Search Results (24)

In this paper, we review the physics of many bodies in the context of general relativity. Starting from the stress–energy tensor for one body and moving onto those for a swarm of bodies and for a perfect fluid, we review the relativistic hydrodynamics, kinetic theory, and statistical physics of N identical bodies. We conclude our excursion with a thermal equivalence principle in physics. Full article

In this work, a comprehensive first-principles investigation of the electronic, magnetic, and optical properties of pristine and Fe-, Co-, and Ni-doped MoS₂ monolayers is presented within the framework of density functional theory. Substitutional transition-metal doping at the Mo site is shown to induce spin-polarized impurity states within the pristine band gap, leading to significant modifications of the electronic structure, including metallic, semimetallic, or half-metallic behavior depending on the dopant species. The calculated spin-resolved band structures and projected density of states reveal a strong hybridization between the dopant $3d$ orbitals and the Mo-$4d$/S-$3p$ states, giving rise to sizable magnetic moments and dopant-dependent exchange splitting. When spin–orbit coupling is included, the combined effect of exchange interactions and relativistic effects leads to an effective valley splitting at the K and $K^{\prime }$ points, whose magnitude and sign depend sensitively on the chemical nature of the dopant. Optical properties are analyzed within a linear-response framework, showing pronounced dopant-induced modifications of the optical spectra. While the pristine monolayer exhibits well-defined excitonic features, transition-metal substitution introduces low-energy optical transitions associated with impurity-related states. Consequently, the exciton binding energies estimated from the difference between the electronic and optical gaps are interpreted as effective measures of dopant-induced perturbations to optical transitions, rather than as quantitative many-body excitonic binding energies in the strict sense. These results provide microscopic insight into the interplay between magnetism, spin–orbit coupling, and optical response in doped MoS₂ monolayers, highlighting the potential of transition-metal substitution as a route to engineer spin- and valley-dependent phenomena in two-dimensional materials. Full article

The notion of twist fields has played a fundamental role in many-body physics. It is used to construct the so-called disorder parameter for the study of phase transitions in the classical Ising model of statistical mechanics, it is involved in the Jordan–Wigner transformation in quantum chains and bosonisation in quantum field theory, and it is related to measures of entanglement in many-body quantum systems. I provide a pedagogical introduction to the notion of twist field and the concepts at its roots, and review some of its applications, focussing on the 1 + 1 dimension. This includes locality and extensivity, internal symmetries, semi-locality, the standard exponential form and HEGT fields, path-integral defects and Riemann surfaces, topological invariance, and twist families. Additional topics touched upon include renormalisation and form factors in relativistic quantum field theory, tau functions of integrable PDEs, thermodynamic and hydrodynamic principles, and branch-point twist fields for entanglement entropy. One-dimensional quantum systems such as chains (e.g., quantum Heisenberg model) and field theory (e.g., quantum sine-Gordon model) are the main focus, but I also explain how the notion applies to equilibrium statistical mechanics (e.g., classical Ising lattice model), and how some aspects can be adapted to one-dimensional classical dynamical systems (e.g., classical Toda chain). Full article

A consistent theory of quantum entanglement requires that constituent single-particle states belong to the same Hilbert space, the coherent eigenstates of a complete set of operators in a given representation, defined with respect to a shared continuous parameterization. Formulating such eigenstates for a single relativistic particle with spin, and applying them to the description of many-body states, presents well-known challenges. In this paper, we review the covariant theory of relativistic spin and entanglement in a framework first proposed by Stueckelberg and developed by Horwitz, Piron, et al. This approach modifies Wigner’s method by introducing an arbitrary timelike unit vector $n^{\mu }$ and then inducing a representation of $SL(2,C)$, based on $p^{\mu }$ rather than on the spacetime momentum. Generalizing this approach, we construct relativistic spin states on an extended phase space $\{(x^{\mu },p^{\mu }),({\zeta }^{\mu },{\pi }^{\mu })\}$, inducing a representation on the momentum ${\pi }^{\mu }$, thus providing a novel dynamical interpretation of the timelike unit vector $n^{\mu }={\pi }^{\mu }/M$. Studying the unitary representations of the Poincaré group on the extended phase space allows us to define basis quantities for quantum states and develop the gauge invariant electromagnetic Hamiltonian in classical and quantum mechanics. We write plane wave solutions for free particles and construct stable singlet states, and relate these to experiments involving temporal interference, analogous to the spatial interference known from double slit experiments. Full article

