Relativistic Degeneracy Research Articles

Two-dimensional cylindrical magnetosonic shock waves in a relativistic degenerated plasma

Abstract In this paper, the characteristics of two-dimensional magnetosonic (MS) shock waves have been studied in a nonplanar relativistic degenerate collisional magnetoplasma whose constituents are non-degenerate warm ions fluid and relativistic degenerated electrons. Employing fluid model equations for such plasma along with Maxwell equations, a set of magnetohydrodynamic (MHD) model equations is obtained. Based on the newly obtained MHD equations, a Burgers-Kadomstev-Petviashvili equation (which describes shock wave structures) is derived in cylindrical geometry using the reductive perturbation technique. The considered plasma system was investigated under the impacts of spin-magnetization, relativistic degeneracy, cylindrical geometry, and dissipation. Numerical results revealed that the relativistic degeneracy, dissipation, and electron spin-magnetization as well as nonplanar geometry significantly altered the MS shock wave properties. Interestingly, it’s found that the shock nature changes and turns into new structures attributed to the transverse perturbation and cylindrical geometry. The implications of our investigation may be applicable to relativistic nonplanar quantum plasmas in astrophysical environments, particularly neutron stars and white dwarfs.

General relativistic self-gravitating equilibrium discs around rotating neutron stars

ABSTRACT In modelling a relativistic disc around a compact object, the self-gravity of the disc is often neglected while it needs to be incorporated for more accurate descriptions in several circumstances. Extending the Komatsu–Eriguchi–Hachisu self-consistent field method, we present numerical models of a rapidly rotating neutron star with a self-gravitating disc in stationary equilibrium. In particular, our approach allows us to obtain numerical solutions involving a massive disc with the rest mass $\mathcal {O}(10^{-1})-\mathcal {O}(10^0)\, \mathrm{ M}_\odot$ closely attached to a rotating neutron star, given that the disc is mainly supported by the relativistic electron degeneracy pressure. We also assess the impact of self-gravity on the internal structure of the disc and the neutron star. These axisymmetric, stationary solutions can be employed for simulations involving the neutron star–disc system in the context of high-energy transients and gravitational-wave emissions.

On acoustic solitary waves in a multispecies degenerate relativistic magnetized plasma using physics informed neural networks

In this paper, we investigate the nonlinear electrostatic wave propagation in a two-dimensional magnetized plasma. The plasma consists of electron and positron components with relativistic degeneracy and stationary ions for neutralizing its background. Using the basic equations for this type of plasma in combination with the reductive perturbation method, we derived the Zakharov–Kuznetsov equation using the Lorentz transformation stretching method (LT). For the first time, we compared the results of the Galilean transformation stretching method (GT) and the LT method to investigate the effect of plasma parameters, such as the relativistic degeneracy parameter of electron particles (re0), the density ratio of ion to electrons (δ), and the normalized electron cyclotron (Ωe), on the amplitude and width of the wave solutions. The plasma parameters used in this research are representative of compact astrophysical objects. Numerical results showed that the amplitude of wave solutions obtained by the LT method is smaller than the GT method, but the width is greater. We provide a physical explanation for these differences. Furthermore, we present a physics-informed neural network (PINN) approach to directly recover the intrinsic nonlinear dynamics from spatiotemporal data. The PINN model uses a deep neural network constrained by the governing equations to learn the optimal parameters, with the aim of enhancing the predictive capabilities of the system. The results of this study provide valuable insight into the propagation of nonlinear waves in white dwarfs, where relativistic effects are significant. These findings could substantially advance the development of emerging machine learning applications in astrophysics.

Electron acoustic solitary waves in relativistically quantum magnetoplasmas with electron exchange correlation effects

The propagating of electron acoustic solitary waves (EASWs) in relativistically magnetized quantum plasmas which consists inertial cold electrons, inertialess hot electrons and stationary background ions have been theoretically investigated. The modified Zakharov-Kuznetsov (ZK) equation is derived by adopting the standard reductive perturbation method to describe the nonlinear evolution of the EASWs. After discussing the effects of various parameter values on the solitary structures, it is shown that the solitary structures are very sensitive to the relativistic degeneracy effect, the cold to hot electrons number density ratio and the electron exchange correlation effects. The numerical analysis can be well described by the existing analytical theory. Our results may be useful in explaining the physics behind the formation of the EASWs in both astrophysical and laboratory plasmas.

