Search Results (38)

Quantum channels define key objects in quantum information theory. They are represented by completely positive trace-preserving linear maps in matrix algebras. We analyze a family of quantum channels defined through the use of the Weyl operators. Such channels provide generalization of the celebrated qubit Pauli channels. Moreover, they are covariant with respective to the finite group generated by Weyl operators. In what follows, we study self-adjoint Weyl channels by providing a special Hermitian representation. For a prime dimension of the corresponding Hilbert space, the self-adjoint Weyl channels contain well-known generalized Pauli channels as a special case. We propose multipartite generalization of Weyl channels. In particular, we analyze the power of prime dimensions using finite fields and study the covariance properties of these objects. Full article

Triaxial shapes in even–even nuclei have been considered since the early days of the nuclear collective model. Although many theoretical approaches have been used over the years for their description, no effort appears to have been made for grouping them together and identifying regions on the nuclear chart where the appearance of triaxiality might be favored. In addition, over the last few years, discussion has started on the appearance of small triaxiality in nuclei considered so far as purely axial rotors. In the present work, we collect the predictions made by various theoretical approaches and show that pronounced triaxiality appears to be favored within specific stripes on the nuclear chart, with low triaxiality being present in the regions between these stripes, in agreement with parameter-free predictions made by the proxy-SU(3) approximation to the shell model, based on the Pauli principle and the short-range nature of the nucleon–nucleon interaction. The robustness of triaxiality within these stripes is supported by global calculations made in the framework of the Finite-Range Droplet Model (FRDM), which is based on completely different assumptions and possesses parameters fitted in order to reproduce fundamental nuclear properties. Full article

We present an economical approach to treat spin–orbit coupling (SOC) in the state-averaged driven similarity renormalization group second-order perturbation theory (SA-DSRG-PT2). The electron correlation is first introduced by forming the SA-DSRG-PT2 dressed spin-free Hamiltonian. This Hamiltonian is then augmented with the Breit–Pauli Hamiltonian and diagonalized using spin-pure reference states to obtain the SOC-corrected energy spectrum. The spin–orbit mean-field approximation is also assumed to reduce the cost associated with the two-electron spin–orbit integrals. The resulting method is termed BP1-SA-DSRG-PT2c, and it possesses the same computational scaling as the non-relativistic counterpart, where only the one- and two-body density cumulants are required to obtain the vertical transition energy. The accuracy of BP1-SA-DSRG-PT2c is assessed on a few atoms and small molecules, including main-group diatomic molecules, transition-metal atoms, and actinide dioxide cations. Numerical results suggest that BP1-SA-DSRG-PT2c performs comparably to other internally contracted multireference perturbation theories with SOC treated using the state interaction scheme. Full article

Understanding the catalytic behavior of heterogeneous systems for the copolymerization of ethylene with polar monomers is essential for developing advanced functional polyolefins. In this study, we conducted a quantum chemical investigation of the SiO₂-supported Ni–allyl–α-imine ketone catalyst (Ni-OH@SiO₂) to uncover the factors governing monomer insertion, selectivity, and reactivity. Using DFT calculations and energy decomposition analysis (ALMO-EDA), we evaluated the coordination and insertion of six industrially relevant polar monomers, comparing their behavior to ethylene homopolymerization. Our results show that special polar monomers (SPMs) with aliphatic spacers, such as vinyltrimethoxysilane (vTMS) and 5-hexenyl acetate (AMA), exhibit favorable insertion profiles due to enhanced electrostatic and orbital interactions with minimal steric hindrance. In contrast, fundamental polar monomers (FPMs), including methyl acrylate (MA) and vinyl chloride (vCl), show higher activation barriers and increased Pauli repulsion due to strong electron-withdrawing effects and conjugation with the vinyl group. AMA displayed the lowest activation barrier (7.4 kcal/mol) and highest insertion thermodynamic stability (−17.6 kcal/mol). These findings provide molecular-level insight into insertion mechanisms and comonomer selectivity in Ni–allyl catalysts supported on silica, extending experimental understanding. This work establishes key structure–reactivity relationships and offers design principles for developing efficient Ni-based heterogeneous catalysts for polar monomer copolymerization. Full article

