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This work investigates the basic features of Nonlinear Ion Acoustic Solitary waves (NIASWs) and their dynamical behaviours in an unmagnetized relativistic collisionless plasma system via the Schamel Korteweg-de Vries (SKdV) equation. Such plasma is composed by the generalized distributed electrons, Boltzmann distributed positrons and relativistic warm ions. The influences of plasma parameters on NIASWs and their dynamical behaviours are investigated by comparing 26−term expansion of relativistic Lorentz factor (RLF) with both of weakly (2−term expansion of RLF) and highly (3−term expansion of RLF) regimes. It is found that the 26−term expansion of RLF are significantly changed NIASWs instead of both weakly and highly relativistic regimes. Therefore, the theoretical results would be very useful for understanding the nature (amplitude, width, polarity, etc.) of wave dynamics not only in astrophysical and space environments but also in further laboratory studies, where the proposed plasma assumptions are existed.

Analytical modeling presents symmetries and aesthetic-mathematical characteristics which are not catchable in numerical computation for science and technology; nanoscience plays a significant role in unification attempts, considering also models including holistic aspects of reality. In this paper we present new discovered results about the complete analytical quantum-relativistic form of the mean square deviation of position R2(t) related to a recently introduced Drude–Lorentz-like model (DS model), already performed at classical, quantum and relativistic level. The function R2(t) gives precise information about the distance crossed by carriers (electrons, ions, etc.) inside a nanostructure, considering both quantum effects and relativistic velocities. The model has a wide scale range of applicability; the nanoscale is considered in this paper, but it holds application from sub-pico-level to macro-level because of the existence of a gauge factor, making it applicable to every oscillating process in nature. Examples of application and suggestions supplement this paper, as well as interesting developments to be studied related to the model and to one of the basic elements of a current unified holistic approach based on vacuum energy.

We briefly review an approach to singular interactions in one dimensional quantum mechanics based on Schwartz distributional theory. The requirements for a well-defined theory and the procedure to determine the interaction distribution are explained in a format that applies both to relativistic and non-relativistic quantum mechanics. Finally, we discuss some results obtained using the method, with particular attention to relativistic point interactions.

From the segmented all-electron basis set of double zeta valence quality plus polarization functions (DZP) for the elements from H to Xe, the zeroth-order regular approximation (ZORA) is used to generate a DZP-ZORA basis set, i.e., the contraction coefficients of the DZP set are re-optimized using the minimum ZORA energy criterion. To properly describe electrons distant from the nuclei, a diffuse function is added to each atomic symmetry ( s , p , d , and f ). The later basis set is designated as DZP-ZORA augmented. To test the effectiveness of the basis sets developed in this work, calculations of ionization energies and mean dipole polarizabilities of some elements are performed using the ZORA-CCSD(T) method. At the same level of theory, bond lengths, dissociation energies, and harmonic vibrational frequencies of some diatoms are also reported. Comparison with experimental data and recommended values available in the literature is made. Except for polarizability, scalar relativistic effects are estimated for the other properties. The performances of the ZORA and second-order Douglas-Kroll-Hess Hamiltonians are evaluated. Graphical abstract

In this work, we investigated the propagation of ion acoustic shock waves IAShWs in an ultra-relativistic degenerate plasma composed of positrons, electrons and ions in the presence of an external magnetic field. We have derived the KdV-B equation using the reductive perturbation technique and analyzed its solution graphically. The impact of the different plasma parameters (positron concentration, kinematic viscosity, strength of the magnetic field, obliqueness, relativistic effects, etc.) on the basic features of the IAShWs have been rigorously examined. It has been found that shock waves co-propagate with solitons in the ultra-relativistic case, whereas in the non-relativistic case, monotonic shock waves are in favor. Moreover, to highlight the relevance of our research in astrophysical environments, we have applied the plasma model to the surface of magnetic neutron stars where the plasma components are ultra-relativistic and degenerate. We have discerned that the parameters taken into account have significant effects on the nature and amplitude of the ion acoustic structures.

