Symmetry Aspects Research Articles

Confinement and dynamical chiral symmetry breaking in a non-perturbative renormalizable quark model

Inspired by the construction of the Gribov–Zwanziger action in the Landau gauge, we introduce a quark model exhibiting both confinement and chiral symmetry aspects. An important feature is the incorporation of spontaneous chiral symmetry breaking in a renormalizable fashion. The quark propagator in the condensed vacuum turns out to be of a confining type. Besides a real pole, it exhibits complex conjugate poles. The resulting spectral form is explicitly shown to violate positivity, indicative of its unphysical character. Moreover, the ensuing quark mass function fits well to existing lattice data. To further validate the physical nature of the model, we identify a massless pseudoscalar (i.e. a pion) in the chiral limit and present estimates for the ρ meson mass and decay constant.

Spectroscopic determination of site symmetry and space group in lanthanide-doped crystals: Resolving intricate symmetry aspects for β-NaLnF4

There exists a controversy in the hitherto reported studies concerning the actual space group that accounts for spectroscopic results observed for the trivalent lanthanide (Ln3+) ions doped into β-NaLnF4 hosts. The two competing assignments of the space group: P6¯ or P63/m, bear on the associated point symmetry groups, which describe the local site symmetry of the dopant Ln ions. This paper aims at resolving this controversy. For this purpose two approaches are utilized. First, several new samples were synthesized and characterized by photoluminescence (PL) spectroscopy. Both the emission and excitation PL spectra have been measured. The analysis of the present experimental data indicates unequivocally that the dopant Ln3+ ions enter the crystal lattice β-NaGF4 and β-NaYF4 at two crystallographically distinct sites. Hence, the correct space group for these hosts is P6¯ and not P63/m. The intricacies arising from the sample preparation methods, which bear on the interpretation of the results, are also clarified. Second, the theoretical modeling of the crystal-field parameters (CFPs) is carried out based on superposition model to correlate the available crystallographic and spectroscopic data. The crystal-field analysis enables to ascribe unambiguously the spectroscopically determined sites to the crystallographic sites 1a and 1f. In this way an interpretation of photoluminescence spectra is achieved that fully corroborates the available crystallographic data. The influence of structural disorder occurring in β-NaLnF4 family of compounds on the 5D0→7F1 photoluminescence spectra of dopant Eu3+ ion and its role in interpretation of experimental data is also discussed.

Circularly polarized high harmonics generated by a bicircular field from inert atomic gases in thepstate: A tool for exploring chirality-sensitive processes

$S$-matrix theory of high-order harmonic generation (HHG) is generalized to multielectron atoms. In the multielectron case the harmonic power is expressed via a coherent sum of the time-dependent dipoles, while for the one-electron models a corresponding incoherent sum appears. This difference is important for the inert atomic gases having a $p$ ground state as used in a recent HHG experiment with a bicircular field [Nat. Photonics 9, 99 (2015)]. We investigate HHG by such a bicircular field, which consists of two coplanar counter-rotating circularly polarized fields of frequency $r\ensuremath{\omega}$ and $s\ensuremath{\omega}$. Selection rules for HHG by a bicircular field are analyzed from the aspects of dynamical symmetry of the system, conservation of the projection of the angular momentum on a fixed quantization axis, and the quantum number of the initial and final atomic ground states. A distinction is made between the selection rules for atoms with closed [J. Phys. B 48, 171001 (2015)] and nonclosed shells. An asymmetry in emission of the left- and right-circularly polarized harmonics is found and explained by using a semiclassical model and the electron probability currents which are related to a nonzero magnetic quantum number. This asymmetry can be important for the application of such harmonics to the exploration of chirality-sensitive processes and for generation of elliptic or even circular attosecond pulse trains. Such attosecond pulse trains are analyzed for longer wavelengths than in Opt. Lett. 40, 2381 (2015), and for various field-component intensities.

