Relativistic Levels Research Articles

The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

In the present paper, we investigate the bound-state solutions of the noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios, namely: the Minkowski spacetime (inertial flat case), the spinning cosmic string (CS) spacetime (inertial curved case), and the spinning CS spacetime with noninertial effects (noninertial curved case). In particular, in the first two scenarios, we have an inertial frame, while in the third, we have a rotating frame. With respect to bound-state solutions, we focus primarily on eigenfunctions (Dirac spinor and wave function) and on energy eigenvalues (Landau levels), where we use the flat and curved Dirac equation in polar coordinates to reach such solutions. However, unlike the literature, here we consider a CS with a non-null angular momentum and also the NC of the positions, and therefore, we seek a more general description for the QHE. Once the solutions are obtained, we discuss the influence of all parameters and physical quantities on relativistic energy levels. Finally, we analyze the nonrelativistic limit, and we also compared our problem with other works, where we verified that our results generalize some particular cases of the literature.

Theoretical investigations of electronic spectra of silver atom using all-electron scalar relativistic basis

Exploration of the tractable size basis set that can provide reliable estimates of computed properties for systems containing heavy elements has been the subject of interest in quantum chemistry over many decades. In this connection, the recently developed segmented all-electron relativistically contracted (SARC) basis set proposed by Rolfes et al. [J. Comput. Chem. 41, 1842 (2020)] appears to be worth studying. In the present attempt, ground and excited state properties of the Ag atom is computed on this basis at the Fock-space multi-reference coupled cluster (FSMRCC) level of theory with four-component relativistic spinors. The computed quantities resulting from the SARC basis are subsequently compared with those obtained using an even-tempered basis to assess the efficacy of the SARC basis. Computations have also been performed with the extended SARC basis to improve the quality of the property of interest. The accuracy of the computed quantities such ionization energy, electron affinity, excitation energies, etc., obtained using the SARC basis at the FSMRCC level of theory demonstrates that the SARC basis (particularly the extended one), which is primarily designed for quantum chemical calculations at the two-component scalar relativistic level for systems containing heavy atoms, can be used for fully relativistic calculations. The magnetic dipole hyperfine structure constant A, oscillator strengths f and transition rates Afi calculated using the SARC basis also agree well with the experiment and with the available theoretical estimates.

The Use of Dirac Oscillator as Medium Substrate for Quantum Heat Engine

The research on Dirac oscillators has been increasing recently. In this paper, a quantum heat engine by means of a Dirac oscillator that interacts with the external magnetic field is proposed. Relativistic Landau energy levels are used to perform the iso-energetic cycle. The large magnetic field is set to obtain a perfect thermodynamic cycle. Some stable performances at a certain magnitude of magnetic field and expansion parameter range are obtained. When the value of efficiency is compared with the non-relativistic case, an opposite result occurs. Therefore, a quantum heat engine using a Dirac oscillator doesn’t govern like a classical oscillator.

Embedded topological semimetals

Topological semimetals, such as Dirac, Weyl, or line-node semimetals, are gapless states of matter characterized by their nodal band structures and surface states. In this work, we consider layered (topologically trivial) insulating systems in $D$ dimensions that are composed of coupled multi-layers of $d$-dimensional topological semimetals. Despite being nominal bulk insulators, we show that crystal defects having co-dimension $(D-d)$ can harbor robust lower dimensional topological semimetals embedded in a trivial insulating background. As an example we show that defect-bound topological semimetals can be localized on stacking faults and partial dislocations. Finally, we propose how an embedded topological Dirac semimetal can be identified in experiment by introducing a magnetic field and resolving the relativistic massless Dirac Landau level spectrum at low energies in an otherwise gapped system.

Study of excitation energies of doubly excited states and identification of EUV, SXR and HXR spectral lines in M1 transitions of W LXXIII and Au LXXVIII

We present excitation energies, wavelength of emitted photon during the transition from upper level to lower level, transitions rates and other transition parameters for doubly excited states of W LXXIII and Au LXXVIII by employing Multi-Configuration Dirac-Fock (MCDF) scheme with the inclusion of relativistic effects. We endorse that contribution of QED and Breit corrections in energies of levels is significant. We have also shown that our results of energies from both, FAC and GRASP matches with each other. We have predicted that 37 Hard X-ray (HXR), 25 Soft X-ray (SXR) and 20 Extreme Ultraviolet (EUV) magnetic dipole (M1) transitions among relativistic levels generated from doubly excited states in W LXXIII and Au LXXVIII. Further, we have studied the convergence in excitation energies and lifetime of excited states and analysed the improvement in accuracy of results by estimation of uncertainty percentage in line strength. Besides, fresh atomic data of W LXXIII and Au LXXVII which is not published in the literature have been reported and can be advantageous in diagnosis and modelling of fusion and astrophysical plasmas.

