Franck–Condon Factors and r‐Centroids for the B–, C–, F–, and G–X Band Systems of YF Molecule

The Franck–Condon factors and r‐centroids, which are very closely related to relative transition probabilities, have been evaluated by a more reliable numerical integration procedure for the B¹π–X¹Σ⁺, C¹Σ⁺–X¹Σ⁺, F¹Σ⁺–X¹Σ⁺, and G¹π–X¹Σ⁺ band systems of the YF molecule, using suitable potentials.     

Atomic structure of the Zr–He,Zr–vac,and Zr–vac–He systems: First-principles calculation

The ab initio investigations have been performed for the atomic structure of the Zr–He, Zr–vac, and Zr–vac–He systems with concentrations of helium atoms and vacancies (vac) of ~6 at %. A heliuminduced instability of the zirconia lattice has been revealed in the Zr–He system, which disappears with the formation of vacancies. The most preferred positions of impurities in the metal lattice have been determined. The energy of helium dissolution and the excess volume introduced by helium have been calculated. It has been established that the presence of helium in the Zr lattice leads to a significant decrease in the energy of vacancy formation.     

Evolution of phase,texture, microstructure and magnetic properties of Fe–Cr–Co–Mo–Ti permanent magnets

Magnetic phase evolution, crystallographic texture, microstructure and magnetic properties of Fe–28Cr–15Co–3.5Mo–1.8Ti alloy have been investigated by X-ray diffractometry, scanning transmission electron microscopy and magnetometry techniques as a function of processing conditions. Heat treatment conditions for obtaining optimum textural, microstructural and magnetic properties have been established by the experimentations. The Goss {110}〈001〉 and cube type {001}〈010〉 textures have been developed in an optimal treated Fe–28Cr–15Co–3.5Mo–1.8Ti magnets. The coercive force in Fe–28Cr–15Co–3.5Mo–1.8Ti magnets depends critically on the shape anisotropy of rod-like Fe Co Ti-rich α₁ particles and remanence on the alignment and elongation of α₁ particles parallel to applied magnetic field 〈100〉 directions. The optimum magnetic properties obtained in Fe–28Cr–15Co–3.5Mo–1.8Ti alloy are intrinsic coercive force, _iH_c, of 78.8 kA/m (990 Oe), remanence, B_r of 1.12 T (11.2 kG) and energy product, (BH)_max of 52.5 kJ/m³ (6.5 MGOe). The development of Fe–28Cr–15Co–3.5Mo–1.8Ti magnets as well as characterization of texture, microstructural and magnetic properties in the current study would be helpful in designing the new Fe–Cr–Co–Mo based magnets suitable for scientific and technological applications.     

Hume-Rothery electron concentration rule across a whole solid solution range in a series of gamma-brasses in Cu–Zn,Cu–Cd,Cu–Al,Cu–Ga,Ni–Zn and Co–Zn alloy systems

The aim of the present work is to examine if the Hume-Rothery stabilisation mechanism holds across whole solid solution ranges in a series of gamma-brasses with especial attention to the role of vacancies introduced into the large unit cell. The concentration dependence of the number of atoms in the unit cell, N, for gamma-brasses in the Cu–Zn, Cu–Cd, Cu–Al, Cu–Ga, Ni–Zn and Co–Zn alloy systems was determined by measuring the density and lattice constants at room temperature. The number of itinerant electrons in the unit cell, e/uc, is evaluated by taking a product of N and the number of itinerant electrons per atom, e/a, for the transition metal element deduced earlier from the full-potential linearised augmented plane wave (FLAPW)-Fourier analysis. The results are discussed within the rigid-band model using as a host the density of states (DOS) derived earlier from the FLAPW band calculations for the stoichiometric gamma-brasses Cu₅Zn₈, Cu₉Al₄ and TM₂Zn₁₁ (TM = Co and Ni). A solid solution range of gamma-brasses in Cu–Zn, Cu–Cd, Cu–Al, Cu–Ga and Ni–Zn alloy systems is found to fall inside the existing pseudogap at the Fermi level. This is taken as confirmation of the validity of the Hume-Rothery stability mechanism for a whole solute concentration range of these gamma-brasses. An exception to this behaviour was found in the Co–Zn gamma-brasses, where orbital hybridisation effects are claimed to play a crucial role in stabilisation.     

