Restricted Symmetry Research Articles

Role of dynamic pairing correlations in fission dynamics. II. Fermium and nobelium isotopes

The competition between the quenching of pairing due to the repulsive Coulomb interaction and dynamic pairing correlations added by particle number symmetry restoration has been studied in a selected set of Fermium and Nobelium isotopes by using a hierarchy of Hartree-Fock-Bogoliubov--based approximations and a restricted variation after particle number projection, all of them based on the $\mathrm{D}1{\mathrm{M}}^{*}$ parametrization of the Gogny force. It is found that Coulomb antipairing is partially compensated by beyond-mean-field pairing correlations. However, the compensation is not perfect and a modulation of the spontaneous fission half-lives, as functions of the neutron number, indicates that the combined effect on fission dynamics of Coulomb antipairing and restricted particle number symmetry restoration cannot be overlooked. Neither can it be accounted for by the Coulomb Slater approximation.

Two Distinct Cu(II)-V(IV) Superexchange Interactions with Similar Bond Angles in a Triangular "CuV2" Fragment.

The strength and sign of superexchange interactions are often predicted on the basis of the bond angles between magnetic ions, but complications may arise in situations with a nontrivial arrangement of the magnetic orbitals. We report on a novel molecular tetramer compound [Cu(H2O)dmbpy]2[V2O2F8] (dmbpy = 4,4'-dimethyl-2,2'-bipyridyl) that is composed of triangular "CuV2" fragments and displays a spin gap behavior. By combining first-principles calculations and electronic models, we reveal that superexchange Cu-V interactions carry drastically different coupling strengths along two Cu-F-V pathways with comparable bond angles in the triangular "CuV2" fragment. Counterintuitively, their strong disparity is found to originate from the restricted symmetry of the half-filled Cu dx2-y2 orbital stabilized by the crystal field, leading to one dominating antiferromagnetic Cu-V coupling in each fragment. We revisit the magnetic properties of the reported spin-gapped chain compound [enH2]Cu(H2O)2[V2O2F8] (enH2 = ethylene diammonium) containing similar triangular "CuV2" fragments, and the magnetic behavior of the molecular tetramer and the chain compounds is rationalized as that of weakly coupled spin dimers and spin trimers, respectively. This work demonstrates that fundamentally different magnetic couplings can be observed between magnetic ions with similar bond angles in a single spin motif, thus providing a strategy to introduce various exchange interactions combined with low dimensionality in heterometallic Cu(II)-V(IV) compounds.

Restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry

In this paper, we elucidate the relation between the restricted Weyl symmetry and spontaneous symmetry breakdown of conformal symmetry. Using a scalar–tensor gravity, we show that the restricted Weyl symmetry leads to spontaneous symmetry breakdown of a global scale symmetry when the vacuum expectation value of a scalar field takes a nonzero value. It is then shown that this spontaneous symmetry breakdown induces spontaneous symmetry breakdown of special conformal symmetry in a flat Minkowski spacetime, but the resultant Nambu–Goldstone boson is not an independent physical mode but expressed in terms of the derivative of the dilaton which is the Nambu–Goldstone boson of the global scale symmetry. In other words, the theories which are invariant under the general coordinate transformation and the restricted Weyl transformation exhibit a Nambu–Goldstone phase where both special conformal transformation and dilatation are spontaneously broken while preserving the Poincaré symmetry.

Control of spin-orbit torques through magnetic symmetry in differently oriented noncollinear antiferromagnetic Mn3Pt

Interconversion of charge and spin currents via spin Hall effect is one of the key physical phenomena in spintronics. However, the spin polarizations are orthogonal to both the charge and spin flows due to the restricted symmetry conditions. Here, we use noncollinear antiferromagnet ${\mathrm{Mn}}_{3}\mathrm{Pt}$, which has different magnetic mirror planes in different orientations, to investigate magnetic symmetry dependent atypical spin-orbit torques. We observed weak generation of out of plane spin polarization $({\ensuremath{\sigma}}_{z})$ in ${\mathrm{Mn}}_{3}\mathrm{Pt}$/permalloy bilayers when current was applied perpendicular to the magnetic mirror plane of ${\mathrm{Mn}}_{3}\mathrm{Pt}$, and strong generation of ${\ensuremath{\sigma}}_{z}$ when current was applied parallel to the magnetic mirror plane. All three oriented ${\mathrm{Mn}}_{3}\mathrm{Pt}$ films show the same pattern, indicating the generation of unconventional ${\ensuremath{\sigma}}_{z}$ has strong dependence on magnetic symmetry. Controlling spin-orbit torques by changing current directions in differently oriented ${\mathrm{Mn}}_{3}\mathrm{Pt}$ films provides a strategy for optimizing antiferromagnetic spintronics.

