Related Treatment Research Articles

Fully relativistic treatment of light neutrinos in N-body simulations

Cosmological N-body simulations are typically purely run with particles using Newtonian equations of motion. However, such simulations can be made fully consistent with general relativity using a well-defined prescription. Here, we extend the formalism previously developed for ΛCDM cosmologies with massless neutrinos to include the effects of massive, but light neutrinos, where the effect of neutrinos on the matter clustering can be adequately modelled using linear perturbation theory for neutrinos. We have implemented the method in two different N-body codes, COnCEPT and PKDGRAV, and demonstrate that they produce consistent results. We furthermore show that we can recover all appropriate limits, including the full GR solution in linear perturbation theory at the per mille level of precision.

Representations of relativistic particles of arbitrary spin in Poincaré, Lorentz, and Euclidean covariant formulations of relativistic quantum mechanics

Relativistic treatments of quantum mechanical systems are important for understanding hadronic structure and dynamics at sub-nucleon distance scales. Hadronic states in different inertial reference frames are needed to compute current matrix elements that probe hadronic structure and dynamics. Relativistic invariance is an important consideration as the resolution of the probe is increased. Many different treatments of relativistic dynamics are used in practice, including Poincar\'e covariant methods, Lorentz covariant methods, Euclidean covariant methods and methods based on quantum fields. Wave functions are typically matrix elements of interacting relativistic states in a basis of non-interacting relativistic states. The purpose of this work is to develop the relation between these different representations of relativistic states that are used in different applications from a unified point of view, starting with positive mass irreducible representations of the Poincar\'e group.

A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations.

Theoretical considerations are discussed for the accurate prediction of cadmium magnetic shielding tensors using relativistic density functional theory (DFT). Comparison is made between calculations that model the extended lattice of the cadmium-containing solids using periodic boundary conditions and pseudopotentials with calculations that use clusters of atoms. The all-electron cluster-based calculations afford an opportunity to examine the importance of (i) relativistic effects on cadmium magnetic shielding tensors, as introduced through the ZORA Hamiltonian at either the scalar (SC) or spin-orbit (SO) levels and (ii) variation in the class of the DFT approximation. Twenty-three combinations of pseudopotentials or all-electron methods, DFT functionals, and relativistic treatments are assessed for the prediction of the principal components of the magnetic shielding tensors of 30 cadmium sites. We find that the inclusion of SO coupling can increase the cadmium magnetic shielding by as much as ca. 1100 ppm for a certain principal values; these effects are most pronounced for cadmium sites featuring bonds to other heavy atoms such as cadmium, iodine, or selenium. The best agreement with experimental values is found at the ZORA SO level in combination with a hybrid DFT method featuring a large admixture of Hartree-Fock exchange such as BH&HLYP. Finally, a theoretical examination is presented of the magnetic shielding tensor of the Cd(I) site in Cd2(AlCl4)2.

Decoherence and Phase Transitions in Quantum Dynamics

A particle with internal degrees of freedom is in contact with a bath of photons (necessitating a relativistic treatment). The occurrence of decoherence is established and the density matrix is found to be diagonal in momentum space. In the case of non-trivial internal degrees of freedom and selection rules there is a first order phase transition separating those degrees of freedom. Finally, because probability amplitudes become probabilities, Einstein’s proposal that more than one detector could respond to a signal is answered.

Landau levels in the presence of a cosmic string in rainbow gravity

In this paper we analyze the energy levels of a charged scalar particle placed in the static cosmic string spacetime, under the action of a uniform magnetic field parallel to the string, in the context of the semi-classical approach of the rainbow gravity. Firstly, we focus on the non-relativistic regime by solving the corresponding Schrödinger equation, following by a complete relativistic treatment of the problem in which we considered the Klein–Gordon equation. In both cases we find exact expressions for the Landau levels in terms of the rainbow functions, used to characterize a rainbow gravity model. In order to achieve the results of this paper we considered three different rainbow gravity models mostly used in the literature and compare the resulting modifications in the Landau levels with the standard case, namely without rainbow gravity.

