Relativistic Framework Research Articles

Magnetized neutron star crust within effective relativistic mean-field model

Even though the crystallize nature of the neutron star crust plays a pivotal role in describing various fascinating astrophysical observations, its microscopic structure is not fully understood in the presence of a colossal magnetic field. In the present work, we study the crustal properties of a neutron star within an effective relativistic mean field framework in the presence of magnetic field strength $\sim 10^{17}$G. We calculate the equilibrium composition of the outer crust by minimizing the Gibbs free energy using the most recent atomic mass evaluations. The magnetic field significantly affects the equation of state (EoS) and the properties of the outer crust, such as neutron drip density, pressure, and melting temperature. For the inner crust, we use the compressible liquid drop model for the first time to study the crustal properties in a magnetic environment. The inner crust properties, such as mass and charge number distribution, isospin asymmetry, cluster density, etc., show typical quantum oscillations (De Haas-van Alphen effect) sensitive to the magnetic field's strength. The density-dependent symmetry energy influences the magnetic inner crust like the field-free case. We study the probable modifications in the pasta structures and it is observed that their mass and thickness changes by $\sim 10-15 \%$ depending upon the magnetic field strength. The fundamental torsional oscillation mode frequency is investigated for the magnetized crust in the context of quasiperiodic oscillations (QPO) in soft gamma repeaters. The magnetic field strengths considered in this work influences only the EoS of outer and shallow regions of the inner crust, which results in no significant change in global neutron star properties. However, the outer crust mass and its moment of inertia increase considerably with increase in magnetic field strength.

Implementation of the quasiparticle finite amplitude method within the relativistic self-consistent mean-field framework (II): The program DIRQFAM v2.0.0

We describe the new version 2.0.0 of the code DIRQFAM that calculates the multipole response of even-even axially symmetric deformed nuclei using the framework of relativistic self-consistent mean-field models. The response is calculated by implementing the finite amplitude method for relativistic quasiparticle random phase approximation. In the new version, we have implemented the following features: (i) meson-exchange interactions, (ii) low-rank method for calculating induced densities and currents, (iii) generalized minimal residual method (GMRES), (iv) evaluation of the nucleon localization function, (v) extraction of the QRPA transition matrix elements and eigenfrequencies, (vi) evaluation of the H11 part of the induced Hamiltonian, (vii) multipole excitation operators up to J≤5 are now included. Program summaryProgram title:DIRQFAM v2.0.0CPC Library link to program files:https://doi.org/10.17632/6gv8nxg4ns.2Licensing provisions: GPLv3Programming language: Fortran 90.External routines/libraries: BLAS/LAPACK, version 3.1. or higher.Journal reference of previous version: A. Bjelčić, T. Nikšić, Comp. Phys. Comm. 253, 107184 (2020).Does the new version supersede the previous version?: YesNature of problem: Multipole response of deformed even-even open-shell nuclei can be calculated using the quasiparticle finite amplitude method (QFAM), based on the relativistic self-consistent mean-field models. The particle-hole channel is described by a zero-range relativistic effective interaction or interaction based on meson exchange, while the particle-particle channel of the effective inter-nucleon interaction is described by a separable finite-range pairing force. The method can be applied to perform systematic studies of collective modes even in heavy deformed nuclei.Solution method: The current implementation computes the multipole response by solving the QFAM equations in a self-consistent iteration scheme. At each iteration the QFAM solutions are updated using the GMRES method. The QFAM amplitudes are expanded in the simplex-y harmonic oscillator basis.Summary of revisions:1.meson-exchange interaction are included in the code;2.calculation of the nucleon localization function;3.extraction of the QRPA transition matrix elements and eigenfrequencies;4.evaluation of the H11 part of the induced Hamiltonian;5.multipoles excitation operators up to J≤5 are included;6.low-rank method for calculating induced densities and currents;7.generalized minimal residual method;8.dynamic memory allocation;9.reduced memory requirements;Additional comments including restrictions and unusual features: Open-shell even-even nuclei with parity conserved axially symmetric ground states are considered. An electric multipole operator with J≤5 is used to calculate the response function.

