Relativistic Framework Research Articles

How relativistic motion affects Einstein–Podolsky–Rosen steering

In this letter, the dynamic behavior of Einstein–Podolsky–Rosen (EPR) steering and the redistribution of EPR steering under a relativistic framework are investigated. Specifically, we explore the scenario that particle A held by Alice is in a flat space–time and another particle B held by Bob entangled with A is in a non-inertial framework. The results show that EPR steering from Alice to Bob is dramatically destroyed by the Unruh effect caused by the acceleration of Bob. Besides, EPR steering possess asymmetry, and EPR steering asymmetry increases with growing intensity of the Unruh effect, implying that the Unruh effect can bring about EPR steering asymmetry. Furthermore, the reduced physically accessible EPR steering from Alice to Bob is distributed to the physically inaccessible EPR steering (from Alice to anti-Bob or from Bob to anti-Bob). Notably, unlike entanglement and quantum discord, only one of the EPR steering from Alice to anti-Bob and Bob to anti-Bob experiences a sudden birth with increase in the acceleration parameter, which means that they cannot simultaneously survive. That is, the monogamous relationship of EPR steering is still tenable in such a scenario. Consequently, we believe that EPR steering could also serve as an important information resource within long-distance quantum secure communication under the relativistic framework.

Calculation of the magnetic hyperfine structure constant of alkali metals and alkaline-earth-metal ions using the relativistic coupled-cluster method

The Z-vector method in the relativistic coupled-cluster framework is used to calculate magnetic hyperfine structure constant ($A_J$) of alkali metals and singly charged alkaline earth metals in their ground state electronic configuration. The Z-vector results are in very good agreement with the experiment. The $A_J$ values of Li, Na, K, Rb, Cs, Be$^{+}$, Mg$^{+}$, Ca$^{+}$, and Sr$^{+}$ obtained in the Z-vector method are compared with the extended coupled-cluster results taken from Phys. Rev. A 91, 022512 (2015). The same basis and cutoff are used for the comparison purpose. The comparison shows that Z-vector method with the singles and double approximation can produce more precise wavefunction in the nuclear region than the ECC method.

Quark degrees of freedom in nuclear matter

The microscopic theory of Nuclear Matter has been approached along the years by different many-body methods and different nucleon-nucleon (NN) interactions. The realistic NN interactions can be classified mainly into two categories. One relies on the meson-nucleon coupling scheme, within relativistic or non-relativistic framework. The so-called chiral interactions are based on the assumption that, once the pion exchange contribution has been explicitly isolated, it is possible to expand the NN interaction in a series of point interaction terms which respect the underlying QCD chiral symmetry. In both schemes three-body (TBF) or higher forces can be constructed, which can have different degrees of phenomenological character. The TBF are essential to get the Nuclear Matter saturation point close to the phenomenological one. However the QCD quark degrees of freedom are not explicitly introduced. It will be shown that a realistic NN interaction that is constructed from the quark degrees of freedom can produce the correct saturation point without the need of TBF. The corresponding Equation of State is compatible with all the phenomenological constraints, including the Neutron Star maximum mass limit. Taking this result literally, one can say that quarks have been revealed in Nuclear Matter. Another conclusion is that the effect of TBF is model dependent.

Effects of magnetic fields in white dwarfs

We perform calculations of white dwarfs endowed with strong magnetic fields. White dwarfs are the progenitors of supernova Type Ia explosions and they are widely used as candles to show that the Universe is expanding and accelerating. However, observations of ultraluminous supernovae have suggested that the progenitor of such an explosion should be a white dwarf with mass above the well-known Chandrasekhar limit ~ 1.4 M⊙. In corroboration with other works, but by using a fully general relativistic framework, we obtained also strongly magnetized white dwarfs with masses M ~ 2.0 M⊙.

Electron–nucleus scalar–pseudoscalar interaction in PbF: Z-vector study in the relativistic coupled-cluster framework

ABSTRACTThe scalar–pseudoscalar interaction constant of PbF in its ground state electronic configuration is calculated using the Z-vector method in the relativistic coupled-cluster framework. The precise calculated value is very important to set upper bound limit on -odd scalar–pseudoscalar interaction constant, ks, from the experimentally observed -odd frequency shift. Further, the ratio of the effective electric field to the scalar–pseudoscalar interaction constant is also calculated which is required to get an independent upper bound limit of electric dipole moment of electron, de, and ks and how these (de and ks) are interrelated is also presented here.

