Mesons and diquarks in a color superconducting regime

The behavior of the mesons and diquarks is studied at finite temperatures, chemical potentials and densities, notably when the color superconductivity is taken into account. The Nambu and Jona-Lasinio model complemented by a Polyakov loop (PNJL description) has been adapted in order to model them in this regime. This paper focuses on the scalar and pseudoscalar mesons and diquarks, in a three-flavor and three-color description, with the isospin symmetry and at zero strange density. An objective of this work is to underline the modifications carried out by the color superconducting regime on the used equations and on the obtained results. It has been observed that the two-flavor color-superconducting (2SC) phase affects the masses and the coupling constants of the mesons and diquarks in a non-negligible way. This observation is particularly true at high densities and low temperatures for the pions, [Formula: see text] and the diquarks [Formula: see text] whose color is [Formula: see text]. This reveals that the inclusion of the color superconductivity in the modeling is relevant to describe the mesons and diquarks near the first-order chiral phase transition.

On the density of certain spectral points for a class of $ C^{2} $ quasiperiodic Schrödinger cocycles

<p style='text-indent:20px;'>For <inline-formula><tex-math id="M2">\begin{document}$ C^2 $\end{document}</tex-math></inline-formula> cos-type potentials, large coupling constants, and fixed <inline-formula><tex-math id="M3">\begin{document}$ Diophantine $\end{document}</tex-math></inline-formula> frequency, we show that the density of the spectral points associated with the Schrödinger operator is larger than 0. In other words, for every fixed spectral point <inline-formula><tex-math id="M4">\begin{document}$ E $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M5">\begin{document}$ \liminf\limits_{\epsilon\to 0}\frac{|(E-\epsilon,E+\epsilon)\bigcap\Sigma_{\alpha,\lambda\upsilon}|}{2\epsilon} = \beta $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$ \beta\in [\frac{1}{2},1] $\end{document}</tex-math></inline-formula>. Our approach is a further improvement on the papers [<xref ref-type="bibr" rid="b15">15</xref>] and [<xref ref-type="bibr" rid="b17">17</xref>].</p>

Beta functions in the quantum field theory

Introduction/purpose: The running of the coupling constant in various Quantum Field Theories and a possible behaviour of the beta function are illustrated. Methods: The Callan-Symanzik equation is used for the study of the beta function evolution. Results: Different behaviours of the coupling constant for high energies are observed for different theories. The phenomenon of asymptotic freedom is of particular interest. Conclusions: Quantum Electrodynamics (QED) and Quantum Chromodinamics (QCD) coupling constants have completely different behaviours in the regime of high energies. While the first one diverges for finite energies, the latter one tends to zero as energy increases. This QCD phenomenon is called asymptotic freedom.

Structural analysis of dexrazoxane: Exploring tautomeric conformations

Structural analysis of dexrazoxane, as a cardioprotective agent, was done in this work by exploring formations of tautomeric conformations and investigating the corresponding effects. Density functional theory (DFT) calculations were performed to optimize the structures to evaluate their molecular and atomic descriptors. In addition to the original structure of dexrazoxane, eight tautomers were obtained with lower stability than the original compound. Movements of two hydrogen atoms in between nitrogen and oxygen atoms of heterocyclic ring put such significant effects. Moreover, electronic molecular orbital features showed effects of such tautomerism processes on distribution patterns and surfaces, in which evaluating the quadrupole coupling constants helped to show the role of atomic sites for resulting the features. As a consequence, the results indicated that the tautomeric formations could significantly change the features of dexrazoxane reminding the importance of carful medication of this drug for patients.

OPTIMIZED QUASIPARTICLE DENSITY FUNCTIONAL AND GREEN’S FUNCTIONS METHOD TO COMPUTING BOND ENERGIES OF DIATOMIC MOLECULES

It is presented an advanced approach to computing the energy and spectral parameters of the diatomic molecules, which is based on the hybrid combined density functional theory (DFT) and the Green’s-functions (GF) approach. The Fermi-liquid quasiparticle version of the density functional theory is modified and used. The density of states, which describe the vibrational structure in photoelectron spectra, is defined with the use of combined DFT-GF approach and is well approximated by using only the first order coupling constants in the optimized one-quasiparticle approximation. Using the combined DFT-GF approach to computing the spectroscopic factors of diatomic molecules leads to significant simplification of the calculation procedure and increasing an accuracy of theoretical prediction. As illustration, the results of computing the bond energies in a number of known diatomic molecules are presented and compared with alternative theoretical results, obtained within discrete-variational , muffin-tin orbitals and other methods.

