Nonrelativistic Research Articles

Introduction to Thermal Field Theory: From First Principles to Applications

This review article provides the basics and discusses some important applications of thermal field theory, namely, the combination of statistical mechanics and relativistic quantum field theory. In the first part, the fundamentals are covered: the density matrix, the corresponding averages, and the treatment of fields of various spin in a medium. The second part is dedicated to the computation of thermal Green’s function for scalars, vectors, and fermions with path-integral methods. These functions play a crucial role in thermal field theory as explained here. A more applicative part of the review is dedicated to the production of particles in a medium and to phase transitions in field theory, including the process of vacuum decay in a general theory featuring a first-order phase transition. To understand this review, the reader should have good knowledge of non-statistical quantum field theory.

A comprehensive approach for elucidating the interplay between 4f n+1 and 4f n 5d1 configurations in Ln2+ complexes.

Lanthanides (Ln) are typically found in the +3 oxidation state. However, in recent decades, their chemistry has been expanded to include the less stable +2 oxidation state across the entire series except promethium (Pm), facilitated by the coordination of ligands such as trimethylsilylcyclopentadienyl, C5H4SiMe3 (Cp'). The complexes have been the workhorse for the synthesis and theoretical study of the fundamental aspects of divalent lanthanide chemistry, where experimental and computational evidence have suggested the existence of different ground state (GS) configurations, 4f n+1 or 4f n 5d1, depending on the specific metal. Standard reduction potentials and 4f n+1 to 4f n 5d1 promotion energies have been two factors usually considered to rationalize the occurrence of these variable GS configurations, however the driving force behind this phenomenon is still not clear. In this work we present a comprehensive theoretical approach to shed light on this matter using the [LnCp3]- model systems. We begin by calculating 4f n+1 to 4f n 5d1 promotion energies and successfully correlate them with existing experimental data. Furthermore, we analyze how changes in the GS charge distribution between the Ln ions, LnCp3 and the reduced [LnCp3]- complexes (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) correlate with experimental trends in redox potentials and the calculated promotion energies. For this purpose, a comprehensive theoretical work that includes relativistic ligand field density functional theory (LFDFT) and relativistic ab initio wavefunction methods was performed. This study will help the rational design of suitable environments to tune the different GS configurations as well as modulating the spectroscopic properties of new Ln2+ complexes.

Exact-exchange relativistic density functional theory in three-dimensional coordinate space

Exact-exchange relativistic density functional theory in three-dimensional coordinate space

Unravelling the electronic structure, bonding, and magnetic properties of inorganic dysprosocene analogues [Dy(E4)2]- (E = N, P, As, CH).

Organometallic sandwich complexes of Dy(III) ion are ubiquitous for designing high-temperature single-ion magnets with blocking temperatures close to the liquid nitrogen boiling point. Magnetic bistability at the molecular level makes them potential candidates for nano-scale information storage materials. In the present contribution, we have thoroughly investigated the electronic structure, bonding, covalency, and magnetic anisotropy of inorganic dysprosocene complexes with a general formula of [Dy(E4)2]- (where E = N, P, As, CH) using state-of-the-art scalar relativistic density functional theory (SR-DFT), and a multiconfigurational complete active space self-consistent field (CASSCF) method with the N-electron valence perturbation theory (NEVPT2). Geometry optimization calculations predict stabilization of the [Dy(E4)2]- complexes with a linear geometry and D4h local symmetry Dy(III) ion in [Dy(N4)2]- (1) and [Dy(P4)2]- (2) complexes, while a bent geometry has been observed for the [Dy(As4)2]- (3), [Dy(P2(CH)2)2]- (4), and [Dy(As2(CH)2)2]- (5) complexes. Energy decomposition analysis (EDA) and natural bonding orbital (NBO) calculations reveal sizable 5d-ligand covalency followed by 6s/6p and weak 4f-ligand covalency in complexes 1-5. Both the natural localized molecular orbitals (NLMOs) at the DFT level and ab initio-based ligand field theory (AILFT) at the NEVPT2 level of theory predict an increase in the Dy-ligand covalency as we move from N to As. Spin-Hamiltonian parameter analysis of complexes 1-5 reveals stabilization of the mJ |±15/2〉 as the ground state with highly axial g values (gxx ∼ gyy ∼ 0 and gzz ∼ 20) and the barrier height of 2902, 1214, 1104, 1845, and 1509 K for 1-5, respectively. The Orbach effective demagnetization barrier (Ueff) for complexes 1-5 ranges between 2416-1175 K, with a record Ueff value of 2416 K observed for 1. In addition, we have explored the role of heavy element effects on the magnetic anisotropy by turning off the spin-orbit coupling of the pnictogens (N, P, and As), and our calculations clearly predict that heavy atoms in the first coordination sphere help in increasing the barrier height for magnetic relaxation. Heavy elements like P and As significantly enhance the SOC contributions, thereby providing a platform for designing and optimizing Dy(III) complexes with tailored magnetic behaviors.