Testing gravity with gravitational waves × electromagnetic probes cross-correlations

In a General Relativistic framework, Gravitational Waves (GW) and Electromagnetic (EM) waves are expected to respond in the same way to the effects of matter perturbations between the emitter and the observer. A different behaviour might be a signature of alternative theories of gravity. In this work we study the cross-correlation of resolved GW events (from compact objects mergers detected by the Einstein Telescope, either assuming or excluding the detection of an EM counterpart) and EM signals (coming both from the Intensity Mapping of the neutral hydrogen distribution and resolved galaxies from the SKA Observatory), considering weak lensing, angular clustering and their cross term (L × C) as observable probes. Cross-correlations of these effects are expected to provide promising information on the behaviour of these two observables, hopefully shedding light on beyond GR signatures. We perform a Fisher matrix analysis with the aim of constraining the {μ 0, η 0, Σ 0} parameters, either opening or keeping fixed the background parameters {w 0, w a}. We find that, although lensing-only forecasts provide significantly unconstrained results, the combination with angular clustering and the cross-correlation of all three considered tracers (GW, IM, resolved galaxies) leads to interesting and competitive constraints. This offers a novel and alternative path to both multi-tracing opportunities for Cosmology and the Modified Gravity sector.

Geometric Event-Based Quantum Mechanics

We propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).

Scattering of e± by C2H6 Molecule over a Wide Range of Energy: A Theoretical Investigation.

The present work reports the theoretical investigation of the scattering of electrons and positrons by the ethane (C2H6) molecule over the energy range 1 eV-1 MeV. The investigation was carried out by taking into account the screening correction arising from a semiclassical analysis of the atomic geometrical overlapping of the scattering observables calculated in the independent atom approximation. The study is presented through the calculations of a broad spectrum of observable quantities, namely differential, integrated elastic, momentum transfer, viscosity, inelastic, grand total, and total ionization cross-sections and the Sherman functions. A comparative study was carried out between scattering observables for electron impact with those for positron impact to exhibit the similarity and dissimilarity arising out of the difference of the collisions of impinging projectiles with the target. Partial-wave decomposition of the scattering states within the Dirac relativistic framework employing a free-atom complex optical model potential was used to calculate the corresponding observable quantities of the constituent atoms. The results, calculated using our recipe, were compared with the experimental and theoretical works available in the literature. The Sherman function for a e±-C2H6 scattering system is presented for the first time in the literature. The addition of the screening correction to the independent atom approximation method was found to substantially reduce the scattering cross-sections, particularly at forward angles for lower incident energies.

Directed flow in relativistic resistive magneto-hydrodynamic expansion for symmetric and asymmetric collision systems

We construct a dynamical model for high-energy heavy-ion collisions based on the relativistic resistive magneto-hydrodynamic framework. Using our newly developed ($3+1$)-dimensional relativistic resistive magneto-hydrodynamics code, we investigate magneto-hydrodynamic expansion in symmetric and asymmetric collision systems as the first application to high-energy heavy-ion collisions. As a realistic initial condition for electromagnetic fields, we consider the solutions of the Maxwell equations with the source term of point charged particles moving in the direction of the beam axis, including finite constant electrical conductivity of the medium. We evaluate the directed flow in the symmetric and asymmetric collisions at BNL Relativistic Heavy Ion Collider energy. We find a significant effect of finite electrical conductivity on the directed flow in the asymmetric collision system. We confirm that a certain amount of energy transfer by dissipation associated with Ohmic conduction occurs in the asymmetric collision system because of the asymmetry of the electric field produced by two different colliding nuclei. Because this energy transfer makes the pressure gradient of the medium flatter, the growth of directed flow decreases.

Fluctuations of conserved charges in hydrodynamics and molecular dynamics

We present an overview of recent theoretical results on fluctuations of conserved charges in heavy-ion collisions obtained in relativistic hydrodynamics and molecular dynamics frameworks. In particular, we discuss the constraints on the location of the QCD critical point based on comparisons of experimental data on proton number cumulants with precision calculations of noncritical contributions. We also cover recent developments on critical fluctuations in molecular dynamics simulations.

К выводу в рамках статистики Тсаллиса релятивистского кинетического уравнения для разреженной идеальной газовой системы высокоэнергетических частиц

In this work we discuss the nonextensive kinetic theory for anomalous gas q-systems in a general relativistic framework. By including nonextensive effects in the collision term of the relativistic equation (violating Boltzmann molecular chaos hypothesis) and in a modified 4-vector expression for the q-entropy flux it is shown that the entropic Tsallis formalism preserves a local form of the relativistic H-theorem according to which the entropy growth in any point of space-time is never negative. It is shown that the local collision equilibrium (the zero-point entropy source term) is described by a generalized version of the Yuttner relativistic distribution. Using this distribution, the particle number, energy and entropy densities and the thermal equation of state for a relativistic q-gas of identical particles in the equilibrium state are determined explicitly. The results are reduced to the standard ones in the extensive limit, thus showing that the nonex-tensive entropic scheme can be consistent with the space-time ideas contained in the general rela-tivistic theory. The constructed kinetic equation is designed to describe a wide range of phenomena in as-trophysics, cosmology and high-energy physics, in particular, multiparticle production processes in relativistic collisions.