Einstein–Podolski–Rosen paradox,non-commuting operator,complete wavefunction and entanglement

Einstein, Podolski and Rosen (EPR) have shown that any wavefunction (subject to the Schrödinger equation) can describe the physical reality completely, and any two observables associated with two non-commuting operators can have simultaneous reality. In contrast, quantum theory claims that the wavefunction can capture the physical reality completely, and the physical quantities associated with two non-commuting operators cannot have simultaneous reality. The above contradiction is known as the EPR paradox. Here, we unambiguously expose that there is a hidden assumption made by EPR, which gives rise to this famous paradox. Putting the assumption right this time leads us not to the paradox, but only reinforces the correctness of the quantum theory. However, it is shown here that the entanglement phenomenon between two physically separated particles (they were entangled prior to separation) can only be proven to exist with a ‘proper’ measurement.     

Structure,thermal behavior,and chemical durability of lead–calcium–phosphate glasses

ABSTRACT

Structure and physical properties of 25CaO–xPbO–(75–x)P₂O₅ (0≤x≤35) glasses are investigated in this paper. Substitution of PbO for P₂O₅ in the binary 25CaO–75P₂O₅ glass was found to increase the density and to decrease the molar volume. Fourier transform infrared (FTIR) and Raman spectroscopies show the evolution of the phosphate skeleton when the PbO content increases: Q³ to Q² species (0<x≤25) and Q² phosphate network (x = 25) to short phosphate groups (x > 25) such as (P₄O₁₃^6?) (x = 35). The glass transition temperature first decreases with x, then increases for x values larger than 10%. The evolution of the glass transition temperatures is interpreted from the structural data: the minimum point observed in T_g is attributed to the transition of the ultraphosphate network from the network containing the modifying cations at isolated sites to a network with modifier sub-structure sharing terminal oxygens. At higher PbO content, the large increase in T_g is due to the reticulation of the phosphate network by PbO₄ groups.     

ICEMS study of isothermal oxidation of Fe–Mn–Al–C–Cr–Si–Mo, Fe–Mn–Al–C–Cr–Si and Fe–9Cr–1Mo alloys

The purpose of this paper is to investigate the isothermal behavior of Fe–27.3Mn–7.6Al–C–6.5Cr–0.25Si–0.88Mo (Mo(0)) and Fe–27.3Mn–7.6Al–1.0C–6.5Cr–0.25Si (Mo(1)) alloys and compare it against Fe–9Cr–1Mo (FCR) commercial alloy. The experiments were carried out at 600°C, 700°C, 750°C and 850°C, each one during 72 h in static air. The oxidation kinetics was measured as a function of time using a Thermogravimetry analyzer (TGA). The structure and composition of the oxide scale were characterized by X-ray diffraction (XRD) and Integral Conversion Electron Mössbauer Spectroscopy (CEMS). The TGA results show that at all oxidation temperatures the sample FCR exhibit the lowest kinetic corrosion and the lowest weight gain, whereas Mo(0) the highest. By CEMS technique it were found a broad magnetic sextet, which has been fit by one hyperfine field distribution with mean hyperfine field characteristic to ferritic/martensite phase, one Fe^3?+? doublet and one singlet for the Mo(0) and Mo(1) alloys. Samples oxidized at highest temperatures exhibit a strong paramagnetic line, probably due that the Cr or Mn oxides may be enriched on the surface. Then, the magnetic phase can be converted partially into austenite phase at highest temperatures.     

Rotational Spectra of CH3CCH–NH3, NCCCH–NH3, and NCCCH–OH2

Microwave spectra of NCCCH–NH₃, CH₃CCH–NH₃, and NCCCH–OH₂have been recorded using a pulsed-nozzle Fourier-transform microwave spectrometer. The complexes NCCCH–NH₃and CH₃CCH–NH₃are found to have symmetric-top structures with the acetylenic proton hydrogen bonded to the nitrogen of the NH₃. The data for CH₃CCH–NH₃are further consistent with free or nearly free internal rotation of the methyl top against the ammonia top. For NCCCH–OH₂, the acetylenic proton is hydrogen bonded to the oxygen of the water. The complex has a dynamicalC_2vstructure, as evidenced by the presence of two nuclear-spin modifications of the complex. The hydrogen bond lengths and hydrogen-bond stretching force constants are 2.212 Å and 10.8 N/m, 2.322 Å and 6.0 N/m, and 2.125 Å and 9.6 N/m for NCCCH–NH₃, CH₃CCH–NH₃, and NCCCH–OH₂, respectively. For the cyanoacetylene complexes, these bond lengths and force constants lie between the values for the related hydrogen cyanide and acetylene complexes of NH₃and H₂O. The NH₃bending and weak-bond stretching force constants for CH₃CCH–NH₃are less than those found in NCCCH–NH₃, NCH–NH₃, and HCCH–NH₃, suggesting that the hydrogen bonding interaction is particularly weak in CH₃CCH–NH₃. The weakness of this hydrogen bond is partially a consequence of the orientation of the monomer electric dipole moments in the complex. In CH₃CCH–NH₃the antialigned monomer dipole moments lead to a repulsive dipole–dipole interaction energy, while in NCH–NH₃and NCCCH–NH₃the aligned dipoles give an attraction interaction.     