The Structure of Space and Problems of Our Time

Since antiquity the image of space as emptiness has been opposed to the image of material space filled with some essence. For a long time this role was played by the theories of ether. During the twentieth century, a model of space filled with metrics, i.e., information, was formed in physics. Since the middle of the last century, the social and psychological sciences have rapidly developed models which treat space as a structured continuum. Many phenomena of quantum and relativistic theory look quite adequate in the sphere of humanities, particularly in the history and theory of architecture. It is shown how the model of structured space can be used to understand architectural and urban planning problems of our time.

Trends in Methanol-Solvated Actinide Ions and Actinide Expanded Porphyrin Complexes.

Trivalent actinide expanded porphyrin complexes have been of synthetic interest since the isolation of the series of trivalent lanthanide texaphyrin complexes in 1992, however, synthesis of these actinide-based complexes has not yet been achieved. In this work, a computational study with relativistic density functional theory was performed to determine how trivalent actinide ions (Ac3+ through Lr3+) interact with Schiff base expanded porphyrin macrocycles in a methanol solvent as an alternate pathway to stabilization. A thorough analysis of structural parameters, electronic structure, stability of microsolvation environments, and relative binding energies provided insight into the most stable structures. Trends in bonding and structure for the full actinide series are reported for methanol solvated ions, which reports actinide contraction along the series for early and mid actinides. Texaphyrin incorporates the actinide ions in a planar fashion, whereas for alaskphyrin a bent structure is more favorable; this bend results in stronger interaction energies than those calculated for the texaphyrin complexes. We also show that the redox-active expanded porphyrin ligands are able to accommodate a variety of actinides through charge transfer stabilization. Based on relative binding energy and energy decomposition analysis, it was found that texaphyrin and alaskaphyrin both exhibit a strong preference for binding to Th.

Impact of intrinsic electromagnetic structure on the nuclear charge radius in relativistic density functional theory

Impact of intrinsic electromagnetic structure on the nuclear charge radius in relativistic density functional theory

Quantum Reference Frames, Measurement Schemes and the Type of Local Algebras in Quantum Field Theory

We develop an operational framework, combining relativistic quantum measurement theory with quantum reference frames (QRFs), in which local measurements of a quantum field on a background with symmetries are performed relative to a QRF. This yields a joint algebra of quantum-field and reference-frame observables that is invariant under the natural action of the group of spacetime isometries. For the appropriate class of quantum reference frames, this algebra is parameterised in terms of crossed products. Provided that the quantum field has good thermal properties (expressed by the existence of a KMS state at some nonzero temperature), one can use modular theory to show that the invariant algebra admits a semifinite trace. If furthermore the quantum reference frame has good thermal behaviour (expressed in terms of the properties of a KMS weight) at the same temperature, this trace is finite. We give precise conditions for the invariant algebra of physical observables to be a type II1 factor. Our results build upon recent work of Chandrasekaran et al. (J High Energy Phys 2023(2): 1–56, 2023. arXiv:2206.10780), providing both a significant mathematical generalisation of these findings and a refined operational understanding of their model.

Nuclear mass predictions of the relativistic continuum Hartree-Bogoliubov theory with the kernel ridge regression. II. Odd-even effects

Nuclear mass predictions of the relativistic continuum Hartree-Bogoliubov theory with the kernel ridge regression. II. Odd-even effects

Einstein's transfer of inertia and dark matter

This paper presents the discontinuous energy fields-field, which is the replacement for spacetime in discontinuum physics, the conservation of the absorption and emission process discontinuity, of Bohr's atomic model, as an emitted electromagnetic radiation discontinuity, and Einstein's theory that electromagnetic radiation transfers inertia from an emitting body to an absorbing body leads to a dark, nonordinary matter that has the property of gravity.