On Landau–Ginzburg systems, quivers and monodromy

Let X be a toric Fano manifold and denote by C r i t ( f X ) ⊂ ( C ∗ ) n the solution scheme of the corresponding Landau–Ginzburg system of equations. For toric Del-Pezzo surfaces and various toric Fano threefolds we define a map L : C r i t ( f X ) → P i c ( X ) such that E L ( X ) : = L ( C r i t ( f X ) ) ⊂ P i c ( X ) is a full strongly exceptional collection of line bundles. We observe the existence of a natural monodromy map M : π 1 ( L ( X ) ∖ R X , f X ) → A u t ( C r i t ( f X ) ) where L ( X ) is the space of all Laurent polynomials whose Newton polytope is equal to the Newton polytope of f X , the Landau–Ginzburg potential of X , and R X ⊂ L ( X ) is the space of all elements whose corresponding solution scheme is reduced. We show that monodromies of C r i t ( f X ) admit non-trivial relations to quiver representations of the exceptional collection E L ( X ) . We refer to this property as the M -aligned property of the maps L : C r i t ( f X ) → P i c ( X ) . We discuss possible applications of the existence of such M -aligned exceptional maps to various aspects of mirror symmetry of toric Fano manifolds.

New aspects of symmetry of elementary cellular automata

We present a new classification of elementary cellular automata. It is based on the structure of the network of states, connected with the transitions between them; the latter are determined by the automaton rule. Recently an algorithm has been proposed to compress the network of states ( Krawczyk, Physica A 390 (2011) 2181). In this algorithm, states are grouped into classes, according to the local symmetry of the network. In the new classification, an automaton is described by the number of classes #(N) as dependent on the system size N. In most cases, the results reflect the known classification into 88 groups. However, the function #(N) also appears to be the same for some rules which have not been grouped together yet. In this way, the automaton 23 is equivalent to 232, 77 to 178, 105 to 150, the pair (43, 113) to the pair (142, 212) and the group (12, 68, 207, 221) to the group (34, 48, 187, 243). Furthermore, automata 51, 204, the pair (15, 85) and the pair (170, 240) are all mutually equivalent. Results are also presented on the structure of networks of states.

Searching for enrichment and gadolinia distributions in BWR fuel lattices through a Heuristic-Knowledge Method

A Heuristic-Knowledge Method was developed to determine the enrichment and gadolinia distribution in a fuel lattice of boiling water reactors. The method was called S15 and is based on the experience obtained for the fuel lattice design for this kind of nuclear reactors. It also takes advantage of the symmetry aspects found in a typical BWR fuel lattice. An objective function was used throughout the searching process, as well as the same degrees of freedom used by five different meta-heuristic techniques based on evolutionary algorithms. Using the S15 method forty iterations were needed to obtain the best solution i.e., the smallest value of the objective function through a minimization process. In order to assess the performance of the S15 method, it was compared to five other evolutionary techniques. The two-dimensional CASMO-4 code was used to obtain the neutronic parameters employed by the objective function. The objective function value was the main criterion used to qualify all the techniques. All the methods were applied to fuel lattices charged in three different real operation cycles of the nuclear reactors at the Laguna Verde Nuclear Power Plant (LVNPP). The results generated with S15 surpass those obtained by the five evolutionary techniques.

Symmetry methods in mathematical biology

Many biological systems have aspects of symmetry. Symmetry is formalized using group theory. This theory applies not just to the geometry of symmetric systems, but to their dynamics. The basic ideas of symmetric dynamics and bifurcation theory are applied to speciation, animal locomotion, the visual cortex, pattern formation in animal markings and geographical location, and the geometry of virus protein coats.

Goldstone’s Theorem on a Light-Like Plane

I review various aspects of chiral symmetry and its spontaneous breaking on null planes, including the interesting manner in which Goldstone’s theorem is realized and the constraints that chiral symmetry imposes on the null-plane Hamiltonians. Specializing to QCD with N massless flavors, I show that there is an interesting limit in which the chiral constraints on the null-plane Hamiltonians can be solved to give the spin-flavor algebra SU(2N), recovering a result originally found by Weinberg using different methods.

