Relativistic Properties Research Articles

Electronic Properties and Persistent Spin Currents of Nanospring under Static Magnetic Field

Relativistic electronic properties of a nanospring under a static magnetic field are theoretically investigated in the present study. The wave equation accounting for the spin–orbit interaction is derived for the nanospring as a special case of the Pauli equation for a spin-1/2 particle confined to a curved surface under an electromagnetic field. We define the helical momentum operator and show that it commutes with the Hamiltonian owing to the helical geometry of the nanospring. The energy eigenstates are hence also the eigenstates of the helical momentum. We solve the equation numerically to obtain the surface wave functions and the energy spectra. The electronic properties are systematically examined by varying the parameters that characterize the system. It is demonstrated that either the nonzero spin–orbit interaction or the nonzero external magnetic field suffices for the occurrence of the persistent spin current on the nanospring. Two different mechanisms are shown to generate the persistent spin current. One employs the spin–orbit interaction coming from the local inversion asymmetry on the surface, while the other employs the curvature coupling with the external magnetic field.

Exciton–polariton condensates near the Dirac point in a triangular lattice

Dirac particles, massless relativistic entities, obey linear energy dispersions and hold important implications in particle physics. The recent discovery of Dirac fermions in condensed matter systems including graphene and topological insulators has generated a great deal of interest in exploring the relativistic properties associated with Dirac physics in solid-state materials. In addition, there are stimulating research activities to engineer Dirac particles, elucidating their exotic physical properties in a controllable setting. One of the successful platforms is the ultracold atom–optical lattice system, whose dynamics can be manipulated and probed in a clean environment. A microcavity exciton–polariton–lattice system offers the advantage of forming high-orbital condensation in non-equilibrium conditions, which enables one to explore novel quantum orbital order in two dimensions. In this paper, we experimentally construct the band structures near Dirac points, the vertices of the first hexagonal Brillouin zone with exciton–polariton condensates trapped in a triangular lattice. Due to the finite spectral linewidth, the direct map of band structures at Dirac points is elusive; however, we identify the linear part above Dirac points and its associated velocity value is ∼0.9–2 × 108 cm s−1, consistent with the theoretical estimate 1 × 108 cm s−1 with a 2 μm lattice constant. We envision that the exciton–polariton condensates in lattices would be a promising solid-state platform, where the system order parameter can be accessed in both real and momentum spaces.

On special relativity teaching using modern experimental data

A new methodological approach to the study of relativistic space-time properties is proposed based on the 20th century's vast experimental research on relativistic accelerator and cosmic ray particles. This approach vividly demonstrates that relativistic effects are the manifestation of fundamental space-time properties and refutes the false notion that relativity is only of relevance to light phenomena.

Oscillating magnetocaloric effect on graphenes

The magnetocaloric effect of non-relativistic diamagnetic materials presents an oscillatory character due to the crossing of the Landau levels with the Fermi energy. This effect occurs at low temperature (ca 1 K) and high magnetic field (ca 10 T). Considering the relativistic properties of graphenes, a 2D massless diamagnetic material, these oscillations could be preserved and the effect occurs in a much higher temperature (ca 100 K), due to the huge Fermi velocity (106 m/s). In addition, the magnetocaloric effect can be tuned as either inverse or normal, by changing the magnetic field change in ca 3.4 T.

Prospects for probing strong gravity with a pulsar-black hole system

AbstractThe discovery of a pulsar (PSR) in orbit around a black hole (BH) is expected to provide a superb new probe of relativistic gravity and BH properties. Apart from a precise mass measurement for the BH, one could expect a clean verification of the dragging of space-time caused by the BH spin. In order to measure the quadrupole moment of the BH for testing the no-hair theorem of general relativity (GR), one has to hope for a sufficiently massive BH. In this respect, a PSR orbiting the super-massive BH in the center of our Galaxy would be the ultimate laboratory for gravity tests with PSRs. But even for gravity theories that predict the same properties for BHs as GR, a PSR-BH system would constitute an excellent test system, due to the high grade of asymmetry in the strong field properties of these two components. Here we highlight some of the potential gravity tests that one could expect from different PSR-BH systems, utilizing present and future radio telescopes, like FAST and SKA.