Factorization breaking of AdT for polarized deuteron targets in a relativistic framework

We discuss the possible factorization of the tensor asymmetry $A^T_d$ measured for polarized deuteron targets within a relativistic framework. We define a reduced asymmetry and find that factorization holds only in plane wave impulse approximation and if p-waves are neglected. Our numerical results show a strong factorization breaking once final state interactions are included. We also compare the d-wave content of the wave functions with the size of the factored, reduced asymmetry and find that there is no systematic relationship of this quantity to the d-wave probability of the various wave functions.

Long gradient mode and large-scale structure observables

We extend the study of long mode perturbations to other large scale observables such as cosmic rulers, galaxy number counts and halo bias. The long mode is a pure gradient mode that is still outside observer's horizon. We insist that gradient mode effects on observables vanish. It is also crucial that the expressions for observables are relativistic. This allows us to show that the effects of a gradient mode on the large scale observables vanishes identically in a relativistic frame work. To study the potential modulation effect of the gradient mode on halo bias, we derive a consistency condition to the first order in gradient expansion. We find that the matter variance at a fixed physical scale is not modulated by the long gradient mode perturbations when the consistency condition holds. This shows that the contribution of long gradient modes to bias vanishes in this frame work.

Entanglement concentration for two-mode Gaussian states in non-inertial frames

Entanglement creation and concentration by means of a beam splitter (BS) is analysed for a generic two-mode bipartite Gaussian state in a relativistic framework. The total correlations, the purity and the entanglement in terms of logarithmic negativity are analytically studied for observers in an inertial state and in a non-inertial state of uniform acceleration. The dependence of entanglement on the BS transmissivity due to the Unruh effect is analysed in the case when one or both observers undergo uniform acceleration. Due to the Unruh effect, depending on the initial Gaussian state parameters and observed accelerations, the best condition for entanglement generation limited to the two modes of the observers in their regions is not always a balanced beam splitter, as it is for the inertial case.

Semirelativistic approximation to the γ*N→N(1520) and γ*N→N(1535) transition form factors

The representation of the wave functions of the nucleon resonances within a relativistic framework is a complex task. In a nonrelativistic framework the orthogonality between states can be imposed naturally. In a relativistic generalization, however, the derivation of the orthogonality condition between states can be problematic, particularly when the states have different masses. In this work we study the $N(1520)$ and $N(1535)$ states using a relativistic framework. We considered wave functions derived in previous works, but impose the orthogonality between the nucleon and resonance states using the properties of the nucleon, ignoring the difference of masses between the states (semirelativistic approximation). The $N(1520)$ and $N(1535)$ wave functions are then defined without any adjustable parameters and are used to make predictions for the valence quark contributions to the transition form factors. The predictions compare well with the data particularly for high momentum transfer, where the dominance of the quark degrees of freedom is expected.

Nonminimal coupling in anisotropic teleparallel inflation

We study an anisotropic inflationary scenario in teleparallel gravity. We consider a model where the inflaton is nonminimally coupled both to torsion and a vector field, which can lead to anisotropic inflation. In the weak-coupling limit, our results coincide with the results obtained in the general relativistic framework. However, in the strong-coupling regime of the Jordan frame, we show that the anisotropy shear to expansion ratio is a constant, and can be much larger than the slow-roll parameter. Applying a conformal transformation we then work in the Einstein frame, which in teleparallel gravity introduces a different form of coupling between the inflaton and torsion. In this frame we show that in the strong coupling regime the anisotropy shear to expansion ratio is a different constant, that can be made suitably small.

Relativistic extension of the complex scaled Green's function method for resonances in deformed nuclei

We have extended the complex scaled Green's function method to the relativistic framework describing deformed nuclei with the theoretical formalism presented in detail. We have checked the applicability and validity of the present formalism for exploration of the resonances in deformed nuclei. Furthermore, we have studied the dependences of resonances on nuclear deformations and the shape of potential, which are helpful to recognize the evolution of resonant levels from stable nuclei to exotic nuclei with axially quadruple deformations.