Atomistic modeling of the channeling process with radiation reaction force included

Methodology is developed that incorporates the radiative reaction force into the relativistic molecular dynamics framework implemented in the MBN Explorer software package. The force leads to a gradual decrease in the projectile’s energy ɛ due to the radiation emission. This effect is especially strong for ultra-relativistic projectiles passing through oriented crystals where they experience the action of strong electrostatic fields as has been shown in recent experiments. A case study has been carried out for the initial approbation of the methodology developed. Simulations of the processes of planar channeling and photon emission have been performed for 150 GeV positrons in a 200μm thick single oriented Si(110) crystal. Several regimes for the decrease in ɛ have been established and characterized. Further steps in developing the code to include the necessary quantum corrections are identified and possible algorithmic modifications are proposed.

Accelerated motion in general relativity: fate of the singularity

Under general relativity, the paths of accelerated test particles are taken into account. It is examined whether such accelerations have any influence on the ‘singularity’ of the spacetime. The Raychaudhuri equation for the congruence of the time-like curves describing the paths of the accelerated particles is considered to calculate a few physical attributes. It is shown that if the acceleration of the test particles exceeds a particular value, then the congruences of the accelerated time-like curves do not encounter any singularity although the usual energy conditions are violated or modified. It is shown further that in the curved spacetime of general relativistic framework one may generate a system of transformations that is a generalization of the Rindler coordinates related to accelerated frame in the flat Minkowski spacetime. To show the influence of the acceleration of test particle on singularity of a particular spacetime the Schwarzschild spacetime is considered. Taking tidal deviation related acceleration term, it is shown that the acceleration may attain a specific value for which the modified Kretschmann scalar vanishes in a spherical neighbourhood of the singularity and thus the Schwarzschild singularity disappears. In the context of singularity as ‘geodesic incompleteness’ of the spacetime manifold it is also proved that prescribing an appropriate acceleration term on the maximal geodesic defined in a finite interval one may extend it up to infinite proper time and hence the spacetime becomes singularity free. Such results hold at the price of violating the usual energy conditions.

Splitting of elliptic flow in a tilted fireball

The splitting of elliptic flow measured in different regions of the momentum space of produced hadrons has been recently studied in transport models and proposed as a sensitive probe of the angular momentum carried by the fireball produced in a relativistic heavy ion collision. The initial state angular momentum also gives rise to rapidity odd directed flow which has been measured. We consider a relativistic hydrodynamic framework with the initial matter distribution suitably calibrated to describe the observed directed flow and apply it to study the spilt in the elliptic flow. Our study suggests that the split in the elliptic flow is mostly driven by directed and triangular flows and may be used to constrain models of initial state rapidity distribution of matter in the fireball.

On the development of relativistic distorted wave approximation for the energies and collision dynamics of atoms or ions subjected to the outside plasma

In this manuscript, we present the development of a relativistic distorted wave method for determining the energies and collision dynamics of plasma-immersed atoms or ions. The methodology is based on the Dirac–Coulomb Hamiltonian, in which contributions from relativity and higher order effects, such as quantum electrodynamics and Breit interaction, are incorporated. The key element in this method is that a modified Debye–Hückel approximation is employed to represent the effect of plasma screening. In order to correctly describe the (bound and continuous state) wave functions, a self-consistent field calculation incorporating the shielding potential is performed within the fully relativistic framework. The particle interaction within the scattering matrix element of the excitation process is described by the shielded Coulomb interaction. The present technique is illustrated by calculations of energy, line shift, transition probability, electron-impact excitation/ionization cross section, and photoionization cross section of a few-electron system confined in plasma environments. The present model is tested and validated against a number of known cases (simulations are made for the He-like Al11+ ion) in the literatures. Numerical results demonstrate that the modifications to the Coulomb potential proposed in the spatial and temporal criteria of the Debye–Hückel approximation allow us to improve the theoretical description of the plasma shielding and thus the dynamical processes in dense plasmas. Comparisons of our computational predictions and the recent experimental measurements are performed. The current work not only has far-reaching implications for our understanding of the dense plasma screening, but also has potential applications in fusion, laboratory astrophysics, and related disciplines.