Pure R2 gravity can gravitate about a flat background

Pure R2 gravity (R2 gravity by itself with no Einstein-Hilbert term) has attracted attention because it is different from other quadratic gravity theories. In a curved de Sitter (dS) or anti-de Sitter (AdS) background, it is equivalent to Einstein gravity with an additional massless scalar and with a cosmological constant. In contrast to other higher-derivative theories, it is therefore unitary. The equivalence with Einstein gravity is not valid for a flat background. In fact, it has been shown that linearizations of pure R2 gravity about flat spacetime does not produce a graviton. In other words, it does not gravitate about flat space. Pure R2 gravity is invariant under restricted Weyl transformations where the metric is scaled by a conformal factor that obeys a harmonic condition. In this work we consider an action composed of pure R2 gravity, a massless scalar field φ non-minimally coupled to gravity plus other terms. The entire action is invariant under restricted Weyl transformations. We show that when the scalar field φ acquires a non-zero vacuum expectation value (VEV), flat spacetime now becomes a viable gravitating background solution. The restricted Weyl symmetry becomes broken, not explicitly but spontaneously. In other words, when φ acquires a non-zero VEV, the equivalent Einstein action has now the possibility of having a zero cosmological constant and therefore solutions in a Minkowski background. The action can also have, as before, a non-zero cosmological constant, so that solutions in a dS and AdS background are still possible.

Quadratic gravity and restricted Weyl symmetry

In this paper, we investigate the relationship between quadratic gravity and a restricted Weyl symmetry where a gauge parameter [Formula: see text] of Weyl transformation satisfies a constraint [Formula: see text] in a curved spacetime. First, we briefly review a model with a restricted gauge symmetry on the basis of QED, where a [Formula: see text] gauge parameter [Formula: see text] obeys a similar constraint [Formula: see text] in a flat Minkowski spacetime, and explain that the restricted gauge symmetry removes one on-shell mode of gauge field, which together with the Feynman gauge leaves only two transverse polarizations as physical states. Next, it is shown that the restricted Weyl symmetry also eliminates one component of a dipole field in quadratic gravity around a flat Minkowski background, leaving only a single scalar state. Finally, we show that the restricted Weyl symmetry cannot remove any dynamical degrees of freedom in static background metrics by using the zero-energy theorem of quadratic gravity. This fact also holds for the Euclidean background metrics without imposing the static condition.

Restricted Weyl symmetry

We discuss the physics of a restricted Weyl symmetry in a curved space-time where a gauge parameter $\Omega(x)$ of Weyl transformation satisfies a constraint $\Box \Omega = 0$. First, we present a model of QED where we have a restricted gauge symmetry in the sense that a $U(1)$ gauge parameter $\theta(x)$ obeys a similar constraint $\Box \theta = 0$ in a flat Minkowski space-time. Next, it is precisely shown that a global scale symmetry must be spontaneously broken at the quantum level. Finally, we discuss the origin of the restricted Weyl symmetry and show that its symmetry can be derived from a full Weyl symmetry by taking a gauge condition $R = 0$ in the BRST formalism.

Analyses on Molecular Properties of the Diamidinate CrI-CrI Complex by Multireference and DFT Approaches.

The model system of the diamidinate CrI-CrI complex is investigated by wave function theory (WFT) and Kohn-Sham density functional theory (KS-DFT). The multireference perturbation theory (RASPT2) estimates a stabilization energy of ca. 20 kcal mol-1 for the δ bonding. The multiconfiguration pair-density functional theory (MC-PDFT) with the ftPBE functional well predicts the singlet energy curve comparable to the RASPT2 level. For the KS-DFT scheme based on a single determinant, seven functionals including BP86, BLYP, PBE, B3LYP, M06-L, M06, and ωB97X-D are assessed: two types of functionals are classified according to the nature of the restricted and broken symmetry potential energy curves. The broken symmetry scheme with the type I functionals can give good results for the energy curve in agreement with the multireference calculations. In regard to the metal-metal bonding, the restricted KS-DFT calculations performed by all of the seven functionals yield inferior description due to the lack of significant multiconfigurational character. The Mayer bond order, the electron localization function, and electron density predicted by the broken symmetry formalism with the type II functionals are consistent with those obtained with the multireference theory.