Semirelativistic Schrödinger Equation for Relativistic Laser-Matter Interactions.

A semirelativistic formulation of light-matter interaction is derived using the so called propagation gauge and the relativistic mass shift. We show that relativistic effects induced by a superintense laser field can, to a surprisingly large extent, be accounted for by the Schrödinger equation, provided that we replace the rest mass in the propagation gauge Hamiltonian by the corresponding time-dependent field-dressed mass. The validity of the semirelativistic approach is tested numerically on a hydrogen atom exposed to an intense extreme ultraviolet laser pulse strong enough to accelerate the electron towards relativistic velocities. It is found that while the results obtained from the ordinary (nonrelativistic) Schrödinger equation generally differ from those of the Dirac equation, demonstrating that relativistic effects are significant, the semirelativistic formulation provides results in quantitative agreement with a fully relativistic treatment.

Relativistic effects on the ring current strengths of the substituted borazine: B3N3H6 (X=H, F, Cl, Br, I, At)

AbstractIn this study, we report about the relativistic effects on the aromaticity of borazine, B3N3H6, and their halogenated derivatives (B3N3F6, B3N3Cl6, B3N3Br6, B3N3I6, and B3N3At6), via the magnetically‐induced current density method. All‐electron density functional theory calculations were carried out using the four‐component Dirac‐Coulomb hamiltonian, including scalar and spin‐orbit relativistic effects. Ring current strengths were obtained by numerical integration over the current flow. These values were compared to the spin‐free (scalar relativistic) and nonrelativistic values, to assess the corresponding contributions to aromaticity. It was found that in B3N3I6 and B3N3At6 there exists a significant spin‐orbit influence, in line with the expected relativistic effects associated to the heavy elements, iodine, and astatine.Borazine, B3N3H6, is known to be slightly aromatic, but much less aromatic than benzene. The application of an external magnetic field induces a current density, that accounts for the delocalization and mobility of electrons in a molecule. Using this theoretical method, the aromaticity of the derivatives B3N3X6(X = H, F, Cl, Br, I, At) was investigated. The inclusion of heavy elements requires a relativistic treatment where the spin‐orbit coupling must be included. The figure shows the three‐dimensional pathways of the current density flow in B3N3At6.

Relativistic calculations on the x-ray satellites of platinum with multiply ionized L shell

The energies, electric dipole rates and oscillator strengths of Kα x-ray satellites from 1s–2p transitions in platinum with a single vacancy in the K shell and variously ionized L shell are calculated using multi-configuration Dirac Fock wavefunctions with the inclusion of Breit interaction and quantum electrodynamics effects. The computations have been performed for low ionized (Pt1+–Pt6+) and also for highly ionized (Pt69+–Pt77+) Pt. As Kα x-ray satellites with spectator vacancies only in the L shell, to the best of our knowledge, have been studied for the first time, to check the accuracy of the present work, calculations have also been performed for H-, He-, Li-, Be-, B- and F-like Pt for which theoretical data for comparison exist. The purpose of choosing a high Z element is that the detailed decay properties of heavy ions due to systematic 1s–2p transitions with spectator vacancies in the L shell using fully relativistic treatment are unexplored and the increasing need for reliable data from such ions in various applications that are under investigations in recent years. Also, for heavy ions like Pt, the contribution from the competing non-radiative transitions is less and hence the atomic properties are largely due to radiative transitions. The K X ray satellite energies, rates and resonance photo- ionization cross sections from H-, He-, Li-, Be-, B- and F-like Pt are compared with available data.