Explaining mass and spin in the visible matter: the next challenge

Understanding in depth …the origin of the nucleon mass, the nucleon spin, and the emergent properties of a dense gluon system… (Electron-ion collider Yellow Report, arXiv:2103.05419v) represents the frontier of modern hadron physics, both on the experimental and theoretical side. In this contribution, after briefly outlining the above challenges in view of the various experimental facilities planned in the near future, some insights into the non-perturbative regime of QCD will be provided. In particular, the most recent achievements in the description of the pion, playing a fundamental role in the hadron dynamics, will be illustrated within a genuinely relativistic quantum-field theoretical framework, based on actual solutions of the homogeneous Bethe-Salpeter equation.

Ammonia: The molecule for establishing 14N and 15N absolute shielding scales and a source of information on nuclear magnetic moments.

Multinuclear Nuclear Magnetic Resonance (NMR) studies of the gaseous mixtures 3He/14NH3 and 3He/15NH3 are reported. Precise analysis of the 3He, 14N, 15N, and 1H resonance frequencies show a linear dependence on the gas density. Extrapolation of these results to the zero-pressure limit gives ν0(1H), ν0(14N), and ν0(15N) resonance frequencies of the isolated ammonia molecule at 300K. The analogous value for 3He atoms in gaseous mixtures ν0(3He) was measured as well. The application of a new scheme to introduce the most important electronic effects on NMR shieldings, together with highly accurate quantum chemical shielding calculations, allows the 14/15N and 1H shielding of the isolated ammonia molecule to be obtained with the greatest accuracy and precision. For the first time, these studies were carried out on ammonia within the so-called four-component relativistic framework. The NMR frequency comparison method provides an approach for determining the 14N and 15N nuclear magnetic moments. The new shielding parameters in ammonia were used for re-evaluation of the entire nitrogen absolute shielding scale. Additionally, the absolute shielding values of several gaseous compounds and secondary reference substances in liquids were presented. It was established that 14N and 15N absolute shielding constants in 14NH3 and 15NH3 are very similar and only differ by less than 0.01 ppm, which is not usually measurable in NMR experiments. Precise calculations of 14N and 15N dipole moments were also made from these accurate shielding values.

Probing cosmic string spacetime through parameter estimation

Quantum metrology studies the ultimate precision limit of physical quantities by using quantum strategy. In this paper we apply the quantum metrology technologies to the relativistic framework for estimating the deficit angle parameter of cosmic string spacetime. We use a two-level atom coupled to electromagnetic fields as the probe and derive its dynamical evolution by treating it as an open quantum system. We estimate the deficit angle parameter by calculating its quantum Fisher information(QFI). It is found that the quantum Fisher information depends on the deficit angle, evolution time, detector initial state, polarization direction, and its position. We then identify the optimal estimation strategies, i.e., maximize the quantum Fisher information via all the associated parameters, and therefore optimize the precision of estimation. Our results show that for different polarization cases the QFIs have different behaviors and different orders of magnitude, which may shed light on the exploration of cosmic string spacetime.

Multimodal image synthesis based on disentanglement representations of anatomical and modality specific features, learned using uncooperative relativistic GAN.

Growing number of methods for attenuation-coefficient map estimation from magnetic resonance (MR) images have recently been proposed because of the increasing interest in MR-guided radiotherapy and the introduction of positron emission tomography (PET) MR hybrid systems. We propose a deep-network ensemble incorporating stochastic-binary-anatomical encoders and imaging-modality variational autoencoders, to disentangle image-latent spaces into a space of modality-invariant anatomical features and spaces of modality attributes. The ensemble integrates modality-modulated decoders to normalize features and image intensities based on imaging modality. Besides promoting disentanglement, the architecture fosters uncooperative learning, offering ability to maintain anatomical structure in a cross-modality reconstruction. Introduction of a modality-invariant structural consistency constraint further enforces faithful embedding of anatomy. To improve training stability and fidelity of synthesized modalities, the ensemble is trained in a relativistic generative adversarial framework incorporating multiscale discriminators. Analyses of priors and network architectures as well as performance validation were performed on computed tomography (CT) and MR pelvis datasets. The proposed method demonstrated robustness against intensity inhomogeneity, improved tissue-class differentiation, and offered synthetic CT in Hounsfield units with intensities consistent and smooth across slices compared to the state-of-the-art approaches, offering median normalized mutual information of 1.28, normalized cross correlation of 0.97, and gradient cross correlation of 0.59 over 324 images.