Gravitating magnetic monopole via the spontaneous symmetry breaking of pure R2 gravity

The pure $R^2$ gravity is equivalent to Einstein gravity with cosmological constant and a massless scalar field and it further possesses the so-called restricted Weyl symmetry which is a symmetry larger than scale symmetry. To incorporate matter, we consider a restricted Weyl invariant action composed of pure $R^2$ gravity, SU(2) Yang-Mills fields and a non-minimally coupled massless Higgs field (a triplet of scalars). When the restricted Weyl symmetry is spontaneously broken, it is equivalent to an Einstein-Yang-Mills-Higgs (EYMH) action with a cosmological constant and a massive Higgs non-minimally coupled to gravity i.e. via a term $\tilde{\xi} R |\Phi|^2$. When the restricted Weyl symmetry is not spontaneously broken, linearization about Minkowski space-time does not yield gravitons in the original $R^2$ gravity and hence it does not gravitate. However, we show that in the broken gauge sector of our theory, where the Higgs field acquires a non-zero vacuum expectation value, Minkowski space-time is a viable gravitating background solution. We then obtain numerically gravitating magnetic monopole solutions for non-zero coupling constant $\tilde{\xi}=1/6$ in three different backgrounds: Minkowski, anti-de Sitter (AdS) and de Sitter (dS), all of which are realized in our restricted Weyl invariant theory.

Axially symmetric shear-free fluids in f(R,T) gravity

In this work, we have discussed the implications of shear-free condition on axially symmetric anisotropic gravitating objects in [Formula: see text] theory. Restricted axial symmetry ignoring rotation and reflection entries containing three independent metric functions is taken into account for establishment of instability range. Implementation of linear perturbation on constitutive modified dynamical equations yield evolution equation. This equation associates adiabatic index [Formula: see text] with material and dark source components of physical parameters defining stable and unstable regions in Newtonian (N) and post-Newtonian (pN) approximations. It is remarked that the axial system evolving under shear-free condition implicates high levels of stability in anisotropic environment.

Raman and DRIFT spectra, vibrational assignments and quantum mechanical calculations of centrosymmetric meso-2,3-Dimercaptosuccinic acid

The Raman spectrum (3700–100cm−1) of meso-2,3-Dimercaptosuccinic acid (meso-DMSA; C4H6O4S2) was recorded in the solid phase using 514.5 and 785nm excitation lines. Whereas, the DRIFT spectrum (4000–400cm−1) of the sample powdered in KBr was obtained. Moreover, DFT-B3LYP/6-31G(d) geometry optimization and frequency calculations were carried out for centrosymmetric trans (Ci), gauche (C1; G+/G−) and eclipsed (Cs; Ef and C1; E+/E−) rotational isomers in favor of a trans conformation, the least energy with real frequencies. However, other conformers were found at either local minima or local maxima as a result of the rotation of carboxyl, hydroxyl and thiol groups according to a potential energy surface scan. Moreover, an imaginary wavenumber was predicted; therefore, they are considered transition states. On the other hand, the mass spectrum of the sample dissolved in an acetonitrile/methanol mixture reveal 4–6% dimer through intermolecular hydrogen bonding interactions via the dicarboxylic groups. Therefore, we have modeled the complex structure obeying Ci restricted symmetry for an isolated dimer unit using DFT-B3LYP/6-31G(d) and for two molecules per unit cell in the solid phase implementing DFT-PBE functional. Thus, the meso-DMSA forms long strands in which individual molecules are bonded together at each termini through hydrogen bonding. Aided by normal coordinate analysis, complete vibrational assignments were provided herein which support Ci configuration of meso-DMSA in the solid state which found consistent with the observed broadening, composite, split bands, and the mutual exclusion rule.

