Relativistic Terms Research Articles

ON THE ANISOTROPIC POTENTIALS OF MANEV–SCHWARZSCHILD TYPE

In this paper, we study the two-body problem that describes the motion of two-point masses in an anisotropic space under the influence of a Newtonian force-law with two relativistic correction terms. We will show that the set of initial conditions leading to collisions and ejections and leading to escapes and captures have positive measure. Using the infinity manifold, we study capture and escape solutions in the zero-energy case. We also show that the flow on the zero energy manifold of a two-body problem given by the sum of the Newtonian potential and three anisotropic perturbations (corresponding to three relativistic correction terms) is chaotic.

Terahertz generation in plasmas using two-color laser pulses

We analyze the generation of terahertz radiation when an intense, short laser pulse is mixed with its frequency-doubled counterpart in plasma. The nonlinear coupling of the fundamental and the frequency-doubled laser pulses in plasma is shown to be characterized by a third order susceptibility which has a time dependence characteristic of the laser pulse durations. The terahertz generation process depends on the relative polarizations of the lasers and the terahertz frequency is omega approximately 1/tau(L), where tau(L) is the laser pulse duration. Since the laser pulse duration is typically in the picosecond or subpicosecond regime the resulting radiation is in the terahertz or multiterahertz regime. To obtain the third order susceptibility we solve the plasma fluid equations correct to third order in the laser fields, including both the relativistic and ponderomotive force terms. The relativistic and ponderomotive contributions to the susceptibility nearly cancel in the absence of electron collisions. Therefore, in this terahertz generation mechanism collisional effects play a critical role. Consistent with recent experimental observations, our model shows that (1) the terahertz field amplitude is proportional to I(1) square root I(2), where I(1) and I(2) are the intensities of the fundamental and second harmonic laser pulses, respectively, (2) the terahertz emission is maximized when the polarization of the laser beams and the terahertz are aligned, (3) for typical experimental parameters, the emitted terahertz field amplitude is on the order of tens of kilovolts/cm with duration comparable to that of the drive laser pulses, and (4) the direction of terahertz emission depends sensitively on experimental parameters.

MEASURING THE SPIN OF THE PRIMARY BLACK HOLE IN OJ287

The compact binary system in OJ287 is modelled to contain a spinning primary black hole with an accretion disk and a non-spinning secondary black hole. Using Post Newtonian (PN) accurate equations that include 2.5PN accurate non-spinning contributions, the leading order general relativistic and classical spin-orbit terms, the orbit of the binary black hole in OJ287 is calculated and as expected it depends on the spin of the primary black hole. Using the orbital solution, the specific times when the orbit of the secondary crosses the accretion disk of the primary are evaluated such that the record of observed outbursts from 1913 up to 2007 is reproduced. The timings of the outbursts are quite sensitive to the spin value. In order to reproduce all the known outbursts, including a newly discovered one in 1957, the Kerr parameter of the primary has to be $0.28 \pm 0.08$. The quadrupole-moment contributions to the equations of motion allow us to constrain the `no-hair' parameter to be $1.0\:\pm\:0.3$ where 0.3 is the one sigma error. This supports the `black hole no-hair theorem' within the achievable precision. It should be possible to test the present estimate in 2015 when the next outburst is due. The timing of the 2015 outburst is a strong function of the spin: if the spin is 0.36 of the maximal value allowed in general relativity, the outburst begins in early November 2015, while the same event starts in the end of January 2016 if the spin is 0.2

Carbon and proton shielding tensors in methyl halides

The series of methyl halides, CH(3)X (X = F, Cl, Br, and I), is prototypic for demonstrating the s.c. normal halogen dependence of light-atom nuclear magnetic resonance shielding constants in the presence of halogen atoms of varying electronegativity. We report a systematic experimental and first-principles theoretical study of the (13)C and (1)H shielding tensors in this series. The experimental shielding constants were obtained from gas-phase NMR experiments and the anisotropies were determined using liquid crystal NMR spectroscopy. After taking into account rovibrational effects and solute-solvent interactions, this provided the currently best experimental estimates for the full shielding tensors. Quantum chemical calculations were carried out at ab initio and density functional theory levels, involving relativistic corrections taken into account at the leading-order Breit-Pauli perturbation level. Anharmonic and harmonic vibrational corrections were performed. The main trends of the shielding constants and anisotropies of the nearby light (13)C and (1)H nuclei as functions of the halogen mass, were confirmed to be mainly due to relativistic spin-orbit effects. For carbon, also the scalar relativistic effects are important for quantitative results. Thermal averaging at 300 K decreases the magnitude of all the parameters but exhibits partial cancellation between the nonrelativistic and smaller relativistic rovibrational averages. For the shielding anisotropy, the relativistic terms add to the negative rovibrational effect. Overall, the current experimental and theoretical results are in excellent agreement for all the shielding parameters, setting a standard for further investigations of normal halogen dependence.

