Relativistic Framework Research Articles

Facing the mirror: A relativist account of immune nonconceptual self-representations

There is a consensus among philosophers that some “I”-thoughts are immune to error through misidentification. In some recent papers, this property has been formulated in the following deflationist way: an “I”-thought is immune to error through misidentification when it can misrepresent the mental or bodily property self-ascribed but cannot misrepresent the subject (if any) possessing that property. However, it has been put forward that the range of mental and bodily states that are immune in that limited sense cannot include nonconceptual forms of self-representation. In this paper, I claim the opposite. I argue in favor of a theoretical framework inspired by semantic relativism that solves the problem of immune nonconceptual self-representations. In order to do so, I refute an argument against the relativist account which is based on the existence of shared representations. This argument, I contend, rests on a confusion between two conditions to which a relativist may appeal when considering whether a certain mental content is relative to the self: a strong invariance condition and a weak invariance condition. I then argue that even if we acknowledge the existence of shared representations, the weak invariance condition is still satisfied, and consequently the relativist framework can make sense of INSRs. I argue that this weak invariance condition is satisfied by a representational function that self-relativizes certain representations. I then provide an empirical instance of such a function by discussing some of the recent literature on motor representations and the sense of agency. In the last part of the paper, I answer several potential objections. These potential objections lead me to distinguish two fundamental kinds of error relative to the self: error through misidentification and error through misapplication. This distinction allows me to answer a fundamental question raised by the very idea of de facto immunity to error through misidentification.

The properties of nuclear matter with lattice NN potential in relativistic Brueckner-Hartree-Fock theory.

We study the properties of nuclear matter with lattice nucleon-nucleon (NN) potential in the relativistic Brueckner-Hartree-Fock (RBHF) theory. To use this potential in such a microscopic many-body theory, we firstly have to construct a one-boson-exchange potential (OBEP) based on the latest lattice NN potential. Three mesons, pion, σ meson, and ω meson, are considered. Their coupling constants and cut-off momenta are determined by fitting the on-shell behaviors and phase shifts of the lattice force, respectively. Therefore, we obtain two parameter sets of the OBEP potential (named as LOBEP1 and LOBEP2) with these two fitting ways. We calculate the properties of symmetric and pure neutron matter with LOBEP1 and LOBEP2. In non-relativistic Brueckner-Hartree-Fock case, the binding energies of symmetric nuclear matter are around −3 and −5 MeV at saturation density, while it becomes −8 and −12 MeV in relativistic framework with 1S0, 3S1, and 3D1 channels using our two parameter sets. For the pure neutron matter, the equations of state in non-relativistic and relativistic cases are very similar due to only consideration 1S0 channel with isospin T = 1 case.

Relativistic dynamics of superfluid-superconducting mixtures in the presence of topological defects and an electromagnetic field with application to neutron stars

The relativistic dynamic equations are derived for a superfluid-superconducting mixture coupled to the electromagnetic field. For definiteness, and bearing in mind possible applications of our results to neutron stars, it is assumed that the mixture is composed of superfluid neutrons, superconducting protons, and normal electrons. Proton superconductivity of both I and II types is analysed, and possible presence of neutron and proton vortices (or magnetic domains in the case of type-I proton superconductivity) is allowed for. The derived equations neglect all dissipative effects except for the mutual friction dissipation and are valid for arbitrary temperatures (i.e. they do not imply that all nucleons are paired), which is especially important for magnetar conditions. It is demonstrated that these general equations can be substantially simplified for typical neutron stars, for which a kind of magnetohydrodynamic approximation is justified. Our results are compared to the nonrelativistic formulations existing in the literature and a number of discrepancies are found. In particular, it is shown that, generally, the electric displacement ${\pmb D}$ does not coincide with the electric field ${\pmb E}$, contrary to what is stated in the previous works. The relativistic framework developed here is easily extendable to account for more sophisticated microphysics models and it provides the necessary basis for realistic modelling of neutron stars.