Application of particle accelerators for the experimental measurement of relativistic length contraction

The subject of length contraction appears very early in textbooks (Moller, 1957) as well as in various forms in papers dedicated to teaching relativity (Weinstein, 1960; Rindler, 1961; Sherwin, 1961; Sears, 1964; Redzic, 2008). Unfortunately, no experiment has been possible to date due to the fact that the predicted effects are very small. In the current paper, we extend the treatment to the case of the arbitrary orientation between two inertial frames. The Michelson–Morley experiment has been viewed as an indirect proof of length contraction, and in the current paper, we describe the experimental setup for a direct measurement of length contraction, a relativistic property that has eluded so far experimental verification. We show how modern technology, in combination with the theory advanced by our paper, makes this experiment feasible.

Collisional-Radiative Modeling of W<sup>27</sup><sup>+</sup>

A detailed collisional radiative model of W27+ ions was constructed based on the atomic data calculated by relativistic atomic properties software Flexible Atomic Code. The strong electric dipole (E1) transitions mainly comes from the 4 f → 4d transition in W27+ ions with wavelength falls into VUV region (4.6 5.1 nm), while the wavelength of magnetic dipole (M1) transition among the fine structures of the first excited states falls into the visible optical region. Synthetic spectra in both regions are given theoretically with plasma condition in EBIT for experiment reference. Finally, the dependence of the intensity ratio on the electron density is provided as a potential diagnostic tool of Maxwellian plasmas.

Fully relativistic theories and methods for NMR parameters

Nuclear magnetic shielding and spin–spin coupling constants are intrinsically all-electron relativistic properties and demand in principle fully relativistic treatments. Here, the magnetic balance (MB) condition plays an essential role, both conceptually and computationally. The various formulations can be unified in terms of the idea of "orbital decomposition." Further combined with the ansatz of "gauge-including atomic orbitals" (GIAO) for distributed gauge origins leads to very efficient four-component relativistic methods at both the mean-field and correlated levels. To illustrate the latter, the no-pair MB-GIAO-MP2 expressions for nuclear shieldings are derived in two different ways, one with the derivative technique and the other through the induced current. Due to the non-variational nature of MP2, the two expressions are not identical. The current-dependent expression is much simpler and appears more natural in view of the experimental measurement.

Two-spinors, oscillator algebras, and qubits: aspects of manifestly covariant approach to relativistic quantum information

The first part of the paper reviews applications of 2-spinor methods to relativistic qubits (analogies between tetrads in Minkowski space and 2-qubit states, qubits defined by means of null directions and their role for elimination of the Peres-Scudo-Terno phenomenon, advantages and disadvantages of relativistic polarization operators defined by the Pauli-Lubanski vector, manifestly covariant approach to unitary representations of inhomogeneous SL(2,C)). The second part deals with electromagnetic fields quantized by means of harmonic oscillator Lie algebras (not necessarily taken in irreducible representations). As opposed to non-relativistic singlets one has to distinguish between maximally symmetric and EPR states. The distinction is one of the sources of `strange' relativistic properties of EPR correlations. As an example, EPR averages are explicitly computed for linear polarizations in states that are antisymmetric in both helicities and momenta. The result takes the familiar form $\pm p\cos 2(\alpha-\beta)$ independently of the choice of representation of harmonic oscillator algebra. Parameter $p$ is determined by spectral properties of detectors and the choice of EPR state, but is unrelated to detector efficiencies. Brief analysis of entanglement with vacuum and vacuum violation of Bell's inequality is given. The effects are related to inequivalent notions of vacuum states. Technical appendices discuss details of the representation I employ in field quantization. In particular, M-shaped delta-sequences are used to define Dirac deltas regular at zero.