Correlation of EMR and optical spectroscopy data for Cr3+ and Mn2+ ions doped into yttrium aluminum borate YAl3(BO3)4 crystal – Extracting low symmetry aspects

In this study, the crystal field analysis for Cr3+ and Mn2+ ions doped into yttrium aluminum borate YAl3(BO3)4, for short YAB, crystal has been carried out to complement earlier study of the zero-field splitting (ZFS) parameters (ZFSPs). This analysis utilizes data on the distortion models obtained from analysis of the ZFSPs obtained experimentally by EMR for Cr3+ and Mn2+ ions at the Y3+ and Al3+ sites in YAB. This approach enables to verify and enhance reliability of the ZFSP modeling based on superposition model (SPM) analysis and the distortion models predicted previously. Subsequently, modeling of the crystal field parameters (CFPs) based on SPM analysis is carried out for Cr3+ and Mn2+ ions located at possible cation sites in YAB. The SPM predicted CFP values serve as input for the Crystal Field Analysis (CFA) package to calculate the CF energy levels. The predicted physical ZFS of the ground spin state, i.e. the 4A2 state for Cr3+ ion and the 6S state Mn2+ ions, enable calculation of the theoretical ZFSP values, D and D & (a–F), respectively, using the microscopic spin Hamiltonian (MSH) module in the CFA package. In this way, data on the distortions around the Cr3+ centers in YAB (and to a certain extent also for Mn2+ centers) obtained using the ZFSP data from EMR measurements may be correlated with data on the CF energy levels measured by optical spectroscopy. This modeling approach uncovers certain incompatibilities in the existing data for Cr3+:YAB, which call for reanalysis of the previous assignments of the energy levels observed in optical spectra and more accurate experimental data.

Medidas faciais em indivíduos adultos sem queixas orofaciais: compatibilidade entre medidas antropométricas e percepção facial

OBJETIVO: verificar a compatibilidade entre os achados de medidas faciais mensuradas pelo paquímetro e a percepção das características faciais realizada subjetivamente por um avaliador experiente. MÉTODOS: foram avaliados 24 sujeitos do sexo feminino e 24 do sexo masculino, pareados por sexo e idade, sem queixas morfológicas e funcionais do sistema estomatognático. Foram avaliados os aspectos de simetria entre os terços médio e inferior, altura e largura da face, e canto externo dos olhos direito e esquerdo às comissuras do lábio direita e esquerda, respectivamente. Cada medida foi realizada três vezes por paquímetro digital para consideração da média entre estes valores, considerando-se assimétricas comparações com diferenças superiores à 4 milímetros. A largura da face foi obtida por meio do paquímetro digital adaptado com prolongamento de 10 centímetros. Já a avaliação da percepção das características faciais foi realizada por um avaliador cegado quanto às medidas obtidas, devendo assinalar simetrias e assimetrias nestes mesmos aspectos avaliativos. RESULTADOS: por meio do teste de concordância de Kappa e Qui-quadrado, pode-se verificar uma boa compatibilidade entre as avaliações realizadas, demonstrando-se a fidedignidade entre os métodos utilizados. Além disso, verificou-se que existe uma relação entre a simetria dos terços da face e a atribuição da tipologia facial na avaliação perceptiva, observando-se simetria em faces médias e curtas e ausência de um padrão determinante para faces longas. CONCLUSÃO: a caracterização da simetria facial por paquímetro apresenta uma boa compatibilidade com a percepção subjetiva de um avaliador experiente.

Observational aspects of symmetries of the neutral B meson system

We revisit various results, which have been obtained by the BABAR and Belle Collaborations over the last 13 years, concerning symmetry properties of the Hamiltonian, which governs the time evolution and the decay of neutral $$B$$ mesons. We find that those measurements, which established CP-violation in $$B$$ meson decay, 13 years ago, had as well established $$T$$ (time-reversal) symmetry violation. They also confirmed CPT symmetry in the decay $$(T_\mathrm{CPT}=0)$$ and symmetry with respect to time-reversal $$(\epsilon = 0)$$ and to CPT $$(\delta = 0)$$ in the $$B^0$$ $$\bar{B}{}^0\,$$ oscillation.