GRMHD simulations of accreting neutron stars with non-dipole fields

ABSTRACT NASA’s NICER telescope has recently provided evidence for non-dipolar magnetic field structures in rotation-powered millisecond pulsars. These stars are assumed to have gone through a prolonged accretion spin-up phase, begging the question of what accretion flows on to stars with complex magnetic fields would look like. We present results from a suite of general relativistic magnetohydrodynamic simulations of accreting neutron stars for dipole, quadrupole, and quadrudipolar stellar field geometries. This is a first step towards simulating realistic hotspot shapes in a general relativistic framework to understand hotspot variability in accreting millisecond pulsars. We find that the location and size of the accretion columns resulting in hotspots changes significantly depending on initial stellar field strength and geometry. We also find that the strongest contributions to the stellar torque are from disc-connected field lines and the pulsar wind, leading to spin-down in almost the entire parameter regime explored here. We further analyse angular momentum transport in the accretion disc due to large-scale magnetic stresses, turbulent stresses, and wind and compressible effects which we identify with convective motions. The disc collimates the initial open stellar flux forming jets. For dipoles, the disc–magnetosphere interaction can either enhance or reduce jet power compared to the isolated case. However for quadrupoles, the disc always leads to an enhanced net open flux making the jet power comparable to the dipolar case. We discuss our results in the context of observed neutron star jets and provide a viable mechanism to explain radio power both in the low- and high-magnetic field case.

Attempt to obtain the general relativistic planet's motion by special relativity techniques

AbstractIt is attempted to derive the general relativistic equation of motion for a planet and its solution solely by the special relativity techniques. The motion of a planet relative to the Sun and that of the Sun to the planet are solved independently in a special relativistic framework using the perturbation theory in celestial mechanics. The solution reveals a nature of the structure of the spacetime under the gravitation of the Sun, and then its effect on the planet's motion is examined. When the motion thus examined are compared with the one obtained by the general relativity theory in post‐Newtonian approximation, both are different concerning the mean motion and the radius of the orbit but exactly the same as for the perihelion precession.

Shocks in Radiatively Driven Time-dependent, Relativistic Jets around Black Holes

We study time-dependent relativistic jets under the influence of the radiation field of the accretion disk. The accretion disk consists of an inner compact corona and an outer sub-Keplerian disk. The thermodynamics of the fluid is governed by a relativistic equation of state (EOS) for multispecies fluid that enables us to study the effect of composition on jet dynamics. Jets originate from the vicinity of the central black hole, where the effect of gravity is significant and traverses large distances where only special relativistic treatment is sufficient. So we have modified the flat metric to include the effect of gravity. In this modified relativistic framework we have developed a new total variation diminishing routine along with a multispecies EOS for the purpose. We show that the acceleration of jets crucially depends on flow composition. All the results presented are transonic in nature; starting from very low injection velocities, the jets can achieve high Lorentz factors. For sub-Eddington luminosities, lepton-dominated jets can be accelerated to Lorentz factors >50. The change in radiation field due to variation in the accretion disk dynamics will be propagated to the jet in a finite amount of time. Hence, any change in radiation field due to a change in disk configuration will affect the lower part of the jet before it affects the outer part. This can drive shock transition in the jet flow. Depending on the disk oscillation frequency, amplitude, and jet parameters, these shocks can collide with each other and may trigger shock cascades.

Two-neutrino double- β decay matrix elements based on a relativistic nuclear energy density functional

Nuclear matrix elements (NMEs) for two-neutrino double-beta decay ($2\nu\beta\beta$) are studied in the framework of relativistic nuclear energy density functional (REDF). The properties of nuclei involved in the decay are obtained using the relativistic Hartree-Bardeen-Cooper-Schrieffer theory and relevant nuclear transitions are described using the relativistic proton-neutron quasiparticle random phase approximation based on relativistic energy density functional (REDF-QRPA). Three effective interactions have been employed, including density-dependent meson-exchange (DD-ME2) and point coupling interactions (DD-PC1 and DD-PCX), and pairing correlations are described consistently both in $T=1$ and $T=0$ channels using a separable pairing interaction. The optimal values of $T=0$ pairing strength parameter $V_{0pp}$ are constrained by the experimental data on $\beta$-decay half lives. The $2\nu\beta\beta$ matrix elements and half-lives are calculated for several nuclides experimentally known to undergo this kind of decay: $^{48}$Ca, $^{76}$Ge, $^{82}$Se, $^{96}$Zr, $^{100}$Mo, $^{116}$Cd, $^{124}$Xe, $^{128}$Te, $^{130}$Te, $^{136}$Xe and $^{150}$Nd. The model dependence of the NMEs and their sensitivity on $V_{0pp}$ is investigated, and the NMEs obtained using optimal values of $V_{0pp}$ are discussed in comparison to previous studies. The results of the present work represent an important benchmark for the future applications of the relativistic framework in studies of neutrinoless double-beta decay.