X-ray constrained unrestricted Hartree–Fock and Douglas–Kroll–Hess wavefunctions

The extension of the X-ray constrained (XC) wavefunction approach to open-shell systems using the unrestricted Hartree-Fock formalism is reported. The XC method is also extended to include relativistic effects using the scalar second-order Douglas-Kroll-Hess approach. The relativistic effects on the charge and spin density on two model compounds containing the copper and iron atom are reported. The size of the relativistic effects is investigated in real and reciprocal space; in addition, picture-change effects are investigated and discussed for the isolated Cu atom. It is found that the relativistic terms lead to changes in the densities that are much smaller than those from the X-ray constraint. Nevertheless, the use of the relativistic corrections in the ab initio model always leads to an improvement in the agreement statistics. An interesting result of the unrestricted XC technique is the possibility of obtaining experimentally derived spin densities from X-ray data.

The principle of locality: Effectiveness, fate, and challenges

The special theory of relativity and quantum mechanics merge in the key principle of quantum field theory, the principle of locality. We review some examples of its “unreasonable effectiveness” in giving rise to most of the conceptual and structural frame of quantum field theory, especially in the absence of massless particles. This effectiveness shows up best in the formulation of quantum field theory in terms of operator algebras of local observables; this formulation is successful in digging out the roots of global gauge invariance, through the analysis of superselection structure and statistics, in the structure of the local observable quantities alone, at least for purely massive theories; but so far it seems unfit to cope with the principle of local gauge invariance. This problem emerges also if one attempts to figure out the fate of the principle of locality in theories describing the gravitational forces between elementary particles as well. An approach based on the need to keep an operational meaning, in terms of localization of events, of the notion of space-time, shows that, in the small, the latter must loose any meaning as a classical pseudo-Riemannian manifold, locally based on Minkowski space, but should acquire a quantum structure at the Planck scale. We review the geometry of a basic model of quantum space-time and some attempts to formulate interaction of quantum fields on quantum space-time. The principle of locality is necessarily lost at the Planck scale, and it is a crucial open problem to unravel a replacement in such theories which is equally mathematically sharp, namely, a principle where the general theory of relativity and quantum mechanics merge, which reduces to the principle of locality at larger scales. Besides exploring its fate, many challenges for the principle of locality remain; among them, the analysis of superselection structure and statistics also in the presence of massless particles, and to give a precise mathematical formulation to the measurement process in local and relativistic terms; for which we outline a qualitative scenario which avoids the Einstein, Podolski, and Rosen paradox.

A phenomenological model for the precession of planets and bending of light

We presented a phenomenological mode that attributes the precession of perihelion of planets to the relativistic correction. This modifies Newton’s equation by adding an inversely cube term with distance. The total energy of the new system is found to be the same as the Newtonian one. Moreover, we have deduced the deflection of light formula from Rutherford scattering. The relativistic term can be accounted for quantum correction of the gravitational potential and/or self energy of objects.

Potential model calculations and predictions forcs¯quarkonia

We investigate the spectroscopy and decays of the charm-strange quarkonium system in a potential model consisting of a relativistic kinetic energy term, a linear confining term including its scalar and vector relativistic corrections, and the complete perturbative one-loop quantum chromodynamic short distance potential. The unperturbed wave functions of the various states are obtained using a variational technique. These are then used in a perturbative treatment of the potential to fit the mass spectrum of the $c\overline{s}$ system and calculate the radiative decay widths. Our results compare well with the available data for the spectrum of ${D}_{s}$ states. We include a discussion of the effect of mixing and investigation of the Lorentz nature of the confining potential.