We introduce a polyadic analog of supersymmetry by considering the polyadization procedure (proposed by the author) applied to the toy model of one-dimensional supersymmetric quantum mechanics. The supercharges are generalized to polyadic ones using the n-ary sigma matrices defined in earlier work. In this way, polyadic analogs of supercharges and Hamiltonians take the cyclic shift block matrix form, and they are different from the N-extended and multigraded SQM. While constructing the corresponding supersymmetry as an n-ary Lie superalgebra (n is the arity of the initial associative multiplication), we have found new brackets with a reduced arity of $2\le m<n$ and a related series of m-ary superalgebras (which is impossible for binary superalgebras). In the case of even reduced arity m, we obtain a tower of higher-order (as differential operators) even Hamiltonians, while for m odd we obtain a tower of higher-order odd supercharges, and the corresponding algebra consists of the odd sector only. Full article

The current study investigates the influence of several R substituents (e.g., Me, SiH₃, F, Cl, Br, OH, NH₂, etc.) on the aromaticity of borazine, also known as the “inorganic benzene”. By performing hybrid DFT methods, blended with several computational techniques, e.g., Natural Bond Orbital (NBO), Quantum Theory of Atoms in Molecules (QTAIM), Gauge-Including Magnetically Induced Current (GIMIC), Nucleus-Independent Chemical Shift (NICS), and following a simultaneous evaluation of four different aromaticity indices (para-delocalization index (PDI), multi-centre bond order (MCBO), ring current strength (RCS), and NICS parameters), it is emphasized that the aromatic character of B-substituted (B₃R₃N₃H₃) and N-substituted (B₃H₃N₃R₃) borazine derivatives can be tailored by modulating the electronic effects of R groups. It is also highlighted that the position of R substituents on the ring structure is crucial in tuning the aromaticity. Systematic comparisons of calculated aromaticity index values (i.e., via regression analyses and correlation matrices) ensure that the reported trends in aromaticity variation are accurately described, while the influence of different R groups on electron delocalization and related aromaticity phenomena is quantitatively assessed based on NBO analyses. The most relevant interactions impacting the aromatic character of investigated systems are (i) the electron conjugations occurring between the p lone pair electrons (LP) on the F, Cl, Br, O or N atoms, of R groups, and the π*(B=N) orbitals on the borazine ring (i.e., LP(R)→π*(B=N) donations), and (ii) the steric-exchange (Pauli) interactions between the same LP and the π(B=N) bonds (i.e., LP(R)↔π(B=N) repulsions), while inductive/field effects influence the aromaticity of the investigated trisubstituted borazine systems to a much lesser extent. This work highlights that although the aromatic character of borazine can be enhanced by grafting electron-donor substituents (F, OH, NH₂, O⁻, NH⁻) on the N atoms, the stabilization due to aromaticity has only a moderate impact on these systems. By replacing the H substituents on the B atoms with similar R groups, the aromatic character of borazine is decreased due to strong exocyclic LP(R)→π*(B=N) donations affecting the delocalization of π-electrons on the borazine ring. Full article