INSIGHTS ON COMPETITION FROM A SCIENCE-BASED ANALYSIS

The work presented here uses a science-based approach to obtain new understandings on the mechanisms and the ramifications of competition in everyday life. Assuming competition of a Darwinian nature we can deduce an S-shaped pattern for growth in most competitive environments. Examples range from a rabbit population growing in a fenced-off grass field to scientists competing for Nobel-Prize awards. There are secrets embedded in the mathematical law that describes growth in competition. The rate of growth being proportional to the amount of growth already achieved makes beginnings difficult and sheds light on such proverbial wisdom as “you need goal to make gold”. It also argues for the necessity to engage teachers in the learning process. Other revelations are linked to the symmetry of a life-cycle pattern, which possesses predictive power and demystifies the easy-come-easy-go phenomenon. Predictive power characterizes the rapid-growth phase of the S-shaped pattern (rheostasis) as well as the end of the pattern when growth reaches a ceiling (homeostasis) where supply and demand are in equilibrium. The latter phenomenon is best exemplified by society’s tolerance of deadly car accidents because deaths from car accidents have remained at an invariant level for many decades reflecting equilibrium. The mathematical equation for growth in competition when cast in discrete form reveals fluctuations of chaotic nature before and after the rapid-growth phase. This can illuminate the turbulent times before and after the formation of the USSR as well as the tumultuous times of the 1930s in America. Extending the quantitative approach to two species competing in the same niche involves introducing coupling constants that account for how one species impacts the growth rate of the other. A celebrated example is the predator-prey relationship, which is only one of six possible interactions all of which can be encountered in the marketplace where products and companies compete like species. There are six possible dimensions for action in a two-species competitive struggle that can be exploited toward managing competition and setting one’s role/image in the marketplace. An example dealt in detail is the evolution of the number of American Noble-Prize winners whose numbers are not about to begin diminishing. Americans are involved in a win-win competitive struggle with non-American scholars, but Americans are drawing more of a benefit.

Magnetic Exchange Interactions in Binuclear and Tetranuclear Iron (III) Complexes Described by Spin-Flip DFT and Heisenberg Effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by the Heisenberg Hamiltonian. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For the series of binuclear complexes with J-values ranging from -6 to -132 cm−1 , our benchmark calculations using the short-range hybrid LRC-ωPBEh functional and 6-31G(d,p) basis set agree well (mean absolute error of 4.7 cm−1) with the experimentally derived values. For the tetranuclear SMMs, the computed J constants are within 6 cm−1 from the values extracted from the experiment. We explore the range of applicability of the Heisenberg model by analyzing the radical character in the binuclear iron (III) complexes using natural orbitals (NO) and their occupations. On the basis of the number of effectively unpaired electrons and the NO occupancies, we attribute larger errors observed in strongly anti-ferromagnetic species to an increased ionic character. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.

Magnetic Exchange Interactions in Binuclear and Tetranuclear Iron (III) Complexes Described by Spin-Flip DFT and Heisenberg Effective Hamiltonians

Low-energy spectra of single-molecule magnets (SMMs) are often described by the Heisenberg Hamiltonian. Within this formalism, exchange interactions between magnetic centers determine the ground-state multiplicity and energy separation between the ground and excited states. In this contribution, we extract exchange coupling constants (J) for a set of iron (III) binuclear and tetranuclear complexes from all-electron calculations using non-collinear spin-flip time-dependent density functional theory (NC-SF-TDDFT). For the series of binuclear complexes with J-values ranging from -6 to -132 cm−1 , our benchmark calculations using the short-range hybrid LRC-ωPBEh functional and 6-31G(d,p) basis set agree well (mean absolute error of 4.7 cm−1) with the experimentally derived values. For the tetranuclear SMMs, the computed J constants are within 6 cm−1 from the values extracted from the experiment. We explore the range of applicability of the Heisenberg model by analyzing the radical character in the binuclear iron (III) complexes using natural orbitals (NO) and their occupations. On the basis of the number of effectively unpaired electrons and the NO occupancies, we attribute larger errors observed in strongly anti-ferromagnetic species to an increased ionic character. The results illustrate the efficiency of the spin-flip protocol for computing the exchange couplings and the utility of the NO analysis in assessing the validity of effective spin Hamiltonians.