On the dynamics of soliton interactions in the stellar environments

The effects of trapping of relativistically degenerate electrons are studied on the formation and interaction of nonlinear ion-acoustic solitary waves (IASWs) in quantum plasmas. These plasmas are detected in high-density astrophysical entities and can be created in the laboratory by interacting powerful lasers with matter. The formula for the number density of electrons in a state of relativistic degeneracy is provided, along with an analysis of the non-relativistic and ultra-relativistic scenarios. While previous studies have delved into specific aspects of relativistic effects, there needs to be a more detailed and systematic examination of the fully relativistic limit, which is essential for gaining a holistic perspective on the behavior of solitons in these extreme conditions. The aim of this work is to comprehensively investigate the fully relativistic limit of the system to fill this gap. The reductive perturbation technique is utilized to deduce the Korteweg–de Vries (KdV) equation, which is used to analyze the properties of the IASWs. Hirota bilinear formalism is applied to obtain single- and multi-soliton solutions for the KdV equation. The numerical analysis is focused on the plasma properties of the white dwarf in the ongoing investigation. The amplitude of the IASWs is found to be maximum for the non-relativistic, intermediate for the ultra-relativistic, and minimum for the fully relativistic limit. Most importantly, it is found that the fastest interaction occurs in the non-relativistic limit and the slowest in the fully relativistic limit.

Nonlinear electron-acoustic structures in two-temperature relativistic degenerate plasmas

Fully nonlinear electron-acoustic (EA) structures are studied in the presence of relativistic degeneracy pressure attributing to electron species in a degenerate plasma. The plasma is taken as a collisionless and unmagnetized, containing mobile cool electrons, inertialess hot electrons and static ions. The fluid equations for such a plasma are incorporated and solved together by using the charge-neutrality hypothesis and diagonalization matrix technique obtaining the characteristic wave equations in the form of inviscid Burgers’ equations. Negative solitary structures are found in the form of potential profiles, which can be developed into nonstationary shocklets, greatly affected by the weak and strong relativistic degenerate densities. The structures are not only modified by the temporal evolution but also by thermal correction parameter. Moreover, the application of Taylor expansion to the eigenvalue may lead to the derivation of nonlinear phase and shock speeds, depending significantly on the electrostatic potential and other plasma parameters. The present findings are important to understand solitary and shocklet structures in dense plasmas, where both cool and hot electrons are regarded as the relativistic and degenerate species.

Electromagnetic solitons and their stability in relativistic degenerate dense plasmas with two electron species

The evolution of electromagnetic (EM) solitons due to nonlinear coupling of circularly polarized intense laser pulses with low-frequency electron-acoustic perturbations is studied in relativistic degenerate dense astrophysical plasmas with two groups of electrons: a sparse population of classical relativistic electrons and a dense population of relativistic degenerate electron gas. Different forms of localized stationary solutions are obtained and their properties are analyzed. Using the Vakhitov-Kolokolov stability criterion, the conditions for the existence and stability of a moving EM soliton are also studied. It is noted that the stable and unstable regions shift around the plane of soliton eigenfrequency and the soliton velocity due to the effects of relativistic degeneracy, the fraction of classical to degenerate electrons and the EM wave frequency. Furthermore, while the standing solitons exhibit stable profiles for a longer time, the moving solitons, however, can be stable or unstable depending on the degree of electron degeneracy, the soliton eigenfrequency and the soliton velocity. The latter with an enhanced value can eventually lead to a soliton collapse. The results should be useful for understanding the formation of solitons in the coupling of highly intense laser pulses with slow response of degenerate dense plasmas in the next generation laser-plasma interaction experiments as well as the novel features of x-ray and γ-ray pulses that originate from compact astrophysical objects.

