic states, the upcoming update of the LHCb experiment as well as other experiments will provide more chances of observing the heavy–heavy hadronic molecules.

The magnetic properties and magnetocaloric effect of an antiferromagnetic/ferromagnetic (AFM/FM) BiFeO₃/Co bilayer with mixed-spin (5/2, 3/2) have been studied based on Monte Carlo simulation. The magnetization, susceptibility, and critical temperature are investigated under various exchange couplings and an external magnetic field. In particular, the influence of exchange couplings and an external magnetic field on the magnetic entropy change, adiabatic temperature change, and the relative cooling power (RCP) are studied. The simulation results indicated that the decrease of the exchange coupling and the increase of external magnetic fields can cause an increase of magnetic entropy change, adiabatic temperature change, and RCP. In addition, the hysteresis loops of the system are presented for different exchange couplings and temperatures.

In this paper, the Joule-Thomson expansion of the higher dimensional nonlinearly anti-de Sitter (AdS) black hole with power Maxwell invariant source is investigated. The results show the Joule-Thomson coefficient has a zero point and a divergent point, which coincide with the inversion temperature T_i and the zero point of the Hawking temperature, respectively. The inversion temperature increases monotonously with inversion pressure. For the high-pressure region, the inversion temperature decreases with the dimensionality D and the nonlinearity parameter s, whereas it increases with the charge Q. However, T_i for the low-pressure region increase with D and s, while it decreases with Q. The ratio $\eta$_BH between the minimum inversion temperature and the critical temperature does not depend on Q, it recovers the higher dimensional Reissner-Nördstrom AdS black hole case when s = 1. However, for s > 1, it becomes smaller and smaller as D increases and approaches a constant when D → ∞ . Finally, we found that an increase of mass M and s, or reducing the charge Q and D can enhance the isenthalpic curve, and the effect of s on the isenthalpic curve is much greater than other parameters.

This is a pedagogical review on ${T}\overline{{T}}$ deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to ${T}\overline{{T}}$deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the ${T}\overline{{T}}$/${J}\overline{{T}}$ deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of ${T}\overline{{T}}$ deformation are presented, including its relation to random geometry, 2D topological gravity and holography. We summarize more recent developments until January 2021 in the last part.

Kinesin is a two-headed biological molecular motor that can walk processively on microtubule via consumption of ATP molecules. The central issue for the molecular motor is how the chemical energy released from ATP hydrolysis is converted to the kinetic energy of the mechanical motion, namely the mechanism of chemomechanical coupling. To address the issue, diverse experimental methods have been employed and a lot of models have been proposed. This review focuses on the proposed models as well as the qualitative and quantitative comparisons between the results derived from the models and those from the structural, biochemical and single-molecule experimental studies.

In the paper, we try to study the mechanism of the existence of Gaussian waves in high degree logarithmic nonlinear wave motions. We first construct two model equations which include the high order dispersion and a second degree logarithmic nonlinearity. And then we prove that the Gaussian waves can exist for high degree logarithmic nonlinear wave equations if the balance between the dispersion and logarithmic nonlinearity is kept. Our mathematical tool is the logarithmic trial equation method.

Improving brittle behavior and mechanical properties is still a big challenge for high-temperature structural materials. By means of first-principles calculations, in this paper, we systematically investigate the effect of vacancy and oxygen occupation on the elastic properties and brittle-or-ductile behavior on Mo₅Si₃. Four vacancies (Si_–Va1, Si_–Va2, Mo_–Va1, Mo_–Va2) and oxygen occupation models (O_–Mo1, O_–Mo2, O_–Si1, O_–Si2) are selected for research. It is found that Mo_–Va2 vacancy has the stronger structural stability in the ground state in comparison with other vacancies. Besides, the deformation resistance and hardness of the parent Mo₅Si₃ are weakened due to the introduction of different vacancy defects and oxygen occupation. The ratio of B/G indicates that oxygen atoms occupation and vacancy defects result in brittle-to-ductile transition for Mo₅Si₃. These vacancies and the oxygen atoms occupation change the localized hybridization between Mo–Si and Mo–Mo atoms. The weaker O–Mo bond is a contributing factor for the excellent ductile behavior in the O_-Si2 model for Mo₅Si₃.

The D’Alembert solution of the wave motion equation is an important basic formula in linear partial differential theory. The study of the D’Alembert wave is worthy of deep consideration in nonlinear partial differential systems. In this paper, we construct a (2+1)-dimensional extended Boiti–Leon–Manna–Pempinelli (eBLMP) equation which fails to pass the Painlevé property. The D’Alembert-type wave of the eBLMP equation is still obtained by introducing one arbitrary function of the traveling-wave variable. The multi-solitary wave which should satisfy the velocity resonance condition is obtained by solving the Hirota bilinear form of the eBLMP equation. The dynamics of the three-soliton molecule, the three-kink soliton molecule, the soliton molecule bound by an asymmetry soliton and a one-soliton, and the interaction between the half periodic wave and a kink soliton molecule from the eBLMP equation are investigated by selecting appropriate parameters.