Orbital dependent interaction of quantum well states for catalytic water splitting

Orientational dependence of catalytic activity for water splitting reaction on a two-dimensional gold cluster supported on MgO/Ag(001) has been identified using first-principles calculations. Strong oscillations are found in water adsorption energy, the dissociation barrier, and the binding energy of the dissociated H atom, with two different orientational patterns. These two patterns correlate with the wavefunction symmetry of frontier orbitals of selected quantum well states (QWSs). This finding reveals a new aspect of orbital symmetry in catalytic reactions without involving changes in the shape or size of the atomic cluster, and is promising for potential applications in chemical reactions using the orbital degree of freedom of QWSs.

Symmetry and asymmetry of configuration and structure of vertebrate skin

The use of vertebrate skin in biosymmetrics, in particular, its configuration, thickness, and spatial structure of the dermal stroma is considered. The theories explaining the ordered arrangement and structure of skin as a result of morphogenesis (Turing, 1952; Gierer and Meinhardt, 1972; Belintsev, 1991) are reviewed. The study of quantitative aspects of bilateral symmetry is considered within the framework of (1) coefficients of symmetry and asymmetry, which provide estimates of symmetry; (2) extent of asymmetry of the curve of normal distribution (Gaussian curve), the inflection of which shows the mean of a sample. The use of these methods for statistical analysis is illustrated by particular examples.

Group theory analysis of phonons in two-dimensional transition metal dichalcogenides

Transition metal dichalcogenides (TMDCs) have emerged as a new two dimensional materials field since the monolayer and few-layer limits show different properties when compared to each other and to their respective bulk materials. For example, in some cases when the bulk material is exfoliated down to a monolayer, an indirect-to-direct band gap in the visible range is observed. The number of layers $N$ ($N$ even or odd) drives changes in space group symmetry that are reflected in the optical properties. The understanding of the space group symmetry as a function of the number of layers is therefore important for the correct interpretation of the experimental data. Here we present a thorough group theory study of the symmetry aspects relevant to optical and spectroscopic analysis, for the most common polytypes of TMDCs, i.e. $2Ha$, $2Hc$ and $1T$, as a function of the number of layers. Real space symmetries, the group of the wave vectors, the relevance of inversion symmetry, irreducible representations of the vibrational modes, optical selection rules and Raman tensors are discussed.

Chlorophylls, Symmetry, Chirality, and Photosynthesis

Chlorophylls are a fundamental class of tetrapyrroles and function as the central reaction center, accessory and photoprotective pigments in photosynthesis. Their unique individual photochemical properties are a consequence of the tetrapyrrole macrocycle, the structural chemistry and coordination behavior of the phytochlorin system, and specific substituent pattern. They achieve their full potential in solar energy conversion by working in concert in highly complex, supramolecular structures such as the reaction centers and light-harvesting complexes of photobiology. The biochemical function of these structures depends on the controlled interplay of structural and functional principles of the apoprotein and pigment cofactors. Chlorophylls and bacteriochlorophylls are optically active molecules with several chiral centers, which are necessary for their natural biological function and the assembly of their supramolecular complexes. However, in many cases the exact role of chromophore stereochemistry in the biological context is unknown. This review gives an overview of chlorophyll research in terms of basic function, biosynthesis and their functional and structural role in photosynthesis. It highlights aspects of chirality and symmetry of chlorophylls to elicit further interest in their role in nature.

Simultaneous determination of bambuterol and its two major metabolites in human plasma by hydrophilic interaction ultra-performance liquid chromatography–tandem mass spectrometry

In this study, a rapid and sensitive hydrophilic interaction ultra-performance liquid chromatography-tandem mass spectrometry (HILIC-UPLC-MS/MS) method was developed for simultaneous determination of bambuterol and its two major metabolites monocarbamate bambuterol and terbutaline in human plasma. All samples were simply precipitated using acetonitrile and separated on a UPLC-HILIC column under gradient elution with a mobile phase consisting of acetonitrile and water with the addition of 10mm ammonium acetate and 0.1% formic acid at 0.4 mL/min. The analytes were detected by a Xevo TQ-S tandem mass spectrometer with positive electrospray ionization in multiple reaction monitoring mode. The established method was highly sensitive with the lower limit of quantification (LLOQ) of 10.00 pg/mL for each analyte, and the intra- and inter-day precisions were <12.8%. The analytical runtime within 4.0 min per sample made this method suitable for high throughput determination. The validated method was successfully applied to a clinical pharmacokinetic study of bambuterol in eight healthy volunteers. Furthermore, the effects of the chromatographic conditions on the retention of the analytes on HILIC were investigated, and the benefits of HILIC were evaluated by comparing with a C18 column. The results indicated that liquid-liquid partition and the electrostatic interactions played an important role in the retention of the analytes on HILIC in this study. And HILIC offered particular advantages over RPLC approach in the aspects of the peak symmetry, the column efficiency, and the column pressure.