Relativistic treatment of scattering of electrons and positrons by mercury atoms

ABSTRACTWith a complex optical potential, , the Dirac relativistic equation is solved, employing the partial wave technique, to evaluate the differential, integrated, momentum transfer and viscosity cross-sections for the elastic scattering of -Hg system over the incident energy range of 1.0 eV 10.0 keV. We also calculate the inelastic and grand total cross sections for this system over the same energy range. The real part of includes the static, the exchange and the polarisation components while the imaginary component incorporates the absorption of particles into various inelastic channels. A detailed comparison of our results with experimental and other theoretical findings show a good overall agreement throughout the studied energy range, apart from some discrepancies at lower energies eV.

New proof of general relativity through the correct physical interpretation of the Mössbauer rotor experiment

In this paper, we give a correct interpretation of a historical experiment by Kündig on the transverse Doppler shift in a rotating system (Mössbauer rotor experiment). This experiment has been recently first reanalyzed, and then replied by an experimental research group. The results of reanalyzing the experiment have shown that a correct re-processing of Kündig’s experimental data gives an interesting deviation of a relative redshift between emission and absorption resonant lines from the standard prediction based on the relativistic dilatation of time. Subsequent new experimental results by the reply of Kündig experiment have shown a deviation from the standard prediction even higher. By using the Equivalence Principle (EP), which states the equivalence between the gravitational “force” and the pseudo-force experienced by an observer in a noninertial frame of reference (included a rotating frame of reference), here the theoretical framework of the Mössbauer rotor experiment is reanalyzed directly in the rotating frame of reference through a general relativistic treatment. It will be shown that previous analyses missed an important effect of clock synchronization. By adding this new effect, the correct general relativistic prevision is in perfect agreement with the new experimental results. Such an effect of clock synchronization has been missed in various papers in the literature, with some subsequent claim of invalidity of the relativity theory and/or some attempts to explain the experimental results through “exotic” effects. The general relativistic interpretation in this paper shows, instead that the new experimental results of the Mössbauer rotor experiment are a new, strong and independent proof of general relativity.

Relativistic Treatment of Spin-zero Particles Subjected to the Shifted Tietz-Wei Potential Model

The approximate solutions of the Klein-Gordon equation with the shifted Tietz-Wei potential function are thoroughly studied for Klein-Gordon equation with both 2V and V potentials by using a suitable approximation scheme for the centrifugal term in the framework of the supersymmetric approach. The non-relativistic limits in both cases are obtained, and the numerical results are computed. We have equally investigated the Fisher information on the shifted Tietz-Wei potential function in the case of the non-relativistic limit of the Klein-Gordon equation with potential V because this is only possible in the non-relativistic regime. The Fisher information is observed to be inversely proportional to both Ch and bh, where Ch is the optimization parameter and bh = β(1 − Ch), with β being the Morse constant.

Acoustics of noise, vibration, and harshness

In this paper, we will go to a more fundamental level of treating acoustics. We introduced the gauge invariance into the acoustic wave equation of motion in 2007. This is an important milestone in the history of gauge invariance. The earliest gauge invariance is shown by Maxwell’s electromagnetic wave equations. The root of acoustics originated from fluid mechanics. We show that the usual form of acoustic wave equation for fluids is in fact the linearized form of the Navier Stokes equations. Hence there is in fact, no need to use acoustic analogy to derive the formula for the jet noise which was done by James Lighthill. In this paper we also treat finite amplitude sound wave and finite amplitude vibration using the deductive approach. This is a generalization of the linear theory to the nonlinear theory using relativistic and curvilinear spacetime treatment. This produces the linear case as a special case of the nonlinear case. The usual method is the reverse which starts from the linear theory and extend to the nonlinear theory. This will miss out some useful information. The treatment of vibration will need to incorporate the theory of elasticity. This paper is also the first introduction of singularities into vibration. Singularities is mathematically more sophisticated than resonance.