Energy Gaps in the 4f135d1 Manifold and Multiple Spontaneous Emissions in Yb2+-Doped CsCaBr3

Multiple spontaneous 4f(13)5d(1) --> 4f(14) emissions are predicted in Yb(2+)-doped CsCaBr(3) crystals by ab initio quantum chemical calculations. Four emission bands are found at 23,900, 26,600, 34,600, and 43,900 cm(-1) that should be experimentally observable at low temperatures. The first, third, and fourth bands are slow, electric dipole forbidden emissions that can be described as spin-forbidden. The second band is a fast, electric dipole-allowed emission that cannot be described as spin-allowed, but as spin-enabled; its radiative emission lifetime is 400 ns. Large energy gaps (23 900, 4600, 4000 cm(-1), respectively), relative to the maximum local phonon energies calculated (around 185 cm(-1)), are found below the emitting levels of the slow bands, which indicates that these states should be significantly stable and multiphonon relaxation to the lower states should be negligible. A smaller gap (2600 cm(-1)) separates the states of the fast band, which should result in a temperature dependent competition between radiative and nonradiative decay. Differential correlation between 4f-4f and 4f-5d pairs, splitting of the 5d shell by interactions with the host, and spin-orbit effects within the 4f(13) subshell, are found to be responsible for the existence of the gaps, which, in turn, split the absorption spectrum into four groups of separate bands, three of which could lie below the host absorption threshold. The quantum chemical methods employed make use of explicit wave functions expanded in terms of flexible basis sets, multiconfigurational self-consistent-field and multireference second-order perturbation methods to account for nondynamic and dynamic electron correlation, scalar and relativistic terms in the (YbBr(6))(4-) defect cluster Hamiltonian, and quantum mechanical embedding potentials to represent the host crystal.

A generalization of the Fermi-Breit equation to non-Coulombic spatial interactions

Starting from the relativistic invariance properties at classical level, we generalize the Darwin equation to the case of non-Coulombic spatial interactions. The relativistic correction terms for vector interactions are derived from a given nonrelativistic potential. We show that, for a Coulombic potential, the results coincide with those obtained in the Coulomb gauge. The results are adapted to the quantum theory obtaining a generalization of the Fermi-Breit equation. An Hermitian interaction operator is constructed. A critical comparison with other possible treatments of the retardation terms is performed also discussing the usual choice of the Coulomb gauge. Special attention is devoted to the construction of a model for quark interaction.

Self-field effects on the wave-mode couplings in a free-electron laser

A relativistic theory for the unstable couplings of wave modes in a free-electron laser (FEL), in the Raman regime, is presented with the self-fields of the electron beam taken into account. Contrary to the usual investigations, relativistic terms to all orders of the wiggler amplitude are retained in the linearized equations. A dispersion relation for the unstable couplings of wave modes is derived. Numerical investigation of this dispersion relation reveals that self-fields reduce the growth rate for the FEL resonance, in group I orbits, and increases it somewhat, in group II orbits with Φ > 0. The growth rate of all of the couplings, in group II orbits with Φ < 0, is reduced by self-fields except for the Rc+ and Sc− coupling, which is increased. It is found that self-fields split the cyclotron mode of the right and left circularly polarized radiation into two separate modes and prevent the slow and fast space-charge waves from coupling to each other.

DNA: The Gateway to Time

The shape of DNA is fundamental to the nature of time. During a postsynaptic potential, positively charged ions flow towards the negatively charged phosphate groups in DNA molecules in brain cells. Due to the small size and unique geometry of DNA, this results in an interesting arrangement of electric and magnetic fields in space and time that assemble neatly to form, from scratch, new electromagnetic waves. The overall system of electromagnetic radiation surrounding DNA in this fashion possesses, due to the gyre of DNA, classical angular momentum. This angular momentum, when portioned off photon by photon, has the same magnitude as the intrinsic angular momentum of all photons. This astounding apparent coincidence results from the ratio of DNA pitch to radius. While ordinary photons can, in relativistic terms, be regarded as frozen at one point in time, existing and oscillating simultaneously at every point along their path in space, the newly formed electromagnetic radiation herein described comprises photons which can be regarded as the temporal analogue of ordinary photons, i.e. frozen at one point in space, but existing and oscillating “simultaneously” at every point along their path in time. Such temporal photons can couple with ordinary photons in satisfaction of Maxwell’s equations to form spin-2 systems equivalent to gravitons, thereby unifying gravity and electromagnetism. The electric and magnetic fields surrounding brain DNA during a postsynaptic potential also form advanced Ψ functions responsible for observation induced wave function collapse. DNA geometry is correlated with time direction. The hypothesis is experimentally falsifiable.

Anomalous Hall Effect in IV-VI Semiconductors

We consider theoretically the topological contribution to the anomalous Hall effect in narrow-gap IV–VI magnetic semiconductors in which the relativistic terms are relatively large and determine both the non-parabolicity of the energy spectrum and strong spin–orbit interaction. We use the relativistic Dirac model and linear response theory to calculate this contribution. Experimental data on the anomalous Hall effect in these compounds are also presented and discussed.