Electron Weibel instability in relativistic counterstreaming plasmas with flow-aligned external magnetic fields.

The Weibel instability driven by two symmetric counterstreaming relativistic electron plasmas, also referred to as current-filamentation instability, is studied in a constant and uniform external magnetic field aligned with the plasma flows. Both the linear and nonlinear stages of the instability are investigated using analytical modeling and particle-in-cell simulations. While previous studies have already described the stabilizing effect of the magnetic field, we show here that the saturation stage is only weakly affected. The different mechanisms responsible for the saturation are discussed in detail in the relativistic cold fluid framework considering a single unstable mode. The application of an external field leads to a slight increase of the saturation level for large wavelengths, while it does not affect the small wavelengths. Multimode and temperature effects are then investigated. While at high temperature the saturation level is independent of the external magnetic field, at low but finite temperature the competition between different modes in the presence of an external magnetic field leads to a saturation level lower with respect to the unmagnetized case.

How the Relativistic Motion Affect Quantum Fisher Information and Bell Non-locality for Multipartite state

In this work, the quantum fisher information (QFI) and Bell non-locality of a multipartite fermionic system are investigated. Unlike the currently existing research of QFI, we focus our attention on the differences between quantum fisher information and Bell non-locality under the relativistic framework. The results show that although the relativistic motion affects the strength of the non-locality, it does not change the physical structure of non-locality. However, unlike the case of non-locality, the relativistic motion not only influence the precision of the QFI Fϕ but also broke the symmetry of the function Fϕ. The results also show that for a special multipartite system, , the number of particles of a initial state do not affect the Fθ. Furthermore, we also find that Fθ is completely unaffected in non-inertial frame if there are inertial observers. Finally, in view of the decay behavior of QFI and non-locality under the non-inertial frame, we proposed a effective scheme to battle against Unruh effect.

The optimisation of low-acceleration interstellar relativistic rocket trajectories using genetic algorithms

A vast wealth of literature exists on the topic of rocket trajectory optimisation, particularly in the area of interplanetary trajectories due to its relevance today. Studies on optimising interstellar and intergalactic trajectories are usually performed in flat spacetime using an analytical approach, with very little focus on optimising interstellar trajectories in a general relativistic framework. This paper examines the use of low-acceleration rockets to reach galactic destinations in the least possible time, with a genetic algorithm being employed for the optimisation process. The fuel required for each journey was calculated for various types of propulsion systems to determine the viability of low-acceleration rockets to colonise the Milky Way. The results showed that to limit the amount of fuel carried on board, an antimatter propulsion system would likely be the minimum technological requirement to reach star systems tens of thousands of light years away. However, using a low-acceleration rocket would require several hundreds of thousands of years to reach these star systems, with minimal time dilation effects since maximum velocities only reached about 0.2c. Such transit times are clearly impractical, and thus, any kind of colonisation using low acceleration rockets would be difficult. High accelerations, on the order of 1g, are likely required to complete interstellar journeys within a reasonable time frame, though they may require prohibitively large amounts of fuel. So for now, it appears that humanity's ultimate goal of a galactic empire may only be possible at significantly higher accelerations, though the propulsion technology requirement for a journey that uses realistic amounts of fuel remains to be determined.

On the calculation of second-order magnetic properties using subsystem approaches in a relativistic framework.

We report an implementation of nuclear magnetic resonance (NMR) shielding (σ), isotope-independent indirect spin-spin coupling (K) and the magnetizability (ξ) tensors in a frozen density embedding scheme using the four-component (4c) relativistic Dirac-Coulomb (DC) Hamiltonian and non-collinear spin density functional theory. The formalism takes into account the magnetic balance between the large and the small components of molecular spinors and assures the gauge-origin independence of the NMR shielding and magnetizability results. This implementation has been applied to hydrogen-bonded HXHOH2 complexes (X = Se, Te, Po) and compared with supermolecular calculations and with an approach based on the integration of the magnetically induced current density vector. A comparison with the approximate zeroth-order regular approximation (ZORA) Hamiltonian indicates non-negligible differences in σ and K in the HPoHOH2 complex, and calls for a thorough comparison of ZORA and DC Hamiltonians in the description of environment effects on NMR parameters for molecular systems with heavy elements.