Calculation of hyperfine structure constants of small molecules using Z-vector method in the relativistic coupled-cluster framework

The Z-vector method in the relativistic coupled-cluster framework is employed to calculate the parallel and perpendicular components of the magnetic hyperfine structure constant of a few small alkaline earth hydrides (BeH, MgH, and CaH) and fluorides (MgF and CaF). We have compared our Z-vector results with the values calculated by the extended coupled-cluster (ECC) method reported in Phys. Rev. A 91 022512 (2015). All these results are compared with the available experimental values. The Z-vector results are found to be in better agreement with the experimental values than those of the ECC values. Magnetic hyperfine structure constants of some small molecules are calculated using Z-vector method in the relativistic coupled-cluster framework and the comparison with the reported extended coupled-cluster results reveals that Z-vector method can produce more accurate wavefunction in the near nuclear region than the extended coupled-cluster method.

Relativistic state-specific multireference coupled cluster theory description for bond-breaking energy surfaces.

A four-component (4c) relativistic state specific multireference coupled cluster (4c-SSMRCC) method has been developed and applied to compute the ground state spectroscopic constants of Ag2, Cu2, Au2, and I2. The reference functions used in these calculations are obtained using computationally inexpensive improved virtual orbital-complete active space configuration interaction scheme. Rigorous size-extensivity and insensitivity towards the intruder state problem make our method an interesting choice for the calculation of the dissociation energy surface. To the best of our knowledge, this study is the first implementation of the SSMRCC within the relativistic framework. The overall agreement of our results, employing the smallest model space, with both theoretical and experimental reference values indicates that the 4c-SSMRCC method can be fruitfully used to describe electronic structures and associated properties of systems containing heavy elements. We observe a relativistic bond stabilization for the coinage metal dimers while the I-I bond is weakened by the relativistic effects.

Relativistic interpretation of Newtonian simulations for cosmic structure formation

The standard numerical tools for studying non-linear collapse of matter are Newtonian N-body simulations. Previous work has shown that these simulations are in accordance with General Relativity (GR) up to first order in perturbation theory, provided that the effects from radiation can be neglected. In this paper we show that the present day matter density receives more than 1% corrections from radiation on large scales if Newtonian simulations are initialised before z=50. We provide a relativistic framework in which unmodified Newtonian simulations are compatible with linear GR even in the presence of radiation. Our idea is to use GR perturbation theory to keep track of the evolution of relativistic species and the relativistic space-time consistent with the Newtonian trajectories computed in N-body simulations. If metric potentials are sufficiently small, they can be computed using a first-order Einstein–Boltzmann code such as CLASS. We make this idea rigorous by defining a class of GR gauges, the Newtonian motion gauges, which are defined such that matter particles follow Newtonian trajectories. We construct a simple example of a relativistic space-time within which unmodified Newtonian simulations can be interpreted.

Magnetic-Field-Induced Relativistic Properties in Type-I and Type-II Weyl Semimetals.

We investigate Weyl semimetals with tilted conical bands in a magnetic field. Even when the cones are overtilted (type-II Weyl semimetal), Landau-level quantization can be possible as long as the magnetic field is oriented close to the tilt direction. Most saliently, the tilt can be described within the relativistic framework of Lorentz transformations that give rise to a rich spectrum, displaying new transitions beyond the usual dipolar ones in the optical conductivity. We identify particular features in the latter that allow one to distinguish between semimetals of different types.

Fully relativistic description of spin-orbit torques by means of linear response theory

Symmetry and magnitude of spin-orbit torques (SOT), i.e., current-induced torques on the magnetization of systems lacking inversion symmetry, are investigated in a fully relativistic linear response framework based on the Kubo formalism. By applying all space-time symmetry operations contained in the magnetic point group of a solid to the relevant response coefficient, the torkance expressed as torque-current correlation function, restrictions to the shape of the direct and inverse response tensors are obtained. These are shown to apply to the corresponding thermal analogues as well, namely the direct and inverse thermal SOT in response to a temperature gradient or heat current. Using an implementation of the Kubo-Bastin formula for the torkance into a first-principles multiple-scattering Green's function framework and accounting for disorder effects via the so-called coherent potential approximation (CPA), all contributions to the SOT in pure systems, dilute as well as concentrated alloys can be treated on equal footing. This way, material specific values for all torkance tensor elements in the fcc (111) trilayer alloy system Pt | Fe$_x$Co$_{1-x}$ | Cu are obtained over a wide concentration range and discussed in comparison to results for electrical and spin conductivity, as well as to previous work - in particular concerning symmetry w.r.t. magnetization reversal and the nature of the various contributions.