Effects of the higher partial waves and relativistic terms on the accuracy of the calculation of the hypertriton electroproduction

We have investigated the accuracies of calculations made by omitting the higher partial waves of nuclear wave functions and the elementary relativistic terms in the hypertriton electroproduction. We found that an accurate calculation would still be obtained if we used at least three lowest partial waves with isospin T = 0 . Furthermore, we found that the omission of the relativistic terms in the elementary process amplitude could lead to a large deviation from the full calculation. We also present the cpu-times required to calculate the cross sections. For future consideration the use of these lowest partial waves is suggested, since the calculated cross section deviates only about 0.17 nb/sr (≈4%), at most, from the full calculation, whereas the cpu-time is reduced by a factor of 60. Comparison of our result with the available experimental data supports these findings.

WEAKLY NONLINEAR PERTURBATIONS OF COSMOLOGICAL FLUIDS: PURE GENERAL RELATIVISTIC EFFECTS

Recently we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. Here, we present results relaxing all the assumptions made in the previous works and present the general relativistic correction terms arising due to pressure, multi-component, background spatial curvature, and rotation. We show that even in the multi-component no general relativistic correction terms appear in the zero-pressure, irrotational fluids in a flat background. Thus, the relativistic/Newtonian correspondence of the density and velocity perturbations equations continues even in the multi-component situation. However, the pressure, background curvature, rotation lead to pure general relativistic correction terms to the second order. For the fluid including the pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the small-scale limit, to the second order, relativistic equations of density and velocity perturbations including the rotation coincide with the ones in Newton's gravity. We include the cosmological constant in the background world model which is consistent with the currently favored cosmology.

Manufactured solutions for the [formula omitted] radiation-hydrodynamics equations

For the purposes of testing numerical methods, we develop two manufactured solutions to the P 1 radiation-hydrodynamics system. One solution is designed to test numerical methods in the equilibrium diffusion limit, while the other solution is valid in the streaming (small absorption) regime. We then use these solutions to test a discontinuous Galerkin (DG) discretization of the radiation-hydrodynamics system. We demonstrate that DG with linear elements, with either the double minmod slope limiter or no limiter, is second-order accurate and preserves the equilibrium diffusion limit. On the other hand, DG fails to obtain the equilibrium diffusion limit for the step method (i.e., DG with piecewise constant elements), or with linear elements using the minmod limiter. We also show that when the relativistic terms are lagged at the previous time step, the DG method converges at a first-order rate in the streaming regime for both piecewise constant and linear elements.

Construction of Scientific Facts – Why is Relativism Essential in Bypassing Incommensurable Gaps in Humanities. Case of Personal Involvement – Biased Scientific Facts

This paper addresses the theory of knowledge in relativistic terms of Paul Feyerabend, stressing the importance of personal involvement in the research and theorizing. Since the topic is a constant and widely accepted premise the author is insisting that it has been actually ignored in the sociology and philosophy of science. It is apparent in discursive form, neglected in actual consequences for science in general. Defending the thesis of relativism had remained unacknowledged by the general scientific community. Biographies of mavericks and their struggle and exclusion from scientific community etc. had been constant in the history of science. Is science nowadays able to accept criticism and implement arguments of knowledge beyond the institutionalized standards? Throughout this article we argue that personal involvement creates biased scientific facts; acknowledging and applying tacit knowledge we move beyond personal involvement and create appropriate interpretations of facts and phenomena under investigation, where we reconsider the construction of facts and personal beliefs, knowing that our fields of expertise are incommensurable.

Effects of Breit interaction on theL2,3x-ray absorption near-edge structures of 3dtransition metals

${L}_{2,3}$ x-ray absorption near-edge structures (XANES) of $3d$ transition metal (TM) ions and their compounds are calculated by the all-electron relativistic configuration interaction method. The Breit interaction term, which is the first relativistic correction term for the electron-electron interaction in the quantum electrodynamics, is taken into account in the many-electron Hamiltonian. Then the effects on the multiplet structure for $3d$ TM ${L}_{2,3}$ XANES are investigated. The energy separation between ${L}_{3}$ and ${L}_{2}$ edges of theoretical spectrum decreases when the Breit interaction term is taken into account. At the final states of ${L}_{2,3}$ XANES, the Breit interaction energies linearly depend on the occupation number of TM $2{p}_{3∕2}$ orbitals. They are not influenced by the valency and the crystal field. This main contribution of the Breit interaction term is, therefore, calculated to be the reduction of the separation between ${L}_{3}$ and ${L}_{2}$ edges, which ranges from $0.49\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}1.52\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for Sc to Cu.