The GNSS satellite atomic clock is subjected to appreciable relativistic effects during its in-orbit operation. These effects include drift due to the gravitational redshift and time dilation due to the relative velocity, the periodic effects of the orbital eccentricity, the oblateness of the Earth’s gravity field, and the tidal potential of the Sun, Moon and other planets. The accuracy of navigation, positioning and timing of satellite navigation systems is thus affected. The small terms, including those relating to the Earth’s oblateness and the tidal potential of other planets, are usually neglected to estimate satellite clock. Inevitably, residual relativistic errors are introduced into the final solutions. Therefore, we comprehensively analyze the characteristics of relativistic effects on satellite clocks of the Beidou navigation satellite system, Galileo and Global Positioning System, including the combined relativistic effect, periodic relativistic effect, J2 relativistic effect and the tidal potential of other planets. The characteristics and performance of the satellite clock before and after the correction for J2 relativistic effect are evaluated. It is found that the amplitude of the satellite clock half-orbital periodic term is reduced by the correction, and the fitting residuals reduce by 6%. The Hadamard variance sequence tends to be stable. Meanwhile, J2 effect correction is applied to satellite clock prediction and improving the accuracy of the quadratic polynomial model by 9% and stability by 11%. Additionally, the results of using the spectral analysis model with and without adding the J2 period are improved.

This paper argues that a conception of physical reality as a universe of processes offers an adequate framework to construct clarifying interpretations of relativistic phenomena such as «time dilation» and «length contraction». It further aims to show that physical reality thus conceived is, without contradiction, intrinsically changing and four-dimensional. Finally, it points out some features of this conception that could be of interest in philosophical debates that go beyond the framework to which this work is restricted: that of what is related to relativistic kinematic phenomena.

A bstract We study linearized stability in first-order relativistic viscous hydrodynamics in the most general frame. There is a region in the parameter space of transport coefficients where the perturbations of the equilibrium state are stable. This defines a class of stable frames, with the Landau-Lifshitz frame falling outside the class. The existence of stable frames suggests that viscous relativistic fluids may admit a sensible hydrodynamic description in terms of temperature, fluid velocity, and the chemical potential only, i.e. in terms of the same hydrodynamic variables as non-relativistic fluids. Alternatively, it suggests that the Israel-Stewart and similar constructions may be unnecessary for a sensible relativistic hydrodynamic theory.

Relativistic dissipative fluid dynamics finds widespread applications in high-energy nuclear physics and astrophysics. However, formulating a causal and stable theory of relativistic dissipative fluid dynamics is far from trivial; efforts to accomplish this reach back more than 50 years. In this review, we give an overview of the field and attempt a comparative assessment of (at least most of) the theories for relativistic dissipative fluid dynamics proposed until today and used in applications.

Lifted Kramers spin degeneracy (LKSD) has been among the central topics of condensed-matter physics since the dawn of the band theory of solids 1 , 2 . It underpins established practical applications as well as current frontier research, ranging from magnetic-memory technology 3 – 7 to topological quantum matter 8 – 14 . Traditionally, LKSD has been considered to originate from two possible internal symmetry-breaking mechanisms. The first refers to time-reversal symmetry breaking by magnetization of ferromagnets and tends to be strong because of the non-relativistic exchange origin 15 . The second applies to crystals with broken inversion symmetry and tends to be comparatively weaker, as it originates from the relativistic spin–orbit coupling (SOC) 16 – 19 . A recent theory work based on spin-symmetry classification has identified an unconventional magnetic phase, dubbed altermagnetic 20 , 21 , that allows for LKSD without net magnetization and inversion-symmetry breaking. Here we provide the confirmation using photoemission spectroscopy and ab initio calculations. We identify two distinct unconventional mechanisms of LKSD generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization 20 – 23 . Our observation of the altermagnetic LKSD can have broad consequences in magnetism. It motivates exploration and exploitation of the unconventional nature of this magnetic phase in an extended family of materials, ranging from insulators and semiconductors to metals and superconductors 20 , 21 , that have been either identified recently or perceived for many decades as conventional antiferromagnets 21 , 24 , 25 . Using photoemission spectroscopy and ab initio calculations, evidence is given of two distinct unconventional mechanisms of lifted Kramers spin degeneracy generated by the altermagnetic phase of centrosymmetric MnTe with vanishing net magnetization.