The development of new materials, having exceptional properties in comparison to existing materials is highly required for bringing advancement in electronic and optoelectronic technologies. Keeping this fact, we investigated structural, electronic, and optical properties of zincblende GaN doped with selected Zn concentrations (6.25%, 12.50%, and 18.70%), using the first-principle calculations based on density functional theory with GGA + U. We conducted the entire study using the WIEN2K code. In this study, we calculated various significant parametric quantities such as cohesive energies, formation energies, bulk moduli, and lattice constants along with the study of optical and electronic properties by substituting Ga atoms with Zn atoms in 1 × 2 × 2 supercell. The structural stability is confirmed by studying the phonon dispersion curves which suggest that Zn:GaN material is stable against the 6.25% and 18.70% Zn concentrations while for 12.50%, it shows instability. The Hubbard values U = 0, 2, 4, 6 eV were added to GGA and the electronic properties were improved with the U = 6 eV. Optical absorption was blue shifted while the refractive index and dielectric constant were increased with increasing the Zn concentrations. Electronic properties are enhanced due to the prime contribution of cations (Zn) 3d states. The optical and electronic properties are further discussed in detail in the entire study.

We have theoretically investigated two-dimensional atom localization using the absorption spectra of birefringence beams of light in a single wavelength domain. The atom localization is controlled and modified through tunneling effect in a conductive chiral atomic medium with absorption spectra of birefringent beams. The significant localization peaks are investigated in the left and right circularly polarized beam. Single and double localized peaks are observed in different quadrants with minimum uncertainty and significant probability. The localized probability is modified by controlling birefringence and tunneling conditions. These results may be useful for the capability of optical microscopy and atom imaging.

The momentum distribution and dynamical structure factor in a weakly interacting Bose gas with a time-dependent periodic modulation in terms of the Bogoliubov treatment are investigated. The evolution equation related to the Bogoliubov weights happens to be a solvable Mathieu equation when the coupling strength is periodically modulated. An exact relation between the time derivatives of momentum distribution and dynamical structure factor is derived, which indicates that the single-particle property is strongly related to the two-body property in the evolutions of Bose-Einstein condensates. It is found that the momentum distribution and dynamical structure factor cannot display periodical behavior. For stable dynamics, some particular peaks in the curves of momentum distribution and dynamical structure factor appear synchronously, which is consistent with the derivative relation.

Dynamic magnetic properties of the mixed-spin (3/2, 5/2) Ising graphene-like monolayer in an oscillating magnetic field are studied by means of Monte Carlo simulation. The effects of Hamiltonian parameters such as crystal field and time-dependent oscillating magnetic field on the dynamic order parameter, susceptibility and internal energy of the system are well presented and explained. Moreover, much attention has also been dedicated to the phase diagrams with different parameters in order to better comprehend the impacts of these parameters on the critical temperature. Our results reveal that the crystal fields of two sublattices have similar effects on the critical temperature, but the bias field and amplitude of oscillating field have opposite effects on it. We hope that our research can be of guiding significance to the theoretical and experimental studies of graphene-like monolayer.

Recently, a novel 4D Einstein–Gauss–Bonnet gravity has been proposed by Glavan and Lin (2020 Phys. Rev. Lett. 124 081301) by rescaling the coupling $\alpha \to \alpha /(D-4)$ and taking the limit $D\to 4$ at the level of equations of motion. This prescription, though was shown to bring non-trivial effects for some spacetimes with particular symmetries, remains mysterious and calls for scrutiny. Indeed, there is no continuous way to take the limit $D\to 4$ in the higher D-dimensional equations of motion because the tensor indices depend on the spacetime dimension and behave discretely. On the other hand, if one works with 4D spacetime indices the contribution corresponding to the Gauss–Bonnet term vanishes identically in the equations of motion. A necessary condition (but may not be sufficient) for this procedure to work is that there is an embedding of the 4D spacetime into the higher D-dimensional spacetime so that the equations in the latter can be properly interpreted after taking the limit. In this note, working with 2D Einstein gravity, we show several subtleties when applying the method used in (2020 Phys. Rev. Lett. 124 081301).