Strain and pseudo-magnetic fields in optical lattices from density-assisted tunneling

Applying time-periodic modulations is routinely used to control and design synthetic matter in quantum-engineered settings. In lattice systems, this approach is explored to engineer band structures with non-trivial topological properties, but also to generate exotic interaction processes. A prime example is density-assisted tunneling, by which the hopping amplitude of a particle between neighboring sites explicitly depends on their respective occupations. Here, we show how density-assisted tunneling can be tailored in view of simulating the effects of strain in synthetic graphene-type systems. Specifically, we consider a mixture of two atomic species on a honeycomb optical lattice: one species forms a Bose-Einstein condensate in an anisotropic harmonic trap, whose inhomogeneous density profile induces an effective uniaxial strain for the second species through density-assisted tunneling processes. In direct analogy with strained graphene, the second species experiences a pseudo-magnetic field, hence exhibiting relativistic Landau levels and the valley Hall effect. Our proposed scheme introduces a unique platform for the investigation of strain-induced gauge fields, opening the door to future studies of their possible interplay with quantum fluctuations and collective excitations.

Computational Investigation of the Metal and Ligand Substitution Effects on the Structure and Electronic States of the Phosphoranimide Tetramer Complexes of Cu(I), Ni(I), Co(I), and Fe(I).

The structurally unique saddle-shaped paramagnetic tetrametallic clusters of Co(I) and Ni(I) with phosphoranimide ligands have been synthesized and proposed as catalyst precursors. The analogous Cu(I) nanocluster is planar and diamagnetic. These notable variations in geometry and ground electronic states indicate that the effect of metal and ligand substituents on the structure and electronic properties of these complexes requires investigation. We present a computational study of a series of these novel homoleptic complexes containing Co(I), Ni(I), and Cu(I) as well as Fe(I) coordinated to phosphoranimides with electron-donating and withdrawing substituents, conducted at the relativistic density functional theory level using ZORA-PBE/TZP. The optimized structures of the saddle-shaped Co(I) and Ni(I) and planar Cu(I) tetramers with linear N-M-N coordination are validated with respect to X-ray diffraction determinations. The ground-state analysis indicates that Cu(I) complexes are diamagnetic, whereas Ni(I) and Co(I) complexes are in high-spin states, in agreement with magnetic susceptibility measurements. The computational results show that Fe(I) complexes are saddle shaped and high spin. The Co(I) complex is stabilized by a metal macrocycle distortion from square to diamond, as elucidated from its Walsh diagram. The effects of metals and ligand substituents on the ground electronic state, metal center coordination environment, and energy of the complexes are investigated. The bulky tertiary butyl substituent causes the largest saddle-shape distortion of the tetramer marcocycle, which partially offsets its electron-donating effect. Macrocycle distortions with N-M-N site angles ranging from obtuse to alternating obtuse reflex are correlated with the increasing number of unpaired electrons. The phenyl-substituted complexes are expected to have the highest reactivity toward electrophiles. Understanding the interplay between structural and electronic parameters is intended to guide the development of synthetic cooperative systems for multielectron redox reactions, models of biological systems, and molecular magnets.

Dirac quantum walks with conserved angular momentum

A quantum walk (QW) simulating the flat \((1 + 2)\)D Dirac equation on a spatial polar grid is constructed. Because fermions are represented by spinors, which do not constitute a representation of the rotation group \({\mathrm{SO}}(3)\), but rather of its double cover \({\mathrm{SU}}(2)\), the QW can only be defined globally on an extended spacetime where the polar angle extends from 0 to \(4 \pi \). The coupling of the QW with arbitrary electromagnetic fields is also presented. Finally, the cylindrical relativistic Landau levels of the Dirac equation are computed explicitly and simulated by the QW.

Does the DM background affect the propagation of extragalactic neutrinos?

Neutrinos ([Formula: see text]) are produced in practically all extragalactic astrophysical processes. They can travel enormous distances from remote parts of the universe at velocities near the speed of light. The interaction of neutrinos with both galactic and extragalactic particles may shed light on the composition of these particles. Dark matter (DM) is perhaps the most favored candidate for such intra- and extragalactic media. In this paper, we study the interaction of neutrinos with cold leptonic DM at the relativistic level. We have calculated cross-sections for the [Formula: see text]–DM interactions by adopting different models for the DM distribution, in order to test DM properties.