One of the oldest problems in physics is that of calculating the motion of N particles under a specified mutual force: the N-body problem. Much is known about this problem if the specified force is non-relativistic gravity, and considerable progress has been made by considering the problem in one spatial dimension. Here, I review what is known about the relativistic gravitational N-body problem. Reduction to one spatial dimension has the feature of the absence of gravitational radiation, thereby allowing for a clear comparison between the physics of one-dimensional relativistic and non-relativistic self-gravitating systems. After describing how to obtain a relativistic theory of gravity coupled to N point particles, I discuss in turn the two-body, three-body, four-body, and N-body problems. Quite general exact solutions can be obtained for the two-body problem, unlike the situation in general relativity in three spatial dimensions for which only highly specified solutions exist. The three-body problem exhibits mild forms of chaos, and provides one of the first theoretical settings in which relativistic chaos can be studied. For $N\ge 4$, other interesting features emerge. Relativistic self-gravitating systems have a number of interesting problems awaiting further investigation, providing us with a new frontier for exploring relativistic many-body systems. Full article

The pseudo-spin symmetry (PSS) provides an important angle to understand nuclear microscopic structure and the novel phenomena found in unstable nuclei. The relativistic Hartree–Fock (RHF) theory, that takes the important degrees of freedom associated with the $\pi$-meson and $\rho$-tensor ($\rho$-T) couplings into account, provides an appropriate description of the PSS restoration in realistic nuclei, particularly for the pseudo-spin (PS) doublets with high angular momenta ($\tilde{l}$). The investigations of the PSS within the RHF theory are recalled in this paper by focusing on the effects of the Fock terms. Aiming at common artificial shell closures appearing in previous relativistic mean-field calculations, the mechanism responsible for the PSS restoration of high-$\tilde{l}$ orbits is stressed, revealing the manifestation of nuclear in-medium effects on the PSS, and thus, providing qualitative guidance on modeling the in-medium balance between nuclear attractions and repulsions. Moreover, the essential role played by the $\rho$-T coupling, that contributes mainly via the Fock terms, is introduced as combined with the relations between the PSS and various nuclear phenomena, including the shell structure and the evolution, novel halo and bubble-like phenomena, and the superheavy magicity. As the consequences of the nuclear force in complicated nuclear many-body systems, the PSS itself and the mechanism therein can not only deepen our understanding of nuclear microscopic structure and relevant phenomena, but also provide special insight into the nature of the nuclear force, which can further enrich our knowledge of nuclear physics. Full article

In this work, a krypton gas impurity seeding experiment was conducted in a Large Helical Device. Emission lines from the Na-like Kr ion in the extreme ultraviolet wavelength region, such as 22.00 nm, 17.89 nm, 16.51 nm, 15.99 nm, and 14.08 nm, respective to $2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{1/2}^{\mathrm{o}})-2{\mathrm{p}}^{6}3\mathrm{s}{(}^2{\mathrm{S}}_{1/2})$, $2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{3/2}^{\mathrm{o}})-2{\mathrm{p}}^{6}3\mathrm{s}{(}^2{\mathrm{S}}_{1/2})$, $2{\mathrm{p}}^{6}3\mathrm{d}{(}^2{\mathrm{D}}_{3/2})-2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{3/2}^{\mathrm{o}})$, $2{\mathrm{p}}^{6}3\mathrm{d}{(}^2{\mathrm{D}}_{5/2})-2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{3/2}^{\mathrm{o}})$, and $2{\mathrm{p}}^{6}3\mathrm{d}{(}^2{\mathrm{D}}_{3/2})-2{\mathrm{p}}^{6}3\mathrm{p}{(}^2{\mathrm{P}}_{1/2}^{\mathrm{o}})$ transitions, are observed. In order to generate a theoretical synthetic spectrum, an extensive calculation concerning the excitation of the ${\mathrm{Kr}}^{25+}$ ion through electron impact was performed for the development of a suitable plasma model. For this, the relativistic multiconfiguration Dirac–Hartree–Fock method was employed along with its extension to the relativistic configuration interaction method to compute the relativistic bound-state wave functions and excitation energies of the fine structure levels using the General Relativistic Atomic Structure Package-2018. In addition, another set of calculations was carried out utilizing the relativistic many-body perturbation theory and relativistic configuration interaction methods integrated within the Flexible Atomic Code. To investigate the reliability of our findings, the results of excitation energies, transition probabilities, and weighted oscillator strengths of different dipole-allowed transitions obtained from these different methods are presented and compared with the available data. Further, the detailed electron impact excitation cross-sections and their respective rate coefficients are obtained for various fine structure resolved transitions using the fully relativistic distorted wave method. Rate coefficients, calculated using the Flexible Atomic Code for population and de-population kinetic processes, are integrated into the collisional-radiative plasma model to generate a theoretical spectrum. Further, the emission lines observed from the ${\mathrm{Kr}}^{25+}$ ion in the impurity seeding experiment were compared with the present plasma model spectrum, demonstrating a noteworthy overall agreement between the measurement and the theoretical synthetic spectrum. Full article