Log Hodge Theoretic Formulation of Mirror Symmetry for Calabi–Yau Threefolds

We hope to understand the Hodge theoretic aspect of mirror symmetry in the framework of the fundamental diagram of log mixed Hodge theory. We give a formulation of mirror conjecture for Calabi–Yau threefolds as the coincidence of log period maps with specified sections under the mirror map. Since a variation of Hodge structure with unipotent monodromies on a product of punctured discs uniquely extends over the puncture to a log Hodge structure, we can work on the boundary point over which the log Riemann–Hilbert correspondence exists, and we can observe clearly in high resolution the behavior of Z-structure over the boundary point (cf. notes in Introduction below). This is an advantage of log Hodge theory.

Topological phase transitions in the vibration–rotation dynamics of an isolated molecule

One of the characteristic features of rotation–vibration dynamics is the existence of a variety of energy bands which result from organization of energy levels into bands depending on control parameters. Symmetry and topology aspects of the organization of energy bands and generic modifications of this structure for molecular systems with symmetry are discussed in a way parallel to the description of topological quantum transitions extensively studied in condensed matter physics. A special class of axially symmetric molecular systems is analyzed. It is shown that only a finite number of different band structures are possible for rotation–vibration problem with a finite number of vibrational states in the case of continuous axial symmetry, whereas for problems with finite group symmetry an arbitrary large number of different band structures are formally allowed.

Analysis of low symmetry aspects revealed by the zero-field splitting parameters and the crystal field parameters for Cr3+ ions doped into yttrium aluminum borate YAl3(BO3)4 crystal

Structural modeling has been carried out for Cr3+ centers in YAl3(BO3), YAB, single crystal, which is a potential laser host material. Superposition model (SPM) analysis is applied to predict the zero-field splitting parameters (ZFSPs) the as well as the crystal field parameters (CFPs) for Cr3+ ions located at possible cation sites in YAB. Our analysis of the crystal structure data and the available EPR spectra has revealed considerable low symmetry features. These findings indicate an approximated nature of the previous interpretation of EPR spectra and necessitate their reconsideration taking into account low symmetry aspects. The theoretically predicted ZFSPs and CFPs corroborate the significance of low symmetry aspects. Comparison of the theoretical and experimental ZFSP values obtained from EPR measurements enables analysis of the structural distortions at the Y3+ and Al3+ sites. It is shown that the ZFSPs of the six-coordinated Cr3+ centers are well described by a structural model for the Y3+ and Al3+ sites based on the angular distortions of the surrounding oxygens. The results obtained from our SPM analysis support the earlier finding that Cr3+ ions substitute for Al3+ ions in YAl3(BO3). The predicted ZFSPs and CFPs may be useful in future studies aimed at technological applications of the Huntite-type borates with the formula RM3(BO3)4.

Interplay of Rashba/Dresselhaus spin splittings probed by photogalvanic spectroscopy –A review

The paper reviews the interplay of Rashba/Dresselhaus spin splittings in various two‐dimensional systems made of zinc‐blende III–V, wurtzite, and SiGe semiconductors. We discuss the symmetry aspects of the linear and cubic in electron wavevector spin splitting in heterostructures prepared on (001)‐, (110)‐, (111)‐, (113)‐, (112)‐, and (013)‐ oriented substrates and address the requirements for suppression of spin relaxation and realization of the persistent spin helix state. In experimental part of the paper, we overview experimental results on the interplay of Rashba/Dresselhaus spin splittings probed by photogalvanic spectroscopy: The method based on the phenomenological equivalence of the linear‐in‐wavevector spin splitting and several photogalvanic phenomena.