MXenes are a family of two-dimensional nanomaterials. Titanium carbide MXene (Ti₃C₂T_x-MXene), reported in 2011, is the first inorganic compound reported among the MXene family. In the present work, we report on the study of the composition and various physical properties of Ti₃C₂T_x-MXene nanomaterial, as well as their temperature evolution, to consider MXenes for space applications. X-ray diffraction, thermal analysis and mass spectroscopy measurements confirmed the structure and terminating groups of the MXene surface, revealing a predominant single OH layer character. The temperature dependence of the specific heat shows a Debye-like character in the measured range of 2 K–300 K with a linear part below 10 K, characteristic of conduction electrons of metallic materials. The electron density of states (DOS) calculations for Ti₃C₂OH-MXene reveal a significant DOS value at the Fermi level, with a large slope, confirming its metallic character, which is consistent with the experimental findings. The temperature dependence of electrical resistivity of the MXene samples was tested for a wide temperature range (3 K–350 K) and shows a decrease on lowering temperature with an upturn at low temperatures, where negative magnetoresistance is observed. The magnetoresistance versus field is approximately linear and increases its magnitude with decreasing temperature. The magnetization curves are straight lines with temperature-independent positive slopes, indicating Pauli paramagnetism due to conduction electrons. Full article

Motivated by a ternary generalization of the Pauli exclusion principle proposed by R. Kerner, we propose a notion of a ${\mathbb{Z}}_3$-skew-symmetric covariant $\mathrm{SO}\left(3\right)$-tensor of the third order, consider it as a 3-dimensional matrix, and study the geometry of the 10-dimensional complex space of these tensors. We split this 10-dimensional space into a direct sum of two 5-dimensional subspaces by means of a primitive third-order root of unity q, and in each subspace, there is an irreducible representation of the rotation group $\mathrm{SO}\left(3\right)\hookrightarrow \mathrm{SU}\left(5\right)$. We find two $\mathrm{SO}\left(3\right)$-invariants of ${\mathbb{Z}}_3$-skew-symmetric tensors: one is the canonical Hermitian metric in five-dimensional complex vector space and the other is a quadratic form denoted by $K(z,z)$. We study the invariant properties of $K(z,z)$ and find its stabilizer. Making use of these invariant properties, we define an $\mathrm{SO}\left(3\right)$-irreducible geometric structure on a five-dimensional complex Hermitian manifold. We study a connection on a five-dimensional complex Hermitian manifold with an $\mathrm{SO}\left(3\right)$-irreducible geometric structure and find its curvature and torsion. Full article

We develop the method of averaging in Clifford (geometric) algebras suggested by the author in previous papers. We consider operators constructed using two different sets of anticommuting elements of real or complexified Clifford algebras. These operators generalize Reynolds operators from the representation theory of finite groups. We prove a number of new properties of these operators. Using the generalized Reynolds operators, we give a complete proof of the generalization of Pauli’s theorem to the case of Clifford algebras of arbitrary dimension. The results can be used in geometry, physics, engineering, computer science, and other applications. Full article

Several ternary rare-earth metals containing titanium aluminum intermetallics in the RE₂TiAl₃ series (RE = Y, Gd–Lu) have been synthesized from the elements using arc-melting techniques. All compounds crystallize in the trigonal crystal system with rhombohedral space group R3m (Z = 3) and lattice parameters ranging between a = 582–570 and c = 1353–1358 pm. They adopt the Mg₂Ni₃Si-type structure, which is an ordered superstructure of the cubic Laves phase MgCu₂ and has been observed for Al intermetallics for the first time. Tetrahedral [TiAl₃] entities that are connected over all corners form a network where the empty [TiAl₃] tetrahedra exhibit a full Ti/Al ordering based on the single crystal results. The Al atoms are arranged into 6³ Kagomé nets, while the Ti atoms connect these nets over the triangular units. In the cavities of this three-dimensional arrangement, the RE cations can be found forming a distorted diamond-type substructure. Magnetic measurements revealed that Y₂TiAl₃ and Lu₂TiAl₃ are Pauli paramagnetic substances, in line with the metallic character. The other compounds exhibit paramagnetism with antiferromagnetic ordering at a maximum Néel temperature of T_N = 26.1(1) K for Gd₂TiAl₃. Full article