The conventional theory of neutron beams interacting with many-body systems treats the beam as a classical system, i.e., with its dynamical variables appearing in the quantum dynamics of the scattering process not as operators but only as c-numbers. Moreover, neutrons are described with plane waves, i.e., the concept of a neutron’s (finite) coherence length is here irrelevant. The same holds for electron, atom or X-ray scattering. This simplification results in the full decoupling of the probe particle’s dynamics from the quantum dynamics of the scatterer—a well-known fact also reflected in the standard formalism of time-correlation functions (see textbooks). Making contact with modern quantum-theoretical approaches (e.g., quantum entanglement, “which-path information” versus interference, von Neumann measurement, Weak Values (WV), etc.), new observable effects of non-relativistic quantum beam scattering may be exposed and/or predicted, for instance, a momentum-transfer deficit and an intensity deficit in neutron scattering from protons of hydrogen-containing samples. A new WV-theoretical treatment is provided, which explains both these “deficit effects” from first principles and on equal footing. Full article

The growing interest in atomic structures of moderately stripped alkali-like ions in the diagnostic study and modeling of astrophysical and laboratory plasma makes an accurate many-body study of atomic properties inevitable. This work presents transition line parameters in the absence or presence of plasma atmosphere for astrophysically important candidates Ar⁷⁺, Kr⁷⁺, Xe⁷⁺, and Rn⁷⁺. We employ relativistic coupled-cluster (RCC) theory, a well-known correlation exhaustive method. In the case of a plasma environment, we use the Debye Model. Our calculations agree with experiments available in the literature for ionization potentials, transition strengths of allowed and forbidden selections, and lifetimes of several low-lying states. The unit ratios of length and velocity forms of transition matrix elements are the critical estimation of the accuracy of the transition data presented here, especially for a few presented for the first time in the literature. We do compare our findings with the available recent theoretical results. Our reported data can be helpful to the astronomer in estimating the density of the plasma environment around the astronomical objects or in the discovery of observational spectra corrected by that environment. The present results should be advantageous in the modeling and diagnostics laboratory plasma, whereas the calculated ionization potential depression parameters reveal important characteristics of atomic structure. Full article

In this work, we present high-accuracy spectroscopic properties, such as line strengths, transition probabilities and oscillator strengths for allowed transitions among $n{D}_{3/2,5/2},n^{\prime }{S}_{1/2}$ and $n^{\prime }{P}_{1/2,3/2}(n=4,n^{\prime }=5,6)$ states of Rb-isoelectronic Tc (Tc VII), Ru (Ru VIII) and Rh (Rh IX) ions for their applications in the analysis of astrophysical phenomena occurring inside celestial bodies containing Tc, Ru and Rh ions. Due to the scarcity of computational data of atomic properties of these transitions, as well as considerable discrepancies within the literature about these ions, the precise determination of these properties is necessary. For this purpose, we have implemented relativistic many-body perturbation theory (RMBPT) for evaluation of the wave functions of the considered states. For better accuracy, we have accounted for electron interactions through random phase approximation, Brückner orbitals and structural radiations of wave functions in our RMBPT method for further precise evaluation of electric dipole amplitudes. Combining these values of the observed wavelengths, the above transition properties and radiative lifetimes, a number of excited states of Tc VII, Ru VIII and Rh IX ions have been calculated. For further validation of our work, we have compared our results with the data already available in the literature. Full article