Chiral dynamics and Zitterbewegung of Weyl quasiparticles in a magnetic field

The relativistic dynamical properties of chiral Weyl quasiparticles (WQPs) are investigated in a stationary magnetic field. The visualized evolution process of quasiparticles’ wavepackets has been calculated with different angles between the spinor and the magnetic field. The results reveal that the chiral WQPs feature anisotropic dynamics, which falls into two typical motion modes, i.e. directional drift (chiral magnetic effect) and periodic oscillation (chiral Zitterbewegung). We theoretically find that the mechanism behind this interesting dynamical phenomenon is the special chiral relativistic Landau level. Since the frequency, amplitude and drift velocity of chiral WQPs can be controlled in a measurable range, one can expect the observation of the phenomenon in the cold atomic system.

Spin-Orbit Coupling Effect on the Electrophilicity Index, Chemical Potential, Hardness and Softness of Neutral Gold Clusters: A Relativistic Ab-initio Study

Electrophilicity index (𝜔) is related to the energy lowering associated with a maximum amount of electron flow between a donor and an acceptor and possesses adequate information regarding structure, stability, reactivity and interactions. Chemical potential (μ) measures charge transfer from a system to another having a lower value of μ, while chemical hardness (η) is a measure of characterizing relative stability of clusters. The main purpose of the present research work is to examine the Spin-Orbit Coupling (SOC) effect on the behavior of the electrophilicity index, chemical potential, hardness and softness of neutral gold clusters Aun (n=2-6). Using the second-order Douglas-Kroll-Hess Hamiltonian, geometries are optimized at the DKH2-B3P86/DZP-DKH level of theory. Spin-orbit coupling energies are computed using the fourth-order Douglas-Kroll-Hess Hamiltonian, generalized Hartree-Fock method and all-electron relativistic double-ζ level basis set. Then, spin-orbit coupling (SOC) corrections to the electrophilicity index, chemical potential, hardness and softness are calculated. It is revealed that spin-orbit correction to the vertical chemical hardness has important effect on Au3 and Au6, i.e. SOC decreases (increases) the hardness of gold trimer (hexamer). Due to the relationship between hardness and softness, σ = , inclusion of spin-orbit coupling increases (decreases) the softness of Au3 (Au6) and thus destabilizes (stabilizes) it. Spin-orbit coupling (SOC) also has more important effect on the chemical potential of Au3 by decreasing its value. It is found that spin-orbit coupling has considerable effect on the electrophilicity index of gold trimer and greatly increases its value. Furthermore, SOC increases the maximal charge acceptance of Au3 more and thus destabilizes it more. As a result, spin-orbit coupling effect appears to be important in calculating the electrophilicity index of the gold trimer. Doi: 10.28991/HIJ-2021-02-01-05 Full Text: PDF

Relativistic Landau levels for a fermion-antifermion pair interacting through Dirac oscillator interaction

We introduce a unique model for a fermion-antifermion pair interacting via Dirac oscillator coupling in the presence of an external uniform magnetic field. This model is based on an exact solution of the corresponding form of a fully-covariant two-body Dirac equation (one-time). The dynamic symmetry of the system allows to study in 2+1 dimensions and we choose the interaction of the particles with the external uniform magnetic field in the symmetric gauge. The corresponding equation leads 4times 4 dimensional matrix equation for such a static composite system. For spin antisymmetric state of the fermion-antifermion pair, we perform an exact solution of the matrix equation and obtain relativistic Landau levels of a fermion-antifermion pair interacting via Dirac oscillator coupling. The results show that such a composite system behaves like a single relativistic quantum oscillator carrying total rest mass of the particles. We discuss several interesting features of this system and show that the obtained energy spectrum agrees well with the previously announced results for one-body systems. We think that the introduced model in this manuscript has a great potential for many theoretical and experimental applications.

Relativistic Landau quantization in the spiral dislocation spacetime

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime. We show that analytical solutions to the Dirac equation can be obtained, where the spectrum of energy corresponds to the relativistic Landau levels. We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.

Relativistic Dynamics of Oppositely Charged Two Fermions Interacting with External Uniform Magnetic Field

We investigated the relativistic dynamics of oppositely charged two fermions interacting with an external uniform magnetic field. We chose the interaction of each fermion with the external magnetic field in the symmetric gauge, and obtained a precise solution of the corresponding fully-covariant two-body Dirac equation that derived from Quantum Electrodynamics via Action principle. The dynamic symmetry of the system we deal with allowed us to determine the relativistic Landau levels of such a spinless composite system, without using any group theoretical method. As a result, we determined the eigenfunctions and eigenvalues of the corresponding two-body Dirac Hamiltonian

An alternative way to present a relativistic Lagrangian definition

As long we known, the non-relativistic Lagrangian definition, L = T − U with T and U as being, respectively, kinetic and potential energy, it is not valid at the relativistic level. This issue partially obstructs the college student’s comprehension of special theory of relativity from the Lagrangian formalism. Further, it is well known that the space-time world demands essentials principles of special theory of relativity: four-vectors and Lorentz invariance. In this work, we departure from these basics concepts of space-time world in order to get a relativistic Lagrangian definition parallel to the non-relativistic one and, as a consequence, this can help the college student to better understand special theory of relativity [1].