Revelation of the overlooked conceptual mistakes in the derivation of the Lorentz transformation factor

The conceptual foundation of Einstein's theory for the derivation of the Lorentz transformation factor (LTF) has been subjected to a thorough examination both analytically and experimentally and there reveals a host of conceptual mistakes that the theory suffers from. The presumed temporal concept of the theory that the time of occurrence of an event measured in a moving frame (t′) should be different from that measured in a stationary frame (t) and the frame's velocity dependent temporal concept that the theory concludes have been conclusively proven to be conceptually incorrect ones. That the LTF theory suffers from a logical flaw—the fallacy of circular reasoning—is quite evident from the fact that what the theory concludes is the same as what it assumes. The experimental observation conclusively proves that t′ = t, that is, the time-measurement readings by all ideal clocks are exactly the same, irrespective of their state of motion. All the key equations involving t′ that Einstein deduced in his LTF theory have also been shown to be the incorrect ones. That the LTF was erroneously derived on the basis of faulty temporal concept has been conclusively proven in this article.

Dirac Theory, Relativistic Fluid Dynamics & Fisher Information

Abstract In previous papers we have shown how Schrödinger equations which include an electromagnetic field interaction can be deduced from a fluid dynamical Lagrangian of a charged potential flow that interacts with an electromagnetic field. The quantum behaviour was derived from Fisher information terms which were added to the classical Lagrangian. It was thus shown that a quantum mechanical system is drived by information and not only electromagnetic fields. This program was applied also to Pauli’s equations by removing the restriction of potential flow and using the Clebsch formalism. Although the analysis was quite successful there were still terms that did not admit interpretation, some of them can be easily traced to the relativistic Dirac theory. It is thus suggested to repeat the analysis for a relativistic flow, relating it to the Dirac theory by adding invariant four dimensional Fisher information terms. It is shown that while the classical parts of a classical fluid and a Dirac fluid can be mapped, the Fisher information term of Dirac theory is non-trivial. L Quantum = L Classical Fluid + L Fisher Information

Magic Number N = 350 Predicted by the Deformed Relativistic Hartree-Bogoliubov Theory in Continuum: Z = 136 Isotopes as an Example

The investigation of magic numbers for nuclei in the hyperheavy region (Z>120) is an interesting topic. The neutron magic number N=350 is carefully validated by the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), via analysing even-even nuclei around N=350 of the Z=136 isotopes in detail. Nuclei with Z=136 and 340≤N≤360 are all found to be spherical in their ground states. A big drop of the two-neutron separation energy S2n is observed from N=350 to N=352 in the isotopic chain of Z=136, and a peak of the two-neutron gap δ2n appears at N=350. There exists a big shell gap above N=350 around the spherical regions of single-neutron levels for nucleus with (Z=136,N=350). These evidences from the DRHBc theory support N=350 to be a neutron magic number in the hyperheavy region.

Charmed hypernuclei within density-dependent relativistic mean-field theory

Charmed hypernuclei within density-dependent relativistic mean-field theory

Relativistic bound state solutions and quantum information theory in D dimensions under exponential-type plus Yukawa potentials

The bound-state solution of the radial Klein-Gordon equation has been obtained under the interaction of an exponential-type and Yukawa potential functions. The Greene-Aldrich approximation has been used to overcome the centrifugal barrier and enable the analytical solutions of the energy and wave functions in closed form. The momentum space wave function in D dimensions has been constructed using the Fourier transform. The mean values have been conjectured for the position and momentum spaces using two equivalent equations. The effects of the potential parameters on the expectation values and quantum information measurement have been investigated. For the 1D case, the results obey the Heisenberg uncertainty principle, Fisher, Shannon, Onicescu, and the Rényi entropic inequalities. Other information complexities measures, such as Shannon Power, Fisher-Shannon, and Lopez-Ruiz-Mancini-Calbet, have been verified. For the ground state, the 1D momentum expectation value \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle p^{2} \\rangle_{00}$$\\end{document} coincides with the 3D \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\langle p^{2} \\rangle_{000}$$\\end{document} values, which is an indication of degeneracy. The total energy of a particle in both 1D and 3D space may be degenerate due to the inter-dimensional degeneracy of the quantum numbers. However, in this present result, the degeneracy in 1D and 3D occurred for fixed quantum states at different momentum intervals. Thus, in 1D, a particle may transit an entire space (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:-\\infty\\:<p<\\infty\\:)$$\\end{document} with a certain kinetic energy, which must be equal to its kinetic energy if it moves through the interval \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:0<p<\\infty\\:$$\\end{document} in 3D space. This may have implications for kinetic energy degeneracy in higher dimensions.