Radiation from rapidly rotating oblate neutron stars

A theoretical framework for emission originating from rapidly rotating oblate compact objects is described in detail. Using a Hamilton-Jacobi formalism, we show that special relativistic rotational effects such as aberration of angles, Doppler boosting, and time dilatation naturally emerge from the general relativistic treatment of rotating compact objects. We use the Butterworth–Ipser metric expanded up to the second order in rotation and hence include effects of light bending, frame-dragging, and quadrupole deviations on our geodesic calculations. We also give detailed descriptions of the numerical algorithms used and provide an open-source implementation of the numerical framework calledBENDER. As an application, we study spectral line profiles (i.e., smearing kernels) from rapidly rotating oblate neutron stars. We find that in this metric description, the second-order quadrupole effects are not strong enough to produce narrow observable features in the spectral energy distribution for almost any physically realistic parameter combination, and hence, actually detecting them is unlikely. The full width at tenth-maximum and full width at half-maximum of the rotation smearing kernels are also reported for all viewing angles. These can then be used to quantitatively estimate the effects of rotational smearing on the observed spectra. We also calculate accurate pulse profiles and observer skymaps of emission from hot spots on rapidly rotating accreting millisecond pulsars. These allow us to quantify the strength of the pulse fractions one expects to observe from typical fast-spinning millisecond pulsars.

Energy Levels of Core-Excited 1s2l2l′ States in Lithium-Like Ions: Argon to Uranium

Energy levels and fine-structure intervals of the 1s2l2l′ core-excited states are calculated for ions along the Li isoelectronic sequence from argon to uranium. The calculation is performed by the relativistic configuration-interaction method adapted for treatment of autoionizing core-excited states. The calculational approach includes the relativistic treatment of the nuclear recoil effect, the leading quantum electrodynamics (QED) shifts as delivered by the model QED operator, and the frequency dependence of the Breit interaction. The 1s2l2l′–1s22l transition energies are obtained by combining the present results for the 1s2l2l′ states with energies of the 1s22l states compiled from previous calculations. All theoretical energies are supplied with uncertainty estimates. Our theoretical predictions for the 1s2l2l′–1s22l transitions are significantly more accurate than the best experimental results available today and can be used for calibrating experimental X-ray spectra.

Influence of dense plasma on the energy levels and transition properties in highly charged ions

The studies of the influence of plasma environments on the level structures and transition properties for highly charged ions are presented. For the relativistic treatment, we implemented the multiconfiguration Dirac-Fock method incorporating the ion sphere (IS) model potential, in which the plasma screening is taken into account as a modified interaction potential between the electron and the nucleus. For the nonrelativistic treatment, analytical solutions of the Schrödinger equation with two types of the IS screened potential are proposed. The Ritz variation method is used with hydrogenic wave function as a trial wave function that contains two unknown variational parameters. Bound energies are derived from an energy equation, and the variational parameters are obtained from the minimisation condition of the expectation value of the energy. Numerical results for hydrogen-like ions in dense plasmas are presented as examples. A detailed analysis of the influence of relativistic effects on the energy levels and transition properties is also reported. Our results are compared with available results in the literature showing a good quantitative agreement.

Two-dimensional Core-collapse Supernova Explosions Aided by General Relativity with Multidimensional Neutrino Transport

Abstract We present results from simulations of core-collapse supernovae in FLASH using a newly implemented multidimensional neutrino transport scheme and a newly implemented general relativistic (GR) treatment of gravity. We use a two-moment method with an analytic closure (so-called M1 transport) for the neutrino transport. This transport is multienergy, multispecies, velocity dependent, and truly multidimensional, i.e., we do not assume the commonly used “ray-by-ray” approximation. Our GR gravity is implemented in our Newtonian hydrodynamics simulations via an effective relativistic potential that closely reproduces the GR structure of neutron stars and has been shown to match GR simulations of core collapse quite well. In axisymmetry, we simulate core-collapse supernovae with four different progenitor models in both Newtonian and GR gravity. We find that the more compact proto–neutron star structure realized in simulations with GR gravity gives higher neutrino luminosities and higher neutrino energies. These differences in turn give higher neutrino heating rates (upward of ∼20%–30% over the corresponding Newtonian gravity simulations) that increase the efficacy of the neutrino mechanism. Three of the four models successfully explode in the simulations assuming GREP gravity. In our Newtonian gravity simulations, two of the four models explode, but at times much later than observed in our GR gravity simulations. Our results, in both Newtonian and GR gravity, compare well with several other studies in the literature. These results conclusively show that the approximation of Newtonian gravity for simulating the core-collapse supernova central engine is not acceptable. We also simulate four additional models in GR gravity to highlight the growing disparity between parameterized 1D models of core-collapse supernovae and the current generation of 2D models.