Relativistic Landau and oscillator levels in a symmetric gauge field in a non-commutative complex space

In this work, we obtain the exact solution for the relativistic Landau problem plus oscillator potential in a complex symmetric gauge field in a non-commutative complex space, using the algebraic techniques of creation and annihilation operators. It is shown that the relativistic Landau problem in a complex symmetric gauge field in a non-commutative complex space has a similar behavior to the Pauli equation in the presence of a symmetric gauge field in a commutative ordinary space. We derive the exact non-commutative Landau and oscillator energy levels, while the non-relativistic limit of the energy spectrum is obtained. We show that the energy is not degenerate and is split into two levels as in the Zeeman effect.

The Quantum Condition That Should Have Been Assumed by Bohr When Deriving the Energy Levels of a Hydrogen Atom

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr’s quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr’s quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr’s quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr’s quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr’s quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

High field X-ray laser physics

High field X-ray laser physics

Microsolvation of heavy halides

AbstractThe fundamental question of how intermolecular interactions lead to the stabilization of heavy halides (Br−, I−, At−) microsolvated with up to six explicit water molecules is addressed here. An exhaustive exploration of the potential energy surfaces using a random search algorithm followed by optimization of molecular geometries using pseudopotentials and at the full four component relativistic levels of theory, affords a good number of structures with high probabilities of occurrence, highlighting the important role of local minima to reproduce experimentally measured properties. Sequential hydration enthalpies for astatide are reported here for the first time in the scientific literature. Closed shell (ionic, long range) as well as intermediate character interactions (contributions from closed shell and covalent) are at play stabilizing the clusters. The ability of water molecules to either donate or to accept electron density dictates the nature and strength of the corresponding hydrogen bonds in solvation shells. Binding energies and molecular geometries are shown to be more sensitive to electron correlation than to relativistic effects.

On extended thermodynamics: From classical to the relativistic regime

The recent monumental detection of gravitational waves by LIGO, the subsequent detection by the LIGO/VIRGO observatories of a binary neutron star merger seen in the gravitational wave signal [Formula: see text], the first photo of the event horizon of the supermassive black hole at the center of Andromeda galaxy released by the EHT telescope and the ongoing experiments on Relativistic Heavy Ion Collisions at the BNL and at the CERN, demonstrate that we are witnessing the second golden era of observational relativistic gravity. These new observational breakthroughs, although in the long run would influence our views regarding this Kosmos, in the short run, they suggest that relativistic dissipative fluids (or magnetofluids) and relativistic continuous media play an important role in astrophysical-and also subnuclear-scales. This realization brings into the frontiers of current research theories of irreversible thermodynamics of relativistic continuous media. Motivated by these considerations, we summarize the progress that has been made in the last few decades in the field of nonequilibrium thermodynamics of relativistic continuous media. For coherence and completeness purposes, we begin with a brief description of the balance laws for classical (Newtonian) continuous media and introduce the classical irreversible thermodynamics (CIT) and point out the role of the local-equilibrium postulate within this theory. Tangentially, we touch the program of rational thermodynamics (RT), the Clausius–Duhem inequality, the theory of constitutive relations and the emergence of the entropy principle in the description of continuous media. We discuss at some length, theories of non equilibrium thermodynamics that sprang out of a fundamental paper written by Müller in 1967, with emphasis on the principles of extended irreversible thermodynamics (EIT) and the rational extended irreversible thermodynamics (REIT). Subsequently, after a brief introduction to the equilibrium thermodynamics of relativistic fluids, we discuss the Israel–Stewart transient (or causal) thermodynamics and its main features. Moreover, we introduce the Liu–Müller–Ruggeri theory describing relativistic fluids. We analyze the structure and compare this theory to the class of dissipative relativistic fluid theories of divergent type developed in the late 1990 by Pennisi, Geroch and Lindblom. As far as theories of nonequilibrium thermodynamics of classical media are concerned, it is fair to state that substantial progress has been made and many predictions of the extended theories have been placed under experimental scrutiny. However, at the relativistic level, the situation is different. Although the efforts aiming to the development of a sensible theory (or theories) of nonequilibrium thermodynamics of relativistic fluids (or continuous media) spans less than a half-century, and even though enormous steps in the right direction have been taken, nevertheless as we shall see in this review, still a successful theory of relativistic dissipation is lacking.