A review of several classical, algebraic models in nuclear structure physics, which use symmetries as an important tool, are presented. After a conceptual introduction to group theory, a selection of models is chosen to illustrate the methods and the power of the usage of symmetries. This enables us to describe very involved systems in a greatly simplified manner. Some problems are also discussed, when ignoring basic principles of nature, such as the Pauli exclusion principle. We also show that occasionally one can rescue these omissions. In a couple of representative models, applications of symmetries are explicitly applied in order to illustrate how extremely complicated systems can be treated. This contribution is meant as a review of the use of algebraic models in nuclear physics, leading to a better understanding of the articles in the same special volume. Full article

Two equations whose variables take values in the Pauli algebra of complex quaternions are shown to be equivalent to the standard Dirac equation and its Hermitian conjugate taken together. They are transformed one into the other by an outer automorphism of the Pauli algebra. Given a solution to the Dirac equation, a new solution is obtained by multiplying it on the right by one of the 16 matrices of the Pauli group. This defines a homomorphism from the Pauli group into the group of discrete symmetries, whose kernel is a cyclic group of order four. The group of discrete symmetries is shown to be the Klein four-group consisting of four elements: the identity Id; the charge conjugation symmetry C; the mass inversion symmetry M; and their composition in either order, CM = MC. The mass inversion symmetry inverts the sign of the mass, leaving the electric charge unchanged. The outer “bar-star” automorphism is identified with the parity operation, resulting in proof of CPT = M or, equivalently, CPTM = Identity. Full article

Can we accurately model the spin state of a quantum particle? If so, we should be able to make identical copies of such a state and also obtain its mirror image. In quantum mechanics, many subatomic particles can form entangled pairs that are mirror images of each other, although the state of an individual particle cannot be duplicated or cloned as experimentally demonstrated by Aspect, Clauser and Zeilinger, the winners of the Nobel Prize in Physics 2022. We show that there is a higher-order symmetry associated with the SL(2,C) group that underlies the singlet state, which means that the singlet pairing preserves Lorentz transformations independently of the metric used. The Pauli exclusion principle can be derived from this symmetry. Full article

The Pauli limiting field represents a fundamental magnetic field at which the superconducting state collapses due to the spin-paramagnetic Cooper pair-breaking effect. Cao et al. (Nature 2021, 595, 526) reported that the magic-angle twisted trilayer graphene (MATNG, N = 3) exhibits the upper critical field which exceeds the Pauli limiting field by two to three times. This observation was interpreted as a violation of the Pauli-limiting field in MAT3G. Similar conclusions were recently reported by the same research group in MATNG (N = 4, 5) superlattices (Park, J.M. et al. Nat. Mater.2022, 21, 877). Here, we point out that Cao et al. (Nature 2021, 595, 526) calculated the Pauli limiting field by the use of reduced form (to the weak-coupling limit) of full equation of the theory of the electron–phonon-mediated superconductivity. Considering that in the same paper, Cao et al. (Nature 2021, 595, 526) reported that MATNGs are strong coupled superconductors, we calculate the Pauli limiting field for a strong coupled case and show that the observed upper critical fields in MATNGs comply with the Pauli limit. This implies that there is no violation of the Pauli limiting field in the Moiré multilayer graphene superlattices. Full article

Verbs and nouns gear θ-dependencies, Case, agreement, or construal relations. Building on Chomsky’s 1974 decomposition of such categories into ±N, ±V features, by translating said features into ±1, ±i scalars that allow for the construction of a vector space, this paper studies the possibility of organizing said features into 2 × 2 square matrices. In the system proposed to explore “head-complement” relations, operating on nouns yields a measurable/observable (Hermitian matrix), which in turn limits other potential combinations with abstract lexical categories. Functional/grammatical categories in the system deploy the same features, albeit organized differently in the matrix diagonal and off-diagonal. The algebraic result is a group with well-defined mathematical properties, which properly includes the Pauli group of standard use in quantum computation. In the system, the presumed difference between categories and interactions—here, in a context of the head-complement sort—reduces to whether the magnitude of the matrix eigenvalue is 1 or not, in the latter instance inducing asymmetric interactions. Full article