Stationary Structures in a Four Component Dense Magnetoplasma With Lateral Perturbations

We considered a dense plasma containing electrons, positrons, ions and dust particles in background magnetic and gravitational fields alongside collisional effects for the heavier species (ions and dust particles). Such plasmas are found in magnetars, black hole accretion disks, and so on. The quantum hydrodynamic (QHD) model was used to construct the governing equations of the plasma. Relativistic degeneracy pressure is taken as the equation of state for the electrons and positrons. Effects of exchange-correlation potential were also considered for the lighter species. We employed the reductive perturbation method (RPM) in order to obtain the Zakharov–Kuznetsov (ZK) equation describing 3-D ion acoustic waves (IAWs) with minimal lateral perturbations. Low order analytical solutions allow us to understand the parametric dependence of said structures. Our newly developed numerical technique: homotopy assisted symbolic simulation (HASS) sheds light on the gradual evolution of higher order stationary formations in the system. The results thus obtained can potentially explain certain astrophysical phenomena as well as dense laboratory plasmas.

Formation of Nonlinear Stationary Structures in Ionospheric Plasma

Solar radiation, along with cosmic radiation, ionizes the Earth's atmosphere and creates a dense layer known as the ionosphere. By considering weakly relativistic degenerate plasma in the planetary ionosphere, we have studied the formation and nature of the solitary structure, electrostatic double layers (DLs), and so on. As we have considered weak relativistic degeneracy, only electrons get accelerated and are the key to stationary structures. We have implemented Sagdeev's pseudopotential method, standard Gardner equation, and accordingly identified regimes where the solitary formation and DLs may be observed. We have studied the parametric influences on solitons and DLs. Furthermore, we extended our investigation to the oscillatory Rossby solitons in the ionospheric plasma. The results may help interpret many high-energy atmospheric observations in the ionospheric plasma.

Possible realization of optical Dirac points in woodpile photonic crystals.

The simulation of fermionic relativistic physics, e.g., Dirac and Weyl physics, has led to the discovery of many unprecedented phenomena in photonics, of which the optical-frequency realization is, however, still challenging. Here, surprisingly, we discover that the woodpile photonic crystals commonly used for optical frequency applications host exotic fermion-like relativistic degeneracies: a Dirac nodal line and a fourfold quadratic point, as protected by the nonsymmorphic crystalline symmetry. Deforming the woodpile photonic crystal leads to the emergence of type-II Dirac points from the fourfold quadratic point. Such type-II Dirac points can be detected by its anomalous refraction property which is manifested as a giant birefringence in a slab setup. Our findings provide a promising route towards 3D optical Dirac physics in all-dielectric photonic crystals.

Magnetosonic waves in ion trapped semiconductor chip plasma with effect of exchange correlation potential and relativistic degeneracy

The generalized dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in Cd+ ion trapped semiconductor electron-hole-ion plasmas is studied with effect of quantum corrections. The important ingredients of these corrections occurred due to Bohm potential, relativistic degeneracy, exchange-correlation potential and spin magnetization and have significant impact on the dispersion properties of perpendicular and oblique modes of MHD wave. The derived results are numerically analyzed by using the numerical parameters of GaAs, GaSb, GaN, and InP semiconductors plasmas. From the numerical analysis it is observed that for higher number density, the phase speed of magnetosonic wave is larger for the InP semiconductor, while for low number density plasma region, it gives lower values for GaAs semiconductor. Similarly the phase speed of magnetosonic wave for GaAs decreases with applied magnetic field for different regime of number density. Due to exchange-correlation potential it is found that the frequencies of magnetosonic waves are blue-shifted means that it has magnified the phase speed. It is also shown that frequency of oblique MHD wave for GaAs semiconductor plasmas increases (decreases) with number density of electrons (holes). The relativistic degeneracy term (γ) for given number density is numerically calculated (1.00011 ∼ 1.0058) for all the above-mentioned semiconductors and it is observed that due to its mild numerical value it has not significant impact on graphical manipulation. The Alfven speed for above compound semiconductors with B 0 ≤ 104 G is also calculated which are in the permissible range of order 104 cm/s to 107 cm/s. The results are helpful to understand the energy transport in semiconductor plasma in the presence of magnetic field.