Gapless nonhydrodynamic modes in relativistic kinetic theory

Gapless nonhydrodynamic modes in relativistic kinetic theory

Exploring wobbling motion in triaxial even-even nuclei

The potential presence of wobbling motions in even-even nuclei 112Ru, 114Pd, 150Nd, and 188Os are explored by the five-dimensional collective Hamiltonian based on the relativistic density functional theory (5DCH-RDFT). The theoretical results successfully reproduce experimental energy spectra and electromagnetic transition probabilities. Analyses of the potential energy surfaces and probability density distributions in the (β,γ) deformation plane as well as the quadrupole asymmetry parameter 〈cos⁡3δ〉 reveal that 150Nd shows near-axial symmetry in contrast to the triaxial deformation in 112Ru, 114Pd, and 188Os. Additionally, spin coherent state (SCS) map is introduced for the first time to the 5DCH framework to visualize the geometry of angular momentum. It is revealed that the wobbling mode, characterized by oscillations of total angular momentum J about the medium axis, is present in 112Ru but absent in 150Nd.

Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory

Convergence of the hydrodynamic gradient expansion in relativistic kinetic theory

Dark energy effects on surface gravitational redshift and Keplerian frequency of neutron stars

Research on the properties of neutron stars with dark energy is a particularly interesting yet unresolved problem in astrophysics. We analyze the influence of dark energy on the equation of state, the maximum mass, the surface gravitational redshift and the Keplerian frequency for the traditional neutron star and the hyperon star matter within the relativistic mean field theory, using the GM1 and TM1 parameter sets by considering the two flavor symmetries of SU(6) and SU(3) combined with the observations of PSR J1614-2230, PSR J0348+0432, PSR J0030+0451, RX J0720.4-3125, and 1E 1207.4-5209. It is found that the existence of dark energy leads to the softened equations of the state of the traditional neutron star and the hyperon star. The radius of a fixed-mass traditional neutron star (or hyperon star) with dark energy becomes smaller, which leads to increased compactness. The existence of dark energy can also enhance the surface gravitational redshift and the Keplerian frequency of traditional neutron stars and hyperon stars. The growth of the Keplerian frequency may cause the spin rate to speed up, which may provide a possible way to understand and explain the pulsar glitch phenomenon. Specifically, we infer that the mass and the surface gravitational redshift of PSR J1748-2446ad without dark energy for the GM1 (TM1) parameter set are 1.141 M ⊙ (1.309 M ⊙) and 0.095 (0.105), respectively. The corresponding values for the GM1 (TM1) parameter set are 0.901 M ⊙ (1.072M ⊙) and 0.079 (0.091) if PSR J1748-2446ad contains dark energy with α = 0.05. PSR J1748-2446ad may be a low-mass pulsar with a lower surface gravitational redshift under our selected models.

Topological material in the III–V family: Heteroepitaxial InBi on InAs

InBi(001) is formed epitaxially on InAs(111)-A by depositing Bi onto an In-rich surface. Angle-resolved photoemission measurements reveal topological electronic surface states, close to the M¯ high symmetry point. This demonstrates a heteroepitaxial system entirely in the III–V family with topological electronic properties. InBi shows coexistence of Bi and In surface terminations, in contradiction with other III–V materials. For the Bi termination, the study gives a consistent physical picture of the topological surface electronic structure of InBi(001) terminated by a Bi bilayer rather than a surface formed by splitting to a Bi monolayer termination. Theoretical calculations based on relativistic density functional theory and the one-step model of photoemission clarify the relationship between the InBi(001) surface termination and the topological surface states, supporting a predominant role of the Bi bilayer termination. Furthermore, a tight-binding model based on this Bi bilayer termination with only Bi–Bi hopping terms, and no Bi–In interaction, gives a deeper insight into the spin texture. Published by the American Physical Society 2024