Unitary fermions and Lüscher’s formula on a crystal

We consider the low-energy particle-particle scattering properties in a periodic simple cubic crystal. In particular, we investigate the relation between the two-body scattering length and the energy shift experienced by the lowest-lying unbound state when this is placed in a periodic finite box. We introduce a continuum model for s-wave contact interactions that respects the symmetry of the Brillouin zone in its regularisation and renormalisation procedures, and corresponds to the naive continuum limit of the Hubbard model. The energy shifts are found to be identical to those obtained in the usual spherically symmetric renormalisation scheme upon resolving an important subtlety regarding the cutoff procedure. We then particularize to the Hubbard model, and find that for large finite lattices the results are identical to those obtained in the continuum limit. The results reported here are valid in the weak, intermediate and unitary limits. These may be used to significantly ease the extraction of scattering information, and therefore effective interactions in condensed matter systems in realistic periodic potentials. This can achieved via exact diagonalisation or Monte Carlo methods, without the need to solve challenging, genuine multichannel collisional problems with very restricted symmetry simplifications.

Yield response of winter wheat cultivars to environments modeled by different variance-covariance structures in linear mixed models

The main objectives of multi-environmental trials (METs) are to assess cultivar adaptation patterns under different environmental conditions and to investigate genotype by environment (G×E) interactions. Linear mixed models (LMMs) with more complex variance-covariance structures have become recognized and widely used for analyzing METs data. Best practice in METs analysis is to carry out a comparison of competing models with different variance-covariance structures. Improperly chosen variance-covariance structures may lead to biased estimation of means resulting in incorrect conclusions. In this work we focused on adaptive response of cultivars on the environments modeled by the LMMs with different variance-covariance structures. We identified possible limitations of inference when using an inadequate variance-covariance structure. In the presented study we used the dataset on grain yield for 63 winter wheat cultivars, evaluated across 18 locations, during three growing seasons (2008/2009-2010/2011) from the Polish Post-registration Variety Testing System. For the evaluation of variance-covariance structures and the description of cultivars adaptation to environments, we calculated adjusted means for the combination of cultivar and location in models with different variance-covariance structures. We concluded that in order to fully describe cultivars adaptive patterns modelers should use the unrestricted variance-covariance structure. The restricted compound symmetry structure may interfere with proper interpretation of cultivars adaptive patterns. We found, that the factor-analytic structure is also a good tool to describe cultivars reaction on environments, and it can be successfully used in METs data after determining the optimal component number for each dataset.

From the Crystal to the Rose: The Route to Biomimetic Self-assembled Nanostructured Materials

Life was able to create (bio)chemical pathways to mineral structures of great complexity, breaking the symmetry of single crystals into complex textures exhibiting morphologies with continuous curvature forbidden in crystal symmetry. Materials with non-crystalline morphologies can be made out of crystalline phases by filling volumes or coating surfaces with curved shapes. However, what wonders and challenges engineers and material scientists is the ability of life to create such a complexity by self-assembly. The formation of architectures such as shells and other exoskeletons of living organisms is governed by organic molecules or matrices, which modify crystallization in a deliberate manner. Their influence provokes the breaking of the single crystal character of the mineral precipitation and often leads to sinuous shapes, which have been thought to be a sign of life, and distinguish these minerals from their inanimate, mostly euhedral counterparts. In this lecture I will review a laboratory inorganic route to these biological structures. It has been discovered that silica -an ubiquitous mineral in the geological record, particularly in the early years of the planet- has a strong influence on the precipitation of carbonate and hydroxides. Under alkaline conditions, the chemical coupling of silica with CO3= and OH- creates abiotic, purely inorganic, self-assembled structures made of millions of nanocrystals building textures of high complexity and showing morphologies with continuous non-crystalographic curvature. The process of self-assembly, driven by a pH-based coupling of the chemistry of carbonate and silicate, is explored for applications in materials science. I will also discuss the geochemical plausibility of these self-organized mineral processes in terms of their implication in the origin of life and primitive life detection. Figure 1: Chemically induced cooperative phenomena break the restricted point symmetry of single crystals into self-assembled nanocrystalline structures with complex shapes of continuous curvature.