Eikonal quasinormal modes of black holes beyond general relativity. III. Scalar Gauss-Bonnet gravity

In a recent series of papers, we have shown how the eikonal/geometrical optics approximation can be used to calculate analytically the fundamental quasinormal mode frequencies associated with coupled systems of wave equations, which arise, for instance, in the study of perturbations of black holes in gravity theories beyond General Relativity. As a continuation to this series, we focus here on the quasinormal modes of nonrotating black holes in scalar Gauss-Bonnet gravity assuming a small-coupling expansion. We show that the axial perturbations are purely tensorial and are described by a modified Regge-Wheeler equation, while the polar perturbations are of mixed scalar-tensor character and are described by a system of two coupled wave equations. When applied to these equations, the eikonal machinery leads to axial quasinormal modes that deviate from the general relativistic results at quadratic order in the Gauss-Bonnet coupling constant. We show that this result is in agreement with an analysis of unstable circular null orbits around black holes in this theory, allowing us to establish the geometrical optics--null geodesic correspondence for the axial quasinormal modes. For the polar quasinormal modes, the small-coupling approximation forces us to consider the ordering between eikonal and small-coupling perturbative parameters, one of which we show, by explicit comparison against numerical data, yields the correct identification of the quasinormal modes of the scalar-tensor coupled system of wave equations. These corrections lift the general relativistic degeneracy between scalar and tensorial eikonal quasinormal modes at quadratic order in Gauss-Bonnet coupling in a way reminiscent of the Zeeman effect. In general, our analytic, eikonal quasinormal mode frequencies (normalized to the General Relativity ones) agree with numerical results with an error of $\mathcal{O}(10%)$ in the regime of small coupling constant. Finally, we find that the analytical expressions for the quasinormal modes are common to a broad class of scalar-Gauss-Bonnet theories to leading eikonal order, showing a degeneracy between the quasinormal modes of nonrotating black holes in particular scalar-Gauss-Bonnet theories in the geometrical optics limit.

Extraordinary and upper-hybrid waves in spin quantum magnetoplasmas with vacuum polarization effect

The propagation of extraordinary and upper-hybrid waves in spin quantum magnetoplasmas with vacuum polarization effect is investigated. Based on the quantum magnetohydrodynamics model including Bohm potential, arbitrary relativistic degeneracy pressure and spin force, and Maxwell's equations modified by the spin current and vacuum polarization current, the dispersion relations of extraordinary and upper-hybrid waves are derived. The analytical and numerical results show that quantum effects (Bohm potential, degeneracy pressure and spin magnetization energy) and the vacuum polarization effect modify the propagation of the extraordinary wave. Under the action of a strong magnetic field, the plasma frequency is obviously increased by the vacuum polarization effect.

POSSIBLE ENERGY SPECTRUM OF THE TWO DIMENSIONAL SPATIAL KLEIN-GORDON OSCILLATOR EQUATION

In the present article, one had found a complete energy spectrum and eigen-function of the solution of two dimensional (2D) spatial Klein-Gordon oscillator equation which shows that its relativistic degeneracy energy is related to the eigen-function.

Ground state energy of hydrogen-like ions in quantum plasmas

Using the asymptotic iteration method (AIM), we investigate the variation in the 1s energy levels of hydrogen and helium-like static ions in fully degenerate electron gas. The semiclassical Thomas–Fermi (TF), Shukla–Eliasson (SE), and corrected Shukla–Eliasson (cSE) models are compared. It is noted that these models merge into the vacuum level for hydrogen and helium-like ions in the dilute classical electron gas regime. While in the TF model, the hydrogen ground state level lifts monotonically toward the continuum limit with an increase in the electron concentration; in the SE and cSE models, a universal bound stabilization valley through the energy minimization occurs at a particular electron concentration range for the hydrogen-like ion which for the cSE model closely matches the electron concentrations in typical metals. The latter stabilizing mechanism appears to be due to the interaction between plasmon excitations and the Fermi length scales in the metallic density regime. In the case of helium-like ions, however, no such stability mechanism is found. The application of the cSE model with electron exchange and correlation effects reveals that the cSE model qualitatively accounts for the number density and lattice parameters of elemental metals within the framework of free electron assumption. According to the cSE model of static charge, screening a simple metal–insulator transition criterion is defined. The effect of the relativistic degeneracy effect on the ground state energy of the hydrogen atom is studied. It is shown that the ground state energy level of the hydrogen atom also undergoes a collapse at the well-known Chandrasekhar mass limit for white dwarf stars.