Modified stochastic variational approach to non-Hermitian quantum systems

The stochastic variational method has proven to be a very efficient and accurate tool to calculate especially bound states of quantum-mechanical few-body systems. It relies on the Rayleigh-Ritz variational principle for minimizing real eigenenergies of Hermitian Hamiltonians. From molecular to atomic, nuclear, and particle physics there is actually a great demand of describing also resonant states to a high degree of reliance. This is especially true with regard to hadron resonances, which have to be treated in a relativistic framework. So far standard methods of dealing with quantum chromodynamics have not yet succeeded in describing hadron resonances in a realistic manner. Resonant states can be handled by non-Hermitian quantum Hamiltonians. These states correspond to poles in the lower half of the unphysical sheet of the complex energy plane and are therefore intimately connected with complex eigenvalues. Consequently the Rayleigh-Ritz variational principle cannot be employed in the usual manner. We have studied alternative selection principles for the choice of test functions to treat resonances along the stochastic variational method. We have found that a stationarity principle for the complex energy eigenvalues provides a viable method for selecting test functions for resonant states in a constructive manner. We discuss several variants thereof and exemplify their practical efficiencies.

GR-AMRVAC code applications: accretion onto compact objects, boson stars versus black holes

In the close vicinity of a compact object strong gravity imprints its signature onto matter. Systems that contain at least one compact object are observed to exhibit extreme physical properties and typically emit highly energetic radiation. The nature of the compact objects that produce the strongest gravitational fields is to date not settled. General relativistic numerical simulations of fluid dynamics around black holes, neutron stars, and other compact objects such as boson stars (BSs) may give invaluable insights into this fundamental question. In order to study the behavior of fluid in the strong gravity regime of an arbitrary compact object we develop a new general relativistic hydrodynamics code. To this end we extend the existing versatile adaptive mesh refinement code MPI-AMRVAC into a general relativistic hydrodynamics framework and adapt it for the use of numerically given spacetime metrics. In the present article we study accretion flows in the vicinity of various types of BSs whose numerical metrics are calculated by the KADATH spectral solver library. We design specific tests to check the reliability of any code intending to study BSs and compare the solutions with those obtained in the context of Schwarzschild black holes. We perform the first ever general relativistic hydrodynamical simulations of gas accretion by a BS. The behavior of matter at small distances from the center of a BS differs notably from the black hole case. In particular we demonstrate that in the context of Bondi spherical accretion the mass accretion rate onto non-rotating BSs remains constant whereas it increases for Schwarzschild black holes. We also address the scenario of non-spherical accretion onto BSs and show that this may trigger mass ejection from the interior of the BS. This striking feature opens the door to forthcoming investigations regarding accretion-ejection flows around such types of compact objects.

Retaining Structure: A Relativistic Perspective

Retention of structure across theory change has been invoked in support of a ‘structural’ alternative to more traditional entity-based scientific realism. In that context the transition from Newtonian mechanics to the Special Theory of Relativity is often regarded as a very significant instance of structural preservation, or retention, associated with correspondence-based recovery. The joint derivation, from a small set of elementary and ontologically neutral assumptions, of both the Galilei and the Lorentz transformation exemplifies the virtues of structural approaches to the foundations of physical theories. The common origination of the resulting two relativistic frameworks sheds light on both the successes and the limitations of correspondence claims. However, the cognitive-operational character of the basic assumptions lends no support to the structural realist’s ‘inference to the best explanation’.

Nuclear response theory for spin-isospin excitations in a relativistic quasiparticle-phonon coupling framework