In this work, we study the theory of inflation with the non-minimally coupled quadratic, standard model Higgs, and hilltop potentials, through ξφ²R term in Palatini gravity. We first analyze observational parameters of the Palatini quadratic potential as functions of ξ for the high-N scenario. In addition to this, taking into account that the inflaton field φ has a non-zero vacuum expectation value v after inflation, we display observational parameters of well-known symmetry-breaking potentials. The types of potentials considered are the Higgs potential and its generalizations, namely hilltop potentials in the Palatini formalism for the high-N scenario and the low-N scenario. We calculate inflationary parameters for the Palatini Higgs potential as functions of v for different ξ values, where inflaton values are both φ > v and φ < v during inflation, as well as calculating observational parameters of the Palatini Higgs potential in the induced gravity limit for high-N scenario. We illustrate differences between the Higgs potential's effect on ξ versus hilltop potentials, which agree with the observations for the inflaton values for φ < v and ξ, in which v < 1 for both these high and low N scenarios. For each considered potential, we also display n_s − r values fitted to the current data given by the Keck Array/BICEP2 and Planck collaborations.

We develop a variational theory for a dipolar condensate in an elongated (cigar shaped) confinement potential. Our formulation provides an effective one-dimensional extended meanfield theory for the ground state and its collective excitations. We apply our theory to investigate the properties of rotons in the system comparing the variational treatment to a full numerical solution. We consider the effect of quantum fluctuations on the scattering length at which the roton excitation softens to zero energy.

In this paper, we investigate the relativistic quantum dynamics of spin-0 massive charged particles in a Gödel-type space–time with electromagnetic interactions. We derive the radial wave equation of the Klein–Gordon equation with an internal magnetic flux field and Coulomb-type potential in the Som–Raychaudhuri space–time with cosmic string. We solve this equation and analyze the analog effect in relation to the Aharonov–Bohm effect for bound states.

We compute the Higgs plus two-quark and one-gluon amplitudes ($H\to q\bar{q}g$) and Higgs plus three-gluon amplitudes ($H\to 3g$) in the Higgs effective theory with a general class of operators. By changing the quadratic Casimir C_F to C_A, the maximally transcendental parts of the $H\to q\bar{q}g$ amplitudes turn out to be equivalent to that of the $H\to 3g$ amplitudes, which also coincide with the counterparts in ${ \mathcal N }=4$ SYM. This generalizes the so-called maximal transcendentality principle to the Higgs amplitudes with external quark states, thus the full QCD theory. We further verify that the correspondence applies also to two-loop form factors of more general operators, in both QCD and scalar-YM theory. Another interesting relation is also observed between the planar $H\to q\bar{q}g$ amplitudes and the minimal density form factors in ${ \mathcal N }=4$ SYM.

The effect of confined one-gluon-exchange potential and instanton-induced interaction potential in the singlet (¹S₀) and triplet (³S₁) channels for nucleon–nucleon interaction has been investigated in the framework of the relativistic harmonic model using the resonating group method in the adiabatic limit with the Born–Oppenheimer approximation. The contributions of the different components of the interaction potentials have been analyzed.

In this study, a harmonic oscillator with position-dependent mass is investigated. Firstly, as an introduction, we give a full description of the system by constructing its classical Lagrangian; thereupon, we derive the related classical equations of motion such as the classical Euler–Lagrange equations. Secondly, we fractionalize the classical Lagrangian of the system, and then we obtain the corresponding fractional Euler–Lagrange equations (FELEs). As a final step, we give the numerical simulations corresponding to the FELEs within different fractional operators. Numerical results based on the Caputo and the Atangana-Baleanu-Caputo (ABC) fractional derivatives are given to verify the theoretical analysis.

Quantum Chaos has been investigated for about a half century. It is an old yet vigorous interdisciplinary field with new concepts and interesting topics emerging constantly. Recent years have witnessed a growing interest in quantum chaos in relativistic quantum systems, leading to the still developing field of relativistic quantum chaos. The purpose of this paper is not to provide a thorough review of this area, but rather to outline the basics and introduce the key concepts and methods in a concise way. A few representative topics are discussed, which may help the readers to quickly grasp the essentials of relativistic quantum chaos. A brief overview of the general topics in quantum chaos has also been provided with rich references.

The consideration of measuring instruments as macroscopic bodies leads to neglect of the microscopic processes that occur during measurements. This disregard is not justified in general cases. As an example of measurements using microscopic instruments, the scattering of a photon by an electron with electron interference at two slits (Compton effect) was used. The amount of information that can be obtained in such a process is inversely proportional to the wavelength of the incident photon. At large photon wavelengths (soft measurements), the pure state of the electron can be disrupted by an arbitrarily small extent; accordingly, the amount of information extracted in such an experiment is also arbitrarily small. It is shown that the energy price for a bit obtained in such a measurement tends toward a constant value for increasing the photon wavelength. Microscopic instruments can be used in situations where energy costs for measurements are important.