Compton scattering of Bessel light with large recoil parameter

Compton scattering of light from a Bessel beam is investigated for which the energy of a photon in the beam is comparable to the mass energy of an electron. Using a fully relativistic treatment, we present numerical results on how the angular distribution and polarization of the scattered photons depend on the opening angle, projection of orbital angular momentum, and the energy of the twisted Bessel photons of the incident beam and compare these results to the standard case of incident plane waves. Compton scattering of a superposition of two Bessel beams is also investigated. The energy of the incident twisted Bessel photon is found to significantly affect the angular distribution and polarization of the scattered radiation and their sensitivity to the other parameters of the incident photon.

Relativistic theory of the falling retroreflector gravimeter**Work of the US government, not subject to copyright.

We develop a relativistic treatment of interference between light reflected from a falling cube retroreflector in the vertical arm of an interferometer, and light in a reference beam in the horizontal arm. Coordinates that are nearly Minkowskian, attached to the falling cube, are used to describe the propagation of light within the cube. Relativistic effects such as the dependence of the coordinate speed of light on gravitational potential, propagation of light along null geodesics, relativity of simultaneity, and Lorentz contraction of the moving cube, are accounted for. The calculation is carried to first order in the gradient of the acceleration of gravity. Analysis of data from a falling cube gravimeter shows that the propagation time of light within the cube itself causes a significant reduction in the value of the acceleration of gravity obtained from measurements, compared to assuming reflection occurs at the face. An expression for the correction to g is derived and found to agree with experiment. Depending on the instrument, the correction can be several microgals, comparable to commonly applied corrections such as those due to polar motion and earth tides. The controversial ‘speed of light’ correction is discussed.

Nonmesonic weak decay of charmed hypernuclei

We present a study of the nonmesonic weak decay (NMWD) of charmed hypernuclei using a relativistic formalism. We work within the framework of the independent particle shell model and employ a (π, K) one-meson-exchange model for the decay dynamics. We implement a fully relativistic treatment of nuclear recoil. Numerical results are obtained for the one-neutron-induced transition NMWD rates of the N. The effect of nuclear recoil is sizable and goes in the direction to decrease the nuclear decay rate. We found that the NMWD decay rate of is of the same order of magnitude as the partial decay rate for the corresponding mesonic decay , suggesting the feasibility of experimental detection of such heavy-flavor nuclear processes.

The X-Ray Polarization of the Accretion Disk Coronae of Active Galactic Nuclei

Abstract Hard X-rays observed in Active Galactic Nuclei (AGNs) are thought to originate from the Comptonization of the optical/UV accretion disk photons in a hot corona. Polarization studies of these photons can help to constrain the corona geometry and the plasma properties. We have developed a ray-tracing code that simulates the Comptonization of accretion disk photons in coronae of arbitrary shapes, and use it here to study the polarization of the X-ray emission from wedge and spherical coronae. We study the predicted polarization signatures for the fully relativistic and various approximate treatments of the elemental Compton scattering processes. We furthermore use the code to evaluate the impact of nonthermal electrons and cyclo-synchrotron photons on the polarization properties. Finally, we model the NuSTAR observations of the Seyfert I galaxy Mrk 335 and predict the associated polarization signal. Our studies show that X-ray polarimetry missions such as NASA’s Imaging X-ray Polarimetry Explorer and the X-ray Imaging Polarimetry Explorer proposed to ESA will provide valuable new information about the physical properties of the plasma close to the event horizon of AGN black holes.