A new theoretical approach to spin-isospin excitations in open-shell nuclei is presented. The developed method is based on the relativistic meson-exchange nuclear Lagrangian of Quantum Hadrodynamics and extends the response theory for superfluid nuclear systems beyond relativistic quasiparticle random phase approximation in the proton-neutron channel (pn-RQRPA). The coupling between quasiparticle degrees of freedom and collective vibrations (phonons) introduces a time-dependent effective interaction, in addition to the exchange of pion and $\rho$-meson taken into account without retardation. The time-dependent contributions are treated in the resonant time-blocking approximation, in analogy to previously developed relativistic quasiparticle time blocking approximation (RQTBA) in the neutral (non-isospin-flip) channel. The new method is called proton-neutron RQTBA (pn-RQTBA) and applied to Gamow-Teller resonance in a chain of neutron-rich Nickel isotopes $^{68-78}$Ni. A strong fragmentation of the resonance along with quenching of the strength, as compared to pn-RQRPA, is obtained. Based on the calculated strength distribution, beta-decay half-lives of the considered isotopes are computed and compared to pn-RQRPA half-lives and to experimental data. It is shown that a considerable improvement of the half-life description is obtained in pn-RQTBA because of the spreading effects, which bring the lifetimes to a very good quantitative agreement with data.

On Einstein’s Program and Quantum Double Slit Experiment

The Einstein’s program enables a theoretical economy for quantum double slit experiment, in its wave-particle duality behavior, with the unification of first and second quantifications for light and matter. It introduces a space-like amplitude function u(r,t), which completes the usual time-like functions ψ(r,t) of quantum mechanics and quantum fields. The Einstein’s program is founded upon a scalar field propagating at speed of light c. It forms a common relativist framework, for classical and quantum properties of matter and interactions. Matter properties derive from standing waves, and interactions from progressive waves. The classical domain arises in the geometrical optics approximation, when frequencies are infinitely high, and then hidden. The quantum domain corresponds to wave optics approximation. Adiabatic variations of frequencies yield electromagnetic interaction and dynamical laws of energy-momentum conservation and least action principle.

Relativistic coupled-cluster study of RaF as a candidate for the parity- and time-reversal-violating interaction

We have employed both Z-vector method and the expectation value approach in the relativistic coupled-cluster framework to calculate the scalar-pseudoscalar (S-PS) P, T -odd interaction constant (W_s) and the effective electric field (Eeff) experienced by the unpaired electron in the ground electronic state of RaF. Further, the magnetic hyperfine structure constants of ^{223}Ra in RaF and ^{223}Ra+ are also calculated and compared with the experimental values wherever available to judge the extent of accuracy obtained in the employed methods. The outcome of our study reveals that the Z-vector method is superior than the expectation value approach in terms of accuracy obtained for the calculation of ground state property. The Z-vector calculation shows that RaF has a high E_eff (52.5 GV/cm) and W_s (141.2 kHz) which makes it a potential candidate for the eEDM experiment.

Numerical simulation of the Moon's rotation in a rigorous relativistic framework

This paper describes a numerical simulation of the rigid rotation of the Moon in a relativistic framework. Following a resolution passed by the International Astronomical Union (IAU) in 2000, we construct a kinematically non-rotating reference system named the Selenocentric Celestial Reference System (SCRS) and give the time transformation between the Selenocentric Coordinate Time (TCS) and Barycentric Coordinate Time (TCB). The post-Newtonian equations of the Moon's rotation are written in the SCRS, and they are integrated numerically. We calculate the correction to the rotation of the Moon due to total relativistic torque which includes post-Newtonian and gravitomagnetic torques as well as geodetic precession. We find two dominant periods associated with this correction: 18.6yr and 80.1 yr. In addition, the precession of the rotating axes caused by fourth-degree and fifth-degree harmonics of the Moon is also analyzed, and we have found that the main periods of this precession are 27.3d, 2.9 yr, 18.6 yr and 80.1 yr.

Numerical models for stationary superfluid neutron stars in general relativity with realistic equations of state

We present a numerical model for uniformly rotating superfluid neutron stars, for the first time with realistic microphysics including entrainment, in a fully general relativistic framework. We compute stationary and axisymmetric configurations of neutron stars composed of two fluids, namely superfluid neutrons and charged particles (protons and electrons), rotating with different rates around a common axis. Both fluids are coupled by entrainment, a non-dissipative interaction which in case of a non-vanishing relative velocity between the fluids, causes the fluid momenta being not aligned with the respective fluid velocities. We extend the formalism by Comer and Joynt (2003) in order to calculate the equation of state (EoS) and entrainment parameters for an arbitrary relative velocity. The resulting entrainment matrix fulfills all necessary sum rules and in the limit of small relative velocity our results agree with Fermi liquid theory ones, derived to lowest order in the velocity. This formalism is applied to two new nuclear equations of state which are implemented in the numerical model. We are able to obtain precise equilibrium configurations. Resulting density profiles and moments of inertia are discussed employing both EoSs, showing the impact of entrainment and the dependence on the EoS.