Properties of Electron-Acoustic Solitary Waves for Weak Relativistic Degeneracy Pressure at Critical Regime

Properties of Electron-Acoustic Solitary Waves for Weak Relativistic Degeneracy Pressure at Critical Regime

Generation of wakefields and electromagnetic solitons in relativistic degenerate plasmas

The nonlinear interaction of intense linearly polarized electromagnetic waves (EMWs) with longitudinal electron density perturbations is revisited in relativistic degenerate plasmas. The nonlinear dynamics of the EMWs and the longitudinal field, driven by the EMW ponderomotive force, is governed by a coupled set of nonlinear partial differential equations. A numerical simulation of these coupled equations reveals that the generation of wakefields is possible in weakly relativistic degenerate plasmas with and , where pF is the Fermi momentum, m is the mass of electrons, c is the speed of light in vacuum, and vg is the EMW group velocity. However, when the ratio vg/c is reduced to ∼0.1, the wakefield generation is suppressed, instead the longitudinal fields get localized to form soliton-like structures. On the other hand, in the regimes of moderate or strong relativistic degeneracy (R0 > 1) with vg/c ∼ 0.1, only the EM solitons can be formed.

Polarized Debye Sheath in Degenerate Plasmas**Support from SERB, Govt. of India for a Research Project with sanction order No. CRG/2018/004475

The force on a charged dust grain in a plasma due to polarization of thermal ions and degenerate electrons around the grain is derived in the limits of weakly relativistic and ultra-relativistic degeneracy of electrons. It is found that in both these cases, the magnitude of the polarization force is enhanced compared to that in classical plasmas. The influence of this force on dust-acoustic (DA) modes is examined and discussed. It is shown that the DA wave frequency in degenerate plasmas is significantly reduced compared to the classical DA mode.

Solitary kinetic Alfvén waves in dense plasmas with relativistic degenerate electrons and positrons

Propagation of solitary kinetic Alfvén waves (KAWs) is investigated in small but finite (particle-to-magnetic pressure ratio) collisionless dense plasma whose constituents are nondegenerate warm ions, and relativistic degenerate electrons and positrons. Through the use of reductive perturbation technique, Kortweg–de Vries equation is derived to obtain small amplitude localized wave solution of KAWs. The effects of plasma positron concentration, electron relativistic degeneracy parameter, ion thermal temperature and obliqueness parameter on solitary KAWs are studied. The results of this theoretical investigation are aimed at elucidating characteristics of kinetic Alfvén solitary waves in relativistic degenerate e–p–i plasmas found in dense astrophysical objects specifically neutron stars and white dwarfs.

Two-dimensional type-II Dirac fermions in layered oxides

Relativistic massless Dirac fermions can be probed with high-energy physics experiments, but appear also as low-energy quasi-particle excitations in electronic band structures. In condensed matter systems, their massless nature can be protected by crystal symmetries. Classification of such symmetry-protected relativistic band degeneracies has been fruitful, although many of the predicted quasi-particles still await their experimental discovery. Here we reveal, using angle-resolved photoemission spectroscopy, the existence of two-dimensional type-II Dirac fermions in the high-temperature superconductor La1.77Sr0.23CuO4. The Dirac point, constituting the crossing of d_{x^2 - y^2} and d_{z^2} bands, is found approximately one electronvolt below the Fermi level (EF) and is protected by mirror symmetry. If spin-orbit coupling is considered, the Dirac point degeneracy is lifted and the bands acquire a topologically non-trivial character. In certain nickelate systems, band structure calculations suggest that the same type-II Dirac fermions can be realised near EF.