The Analysis of Lagrangian and Hamiltonian Properties of the Classical Relativistic Electrodynamics Models and Their Quantization

The Lagrangian and Hamiltonian properties of classical electrodynamics models and their associated Dirac quantizations are studied. Using the vacuum field theory approach developed in (Prykarpatsky et al. Theor. Math. Phys. 160(2): 1079–1095, 2009 and The field structure of a vacuum, Maxwell equations and relativity theory aspects. Preprint ICTP) consistent canonical Hamiltonian reformulations of some alternative classical electrodynamics models are devised, and these formulations include the Lorentz condition in a natural way. The Dirac quantization procedure corresponding to the Hamiltonian formulations is developed. The crucial importance of the rest reference systems, with respect to which the dynamics of charged point particles is framed, is explained and emphasized. A concise expression for the Lorentz force is derived by suitably taking into account the duality of electromagnetic field and charged particle interactions. Finally, a physical explanation of the vacuum field medium and its relativistic properties fitting the mathematical framework developed is formulated and discussed.

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.

Relativistic thermodynamic properties of a weakly interacting Fermi gas in a weak magnetic field

This paper derives the analytical expression of free energy for a weakly interacting Fermi gas in a weak magnetic field, by using the methods of quantum statistics as well as considering the relativistic effect. Based on the derived expression, the thermodynamic properties of the system at both high and low temperatures are given and the relativistic effect on the properties of the system is discussed. It shows that, in comparison with a nonrelativistic situation, the relativistic effect changes the influence of temperature on the thermodynamic properties of the system at high temperatures, and changes the influence of particle-number density on them at extremely low temperature. But the relativistic effect does not change the influence of the magnetic field and inter-particle interactions on the thermodynamic properties of the system at both high and extremely low temperatures.

Response of the radiation belt electron flux to the solar wind velocity: Parameterization by radial distance and energy

The solar wind velocity is the primary driver of the electron flux variability in Earth's radiation belts. The response of the logarithmic flux (“log-flux”) to this driver has been determined at the geosynchronous orbit and at a fixed energy [Baker, D.N., McPherron, R.L., Cayton, T.E., Klebesadel, R.W., 1990. Linear prediction filter analysis of relativistic electron properties at 6.6 RE. Journal of Geophysical Research 95(A9), 15,133–15,140) and as a function of L shell and fixed energy [Vassiliadis, D., Klimas, A.J., Kanekal, S.G., Baker, D.N., Weigel, R.S., 2002. Long-term average, solar-cycle, and seasonal response of magnetospheric energetic electrons to the solar wind speed. Journal of Geophysical Research 107, doi:10.1029/2001JA000506). In this paper we generalize the response model as a function of particle energy (0.8–6.4 MeV) using POLAR HIST measurements. All three response peaks identified earlier figure prominently in the high-altitude POLAR measurements. The positive response around the geosynchronous orbit is peak P 1 ( τ=2±1 d; L=5.8±0.5; E=0.8–6.4 MeV), associated with high-speed, low-density streams and the ULF wave activity they produce. Deeper in the magnetosphere, the response is dominated by a positive peak P 0 (0±1 d; 2.9±0.5 R E; 0.8–1.1 MeV), of a shorter duration and producing lower-energy electrons. The P 0 response occurs during the passage of geoeffective structures containing high IMF and high-density parts, such as ICMEs and other mass ejecta. Finally, the negative peak V 1 (0±0.5 d; 5.7±0.5 R E; 0.8–6.4 MeV) is associated with the “ D st effect” or the quasiadiabatic transport produced by ring-current intensifications. As energies increase, the P 1 and V 1 peaks appear at lower L, while the D st effect becomes more pronounced in the region L<3. The P 0 effectively disappears for E>1.6 MeV because of low statistics, although it is evident in individual events. The continuity of the response across radial and energy scales supports the earlier hypothesis that each of the three modes corresponds to a qualitatively different type of large-scale electron acceleration and transport.

GROUND STATE PROPERTIES OF SUPERHEAVY NUCLEI IN RELATIVISTIC MEAN FIELD THEORY

In the framework of the relativistic mean field (RMF) theory, the stability and ground properties of super-heavy nuclei are discussed. Our study indicated that the current synthesized super-heavy nuclei (SHN) actually appear in the stable region, and adding more neutrons will not increase their stability. The study of nuclei from 287115 α decay chain showed that they are usually deformed, the magnitudes of their shell gaps are much smaller than those of nuclei before the actinium region, so that the shell effect is weakened, and SHN are usually not stable. A common phenomenon is that the Fermi surface of the proton is close to the continuum, the resonant continuums exist in SHN, because the SHN are usually neutron deficient. Although bulk properties can be described by the RMF+BCS theory, further study is needed. Density dependent delta pairing interaction can improve the treatment of the pairing and thus improve the level distribution in the continuum.