4成分相対論における超微細結合定数の定式化に関する考察

4成分相対論における超微細結合定数の定式化に関する考察

A new model for spherically symmetric charged compact stars of embedding class 1

In the present study we search for a new stellar model with spherically symmetric matter and a charged distribution in a general relativistic framework. The model represents a compact star of embedding class 1. The solutions obtained here are general in nature, having the following two features: first of all, the metric becomes flat and also the expressions for the pressure, energy density, and electric charge become zero in all the cases if we consider the constant A=0, which shows that our solutions represent the so-called ‘electromagnetic mass model’ [17], and, secondly, the metric function nu (r), for the limit n tending to infinity, converts to nu (r)=C{r}^{2}+ ln~B, which is the same as considered by Maurya et al. [11]. We have investigated several physical aspects of the model and find that all the features are acceptable within the requirements of contemporary theoretical studies and observational evidence.

Relativistic frameworks and the case for (or against) incommensurability

The aim of this paper is to address, from a fresh perspective, the question of whether Newtonian mechanics can legitimately be regarded as a limiting case of the special theory of relativity (STR), or whether the two theories should be deemed so radically different as to be incommensurable in the sense of Feyerabend and Kuhn. Firstly, it is argued that focusing on the concept of mass and its transformation across the two varieties of mechanics is bound to leave the issue unsettled. On the one hand, the idea of a speed-dependent ‘relativistic mass’, which has been invoked in support of incommensurability claims, results from a particular, often innocuous but unnecessary and inappropriate reading of certain basic formulae. On the other hand, the existence of an invariant rest mass in STR does not warrant its identification with the Newtonian mass, be it in a suitable limit. This invariant notwithstanding, those who follow Feyerabend and Kuhn can still uphold their views with regard to the two theories. It is shown, however, that the two mechanics embody relativistic frameworks that are direct consequences of the same set of assumptions. As a result, if Newton’s mechanics cannot simply be regarded as a limiting case of STR, the possibility of ‘recovering’ from the latter some elements of the former can be traced to a common source, belying claims of logical disconnection between the two theories.

Plasma-screening effects in the astrophysically relevant He-like and Li-like Mg and Fe ions*

The effect of plasma environment on the atomic energy levels of He-like and Li-like Mg and Fe ions have been studied using Debye model. The equation-of-motion coupled-cluster (EOMCC) and Fock-space coupled-cluster (FSCC) formalisms in the relativistic frame work have been adopted to describe the atomic states and the energy levels of the above plasma embedded ions. Salient features of these methods have been described to account the two electron screening effects through the Debye potentials. The two-body screening potential has been derived in the multipole expansion form to evaluate the reduced matrix elements in solving the equation of motion. Using this extended model, we have also predicted that quasi-degeneracy among the energy states having same principal quantum number ($n$) but different angular momentum ($l$) is slacken, whereas fine structure splitting is unaffected with increasing plasma strength. These knowledge are useful in estimatingradiative opacity, photoionization cross sections, line intensities, etc of the aforementioned astrophysical plasmas.

Structural and decay properties of Z = 132, 138 superheavy nuclei

In this paper, we analyze the structural properties of Z = 132 and Z = 138 superheavy nuclei within the ambit of axially deformed relativistic mean-field framework with NL3 * parametrization and calculate the total binding energies, radii, quadrupole deformation parameter, separation energies, density distributions. We also investigate the phenomenon of shape coexistence by performing the calculations for prolate, oblate and spherical configurations. For clear presentation of nucleon distributions, the two-dimensional contour representation of individual nucleon density and total matter density has been made. Further, a competition between possible decay modes such as $\alpha$ -decay, $\beta$ -decay and spontaneous fission of the isotopic chain of superheavy nuclei with Z = 132 within the range $ 312 \le A \le 392$ and $318 \le A \le 398$ for Z = 138 is systematically analyzed within self-consistent relativistic mean-field model. From our analysis, we inferred that the $\alpha$ -decay and spontaneous fission are the principal modes of decay in majority of the isotopes of superheavy nuclei under investigation apart from $\beta$ -decay as dominant mode of decay in 318-322138 isotopes.