Third-order cosmological perturbations of zero-pressure multi-component fluids: puregeneral relativistic non-linear effects

The present expansion stage of the universe is believed to be mainly governed bythe cosmological constant, collisionless dark matter and baryonic matter. Thelatter two components are often modeled as zero-pressure fluids. In our previouswork we have shown that to second order in the cosmological perturbations, therelativistic equations for the density and velocity perturbations of the zero-pressure,irrotational, multi-component fluids in a spatially near flat background withoutgravitational waves effectively coincide with the Newtonian equations. As the Newtonianequations only have quadratic order non-linearity, it is of practical interest toderive the third-order perturbation terms in a general relativistic treatment, whichcorrespond to pure general relativistic corrections. In our previous work we haveshown that even in a single-component fluid there exist a substantial numberof pure relativistic third-order correction terms. We have, however, shown thatthose correction terms are independent of the horizon scale, and are quite small(∼5 × 10−5 smaller compared with the relativistic/Newtonian second-order terms) near thehorizon scale due to the weak level anisotropy of the cosmic microwave backgroundradiation. Here, we present pure general relativistic correction terms appearing inthe third-order perturbations of the multi-component zero-pressure fluids. Theforms of the pure general relativistic correction terms are quite similar to theones in a single-component situation. The third-order correction terms involveonly the ‘linear order spatial curvature perturbation in the comoving gauge’φv which has the order of the ‘perturbed Newtonian gravitational potential divided byc2 ’, and thus is small on nearly all scales. Consequently, we show that, as ina single-component situation, the third-order correction terms are quite small(∼5 × 10−5 smaller) near the horizon, and independent of the horizon scale. We emphasize that theseresults are based on our proper choice of perturbation variables and gauge conditions fordescribing the relativistic perturbations. Still, there do exist a substantial number of puregeneral relativistic correction terms in third-order perturbations which couldpotentially become important in future development of precision cosmology. Althoughφv is small on nearly all scales, our third-order corrections are applicable only in weaklynon-linear regimes where perturbation analysis is viable. We include the cosmologicalconstant in all our analyses.

Second-order perturbations of cosmological fluids: Relativistic effects of pressure, multicomponent, curvature, and rotation

We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity perturbation equations of general relativistic zero-pressure, irrotational, single-component fluid in a spatially flat background coincide exactly with the ones known in Newton's theory without using the gravitational potential. We also have shown the effect of gravitational waves to the second order, and pure general relativistic correction terms appearing in the third-order perturbations. Here, we present results of second-order perturbations relaxing all the assumptions made in our previous works. We derive the general relativistic correction terms arising due to (i) pressure, (ii) multicomponent, (iii) background spatial curvature, and (iv) rotation. In the case of multicomponent zero-pressure, irrotational fluids under the flat background, we effectively do not have relativistic correction terms, thus the relativistic equations expressed in terms of density and velocity perturbations again coincide with the Newtonian ones. In the other three cases we generally have pure general relativistic correction terms. In the case of pressure, the relativistic corrections appear even in the level of background and linear perturbation equations. In the presence of background spatial curvature, or rotation, pure relativistic correction terms directly appear in the Newtonian equations of motion of density and velocity perturbations to the second order; to the linear order, without using the gravitational potential (or metric perturbations), we have relativistic/Newtonian correspondences for density and velocity perturbations of a single-component fluid including the rotation even in the presence of background spatial curvature. In the small-scale limit (far inside the horizon), to the second-order, relativistic equations of density and velocity perturbations including the rotation coincide with the ones in Newton's gravity. All equations in this work include the cosmological constant in the background world model. We emphasize that our relativistic/Newtonian correspondences in several situations and pure general relativistic corrections in the context of Newtonian equations are mainly about the dynamic equations of density and velocity perturbations without using the gravitational potential (metric perturbations). Consequently, our relativistic/Newtonian correspondences do not imply the absence of many space-time (i.e., pure general relativistic) effects like frame dragging, and redshift and deflection of photons even in such cases. We also present the case of multiple minimally coupled scalar fields, and properly derive the large-scale conservation properties of curvature perturbation variable in various temporal gauge conditions to the second order.