Unstable longitudinal plasma oscillations in a magnetic field: Nonrelativistic and relativistic considerations

The nonrelativistic and relativistic stability properties are investigated of longitudinal waves propagating in a plasma embedded in an ambient magnetic field, when the wave propagation direction is not necessarily either parallel or perpendicular to the ambient magnetic field. The analysis is based on the concept introduced by Harris [Phys. Rev. Lett. 2, 34 (1959)] of neutral points in wavenumber space to determine plasma instability to one side or the other of such neutral points. The critical need is to determine whether a particular plasma distribution function permits the existence of a neutral point. Relativistic considerations, although necessary to include for many astrophysical plasmas, complicate significantly the determination of instability conditions. In this paper it is shown how one can provide a general argument for such neutral point determination and for determining instability rates in the neighborhood of such neutral points. Only waves independent of resonant wave-particle effects are considered.

Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.

Eclipsing Light-Curve Asymmetry for Black-Hole Accretion Flows

We propose an eclipsing light-curve diagnosis for black-hole accretion flows. When emission from an inner accretion disk around a black hole is occulted by a companion star, the observed light curve becomes asymmetric at ingress and egress on a time scale of 0.1–1 seconds. This light-curve analysis provides a means of verifying the relativistic properties of the accretion flow, based on the special/general relativistic effects of black holes. The “skewness” for the eclipsing light curve of a thin disk is $\sim 0.08$, whereas that of a slim disk is $\sim 0$, since the innermost part is self-occulted by the disk’s outer rim.

Relativistic central-field Green's functions for the Ratip package

From perturbation theory, Green’s functions are known for providing a simple and convenient access to the (complete) spectrum of atoms and ions. Having these functions available, they may help carry out perturbation expansions to any order beyond the first one. For most realistic potentials, however, the Green’s functions need to be calculated numerically since an analytic form is known only for free electrons or for their motion in a pure Coulomb field. Therefore, in order to facilitate the use of Green’s functions also for atoms and ions other than the hydrogen-like ions, here we provide an extension to the R ATIP program which supports the computation of relativistic (one-electron) Green’s functions in an—arbitrarily given—central-field potential V(r). Different computational modes have been implemented to define these effective potentials and to generate the radial Green’s functions for all bound-state energies E< 0. In addition, care has been taken to provide a user-friendly component of the RATIP package by utilizing features of the Fortran 90/95 standard such as data structures, allocatable arrays, or a module-oriented design. Program summary

Relativistic effects on experimentally studied gas-phase properties of the heaviest elements

Influence of relativistic effects on atomic properties and volatility of element 112 and its homolog Hg has been studied using results of relativistic atomic and molecular calculations. Volatility was considered as sublimation of macro-amounts or adsorption of single atoms on inert and metal surfaces. For predictions of adsorption on metal (gold) surfaces, fully relativistic and non-relativistic density functional theory calculations were performed for various intermetallic compounds of Hg and element 112: dimers and metal–gold cluster systems. Results show that influence of relativistic effects on volatility is different depending on the process. For element 112 as metal the sublimation enthalpy will be drastically decreased by relativistic effects, so that it will be the most volatile in the group, probably a gas. Upon adsorption on an inert surface, element 112 will have the strongest dispersion interaction with the surface in group 12 and hence will be the least volatile. On the contrary, upon adsorption on transition metal surfaces, e.g., on the (100) surface of gold, element 112 will be more volatile than Hg, though the influence of relativistic effects on the adsorption energy is different depending on the adsorption position. For example, relativistic effects do not increase (or could even decrease) the adsorption energy of element 112 when adsorbed in the on-top position, while for the hollow position, relativistic effects substantially increase the interaction energy, so that relativistically element 112 will be less volatile than non-relativistically. The calculations have shown that the relativistic and non-relativistic properties have opposite trends from Hg to element 112.

Electronic Structure Calculations of Low‐Dimensional Transition Metals

AbstractFor Abstract see ChemInform Abstract in Full Text.