In this study, comprehensive calculations of energies, hyperfine structure constants, Landé $g_J$ factors and isotope shifts have been performed for the lowest 71 states of Na-like Ar${}^{7+}$, Kr${}^{25+}$ and Xe${}^{43+}$ ions. Radiative parameters viz., wavelengths, transition rates, oscillator strengths and lifetimes are estimated for the electric dipole E1 transitions among these levels. The states under consideration include $1s^{2}2s^{2}2p^{6}nl$ for n = 3–9, l = 0–6, and the fully relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) method integrated in the latest version of the general-purpose relativistic atomic structure package (GRASP2018) is used for the calculations. The additional corrections, such as the Breit interaction and quantum electrodynamics effects are included in the relativistic configuration interaction calculations, and their effects on energies and other parameters are analysed. We examined the impact of including the core–core and core–valence correlations on level energies. Furthermore, to inspect the reliability of our MCDHF results, we performed another set of calculations using the many-body perturbation theory built into the Flexible Atomic Code (FAC). Moreover, we estimated the uncertainties in the computed lifetimes and transition parameters and assigned their accuracy class. A thorough comparison between the two obtained calculations and with the previous theoretical and experimental results, wherever available, is carried out and a good agreement is observed. Full article

The theory of one-photon ionization and two-photon above-threshold ionization is formulated for applications to heavy atoms in attosecond science by using Dirac–Fock formalism. A direct comparison of Wigner–Smith–Eisenbud delays for photoionization is made with delays from the Reconstruction of Attosecond Beating By Interference of Two-photon Transitions (RABBIT) method. Photoionization by an attosecond pulse train, consisting of monochromatic fields in the extreme ultraviolet range, is computed with many-body effects at the level of the relativistic random phase approximation (RRPA). Subsequent absorption and emission processes of infrared laser photons in RABBIT are evaluated by using static ionic potentials as well as asymptotic properties of relativistic Coulomb functions. As expected, light elements, such as argon, show negligible relativistic effects, whereas heavier elements, such a krypton and xenon, exhibit delays that depend on the fine-structure of the ionic target. The relativistic effects are notably close to ionization thresholds and Cooper minima with differences in fine-structure delays predicted to be as large as tens of attoseconds. The separability of relativistic RABBIT delays into a Wigner–Smith–Eisenbud delay and a universal continuum–continuum delay is studied with reasonable separability found for photoelectrons emitted along the laser polarization axis in agreement with prior non-relativistic results. Full article

This paper analyzes how special relativity changes the equation for the many-body-induced current density starting from the Foldy–Wouthuysen diagonalization of the Dirac–Coulomb Hamiltonian. This current density differs from that obtained with the Gordon decomposition due to the presence of a spin-orbit coupling contribution not considered before for many-body molecular systems. This contribution diverges on atomic nuclei due to the nature of the point charges considered in the nonrelativistic approach, demonstrating that conventionally used nonrelativistic methods are not suitable for dealing with spin effects such as spin-orbit coupling or effects smaller than ${\alpha }^2$, with $\alpha$ the fine structure constant, and that a fully relativistic approach with a finite charge should be used. Despite the singularity, the spin-orbit coupling current becomes an important contribution to the total current in open-shell systems with high-spin multiplicity and a high atomic number in the nuclear proximity. On long ranges, this contribution is overcome by the Coulomb potential and the derived electric field which decays very quickly for small distances from nuclear charges. An evaluation of this spin-orbit current has been performed in the linear response approach at the HF/DFT level of theory. Full article

Heavy atoms present challenges to atomic theory calculations due to the large number of electrons and their complicated interactions. Conventional approaches such as calculations based on Cowan’s code are limited and require a large number of parameters for energy agreement. One promising approach is relativistic configuration-interaction and many-body perturbation theory (CI-MBPT) methods. We present CI-MBPT results for various atomic systems where this approach can lead to reasonable agreement: La I, La II, Th I, Th II, U I, Pu II. Among atomic properties, energies, g-factors, electric dipole moments, lifetimes, hyperfine structure constants, and isotopic shifts are discussed. While in La I and La II accuracy for transitions is better than that obtained with other methods, more work is needed for actinides. Full article