Search for parity and time reversal violating effects in HgH: Relativistic coupled-cluster study.

The high effective electric field (Eeff) experienced by the unpaired electron in an atom or a molecule is one of the key ingredients in the success of electron electric dipole moment (eEDM) experiment and its precise calculation requires a very accurate theory. We, therefore, employed the Z-vector method in the relativistic coupled-cluster framework and found that HgH has a very large Eeff value (123.2 GV/cm) which makes it a potential candidate for the next generation eEDM experiment. Our study also reveals that it has a large scalar-pseudoscalar (S-PS) P,T-violating interaction constant, Ws = 284.2 kHz. To judge the accuracy of the obtained results, we have calculated parallel and perpendicular magnetic hyperfine structure (HFS) constants and compared with the available experimental values. The results of our calculation are found to be in nice agreement with the experimental values. Therefore, by looking at the HFS results, we can say that both Eeff and Ws values are also very accurate. Further, We have derived the relationship between these quantities and the ratio which will help to get model independent value of eEDM and S-PS interaction constant.

Growth of spherical overdensities in scalar–tensor cosmologies

The accelerated expansion of the universe is a rather established fact in cosmology and many different models have been proposed as a viable explanation. Many of these models are based on the standard general relativistic framework of non-interacting fluids or more recently of coupled (interacting) dark energy models, where dark energy (the scalar field) is coupled to the dark matter component giving rise to a fifth-force. An interesting alternative is to couple the scalar field directly to the gravity sector via the Ricci scalar. These models are dubbed non-minimally coupled models and give rise to a time-dependent gravitational constant. In this work we study few models falling into this category and describe how observables depend on the strength of the coupling. We extend recent work on the subject by taking into account also the effects of the perturbations of the scalar field and showing their relative importance on the evolution of the mass function. By working in the framework of the spherical collapse model, we show that perturbations of the scalar field have a limited impact on the growth factor (for small coupling constant) and on the mass function with respect to the case where perturbations are neglected.

Relativistic evaluation of the two-photon decay of the metastable1s22s2p3P0state in berylliumlike ions with an effective-potential model

The two-photon ${1s}^{2} 2s 2p~^3\mbox{P}_0 \rightarrow {1s}^{2} {2s}^2$ $^1\mbox{S}_0$ transition in berylliumlike ions is theoretically investigated within a full relativistic framework and a second-order perturbation theory. We focus our analysis on how electron correlation, as well as the negative-energy spectrum can affect the forbidden $E1M1$ decay rate. For this purpose we include the electronic correlation by an effective potential and within an active-electron model. Due to its experimental interest, evaluation of decay rates are performed for berylliumlike xenon and uranium. We find that the negative-energy contribution can be neglected in the present decay rate. On the other hand, if contributions of electronic correlation are not carefully taken into account, it may change the lifetime of the metastable state by 20\%. By performing a full-relativistic $jj$-coupling calculation, we found discrepancies for the decay rate of an order of 2 compared to non-relativistic $LS$-coupling calculations, for the selected heavy ions.

Pion–nucleon correlations in finite nuclei in a relativistic framework: Effects on the shell structure

The relativistic particle-vibration coupling (RPVC) model is extended by the inclusion of spin- and isospin-flip excitation modes into the phonon space, introducing a new mechanism of dynamical interaction between nucleons with different isospin in the nuclear medium. Protons and neutrons exchange by collective modes which are formed by isovector $\pi$ and $\rho$-mesons, in turn, softened considerably because of coupling to nucleons of the medium. These modes are investigated within the proton-neutron relativistic random phase approximation (pn-RRPA) and relativistic proton-neutron time blocking approximation (pn-RTBA). The appearance of isospin-flip states with sizable transition probabilities at low energies points out that they are likely to couple to the single-particle degrees of freedom and, in addition to isoscalar low-lying phonons, to modify their spectroscopic characteristics. Such a coupling is quantified for the shell structure of $^{100,132}$Sn and found significant for the location of the dominant single-particle states.