Entanglement classification of restricted Greenberger-Horne-Zeilinger–symmetric states in a four-qubit system

Similar to the three-qubit Greenberger-Horne-Zeilinger (GHZ) symmetry we explore the four-qubit GHZ symmetry group and its subgroup called restricted GHZ symmetry group. While the set of symmetric states under the whole group transformation is represented by three real parameters, the set of symmetric states under the subgroup transformation is represented by two real parameters. After comparing the symmetric states for whole and subgroup, the entanglement is examined for the latter set. It is shown that the set has only two SLOCC classes, $L_{abc_2}$ and $G_{abcd}$. Extension to the multi-qubit system is briefly discussed.

Stability analysis of restricted non-static axial symmetry

This paper aims to investigate the instability of very restrictedclass of non-static axially symmetric spacetime with anisotropicmatter configuration. The perturbation scheme is established for theEinstein field equations and conservation laws. The instabilityrange in the Newtonian and post-Newtonian regions are explored byconstructing the collapse equation in this scenario. It is foundthat the adiabatic index plays an important role in the stabilityanalysis which depends upon the physical parameters i.e., energydensity and anisotropic pressure of the fluid distribution.

Assembly of Trigonal and Tetragonal Prismatic Cages from Octahedral Metal Ions and a Flexible Molecular Clip

Reaction of a semirigid ligand with two octahedral metal ions with restricted coordination symmetry afforded metalated container complexes showing trigonal or tetragonal outer shapes and inner cavities.

Study of viable models with non-universal gaugino mediation with CompHEP and ISAJET

We study the recently proposed scenario for SUSY GUT models in which compactification of the extra dimension(s) leads to a breakdown of the gauge symmetry and/or supersymmetry. SUSY breaking occurs on a hidden brane, and is communicated to the visible brane via gaugino mediation. The non-universal gaugino masses are developed at the compactification scale as a consequence of a restricted gauge symmetry on the hidden brane. For gaugino masses related due to a Pati–Salam symmetry on the hidden brane, we find the limited, but significant, regions of the model parameter space where a viable spectra of SUSY matter is generated. In the more general case of three independent gaugino masses, large parameter space regions open up for large values of the U(1) gaugino mass M 1 . We also find the relic density of neutralinos for these models to be generally below the expectations from cosmological observations, thus leaving room for hidden sector states to make up the bulk of cold dark matter .

Viable models with non-universal gaugino mediated supersymmetry breaking

Recently, extra dimensional SUSY GUT models have been proposed in which compactification of the extra dimension(s) leads to a breakdown of the gauge symmetry and/or supersymmetry. We examine a particular class of higher-dimensional models exhibiting supersymmetry and SU(5) or SO(10) GUT symmetry. SUSY breaking occurs on a hidden brane, and is communicated to the visible brane via gaugino mediation. Non-universal gaugino masses are developed at the compactification scale as a consequence of a restricted gauge symmetry on the hidden brane. In this case, the compactification scale is at or slightly below the GUT scale. We examine the parameter space of such models where gaugino masses are related due to a Pati-Salam symmetry on the hidden brane. We find limited but significant regions of model parameter space where a viable spectra of SUSY matter is generated. Our results are extended to the more general case of three independent gaugino masses; here we find that large parameter space regions open up for large values of the U(1) gaugino mass M_1. We also find the relic density of neutralinos for these models to be generally below expectations from cosmological observations, thus leaving room for hidden sector states to make up the bulk of cold dark matter. Finally, we evaluate the branching fraction BF(b -> s gamma) and muon anomalous magnetic moment a_\mu.

5d super-Yang–Mills theory in 4d superspace, superfield brane operators, and applications to orbifold GUTs

A manifestly gauge invariant formulation of 5-dimensional supersymmetric Yang–Mills theories in terms of 4d superfields is derived. It relies on a supersymmetry and gauge-covariant derivative operator in the x 5 direction. This formulation allows for a systematic study of higher-derivative operators by combining invariant 4d superfield expressions under the additional restriction of 5d Lorentz symmetry. In cases where the 5d theory is compactified on a gauge-symmetry-breaking orbifold, the formalism can be used for a simple discussion of possible brane operators invariant under the restricted symmetry of the fixed points. This is particularly relevant to recently constructed grand unified theories in higher dimensions (orbifold GUTs). Several applications, including proton decay operators and brane-localized mass terms, are discussed.