Hitchin–Kobayashi Correspondence, Quivers, and Vortices

 A twisted quiver bundle is a set of holomorphic vector bundles over a complex manifold, labelled by the vertices of a quiver, linked by a set of morphisms twisted by a fixed collection of holomorphic vector bundles, labelled by the arrows. When the manifold is K?hler, quiver bundles admit natural gauge-theoretic equations, which unify many known equations for bundles with extra structure. In this paper we prove a Hitchin–Kobayashi correspondence for twisted quiver bundles over a compact K?hler manifold, relating the existence of solutions to the gauge equations to a stability criterion, and consider its application to a number of situations related to Higgs bundles and dimensional reductions of the Hermitian–Einstein equations. Received: 10 December 2001 / Accepted: 10 November 2002 Published online: 28 May 2003 RID="⋆" ID="⋆" Current address: Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK. E-mail:L.Alvarez-Consul@maths.bath.ac.uk RID="⋆⋆" ID="⋆⋆" Current address: Instituto de Matemáticas y Física Fundamental, CSIC, Serrano 113 bis, 28006 Madrid, Spain. E-mail:oscar.garcia-prada@uam.es Communicated by R.H. Dijkgraaf     

Born–Infeld–Chern–Simons theory: Hamiltonian embedding,duality and bosonization

In this paper we study in detail the equivalence of the recently introduced Born–Infeld self-dual model to the Abelian Born–Infeld–Chern–Simons model in 2+1 dimensions. We first apply the improved Batalin, Fradkin and Tyutin scheme, to embed the Born–Infeld self-dual model to a gauge system and show that the embedded model is equivalent to Abelian Born–Infeld–Chern–Simons theory. Next, using Buscher's duality procedure, we demonstrate this equivalence in a covariant Lagrangian formulation and also derive the mapping between the n-point correlators of the (dual) field strength in Born–Infeld–Chern–Simons theory and of basic field in Born–Infeld self-dual model. Using this equivalence, the bosonization of a massive Dirac theory with a non-polynomial Thirring type current–current coupling, to leading order in (inverse) fermion mass is also discussed. We also rederive it using a master Lagrangian. Finally, the operator equivalence between the fermionic current and (dual) field strength of Born–Infeld–Chern–Simons theory is deduced at the level of correlators and using this the current–current commutators are obtained.     

Kirillov’s character formula,the holomorphic Peter–Weyl theorem,and the Blattner–Kostant–Sternberg pairing

By means of the orbit method we show that, for a compact Lie group, the Blattner–Kostant–Sternberg pairing map, with the constants being appropriately fixed, is unitary. Along the way we establish a holomorphic Peter–Weyl theorem for the complexification of a compact Lie group. Among our crucial tools is Kirillov’s character formula. The basic observation is that the Weyl vector is lurking behind the Kirillov character formula, as well as behind the requisite half-form correction on which the Blatter–Kostant–Sternberg-pairing for the compact Lie group relies, and thus produces the appropriate shift which, in turn, controls the unitarity of the BKS-pairing map. Our methods are independent of heat kernel harmonic analysis, which is used by B. C. Hall to obtain a number of these results [B.C. Hall, The Segal–Bargmann Coherent State Transform for compact Lie groups, J. Funct. Anal. 122 (1994) 103–151; B.C. Hall, Geometric quantization and the generalized Segal–Bargmann transform for Lie groups of compact type, Comm. Math. Phys. 226 (2002) 233–268, quant.ph/0012015].     

Gauge-theoretic invariants for topological insulators: a bridge between Berry,Wess–Zumino,and Fu–Kane–Mele

We establish a connection between two recently proposed approaches to the understanding of the geometric origin of the Fu–Kane–Mele invariant \(\mathrm {FKM}\in \mathbb {Z}_2\), arising in the context of two-dimensional time-reversal symmetric topological insulators. On the one hand, the \(\mathbb {Z}_2\) invariant can be formulated in terms of the Berry connection and the Berry curvature of the Bloch bundle of occupied states over the Brillouin torus. On the other, using techniques from the theory of bundle gerbes, it is possible to provide an expression for \(\mathrm {FKM}\) containing the square root of the Wess–Zumino amplitude for a certain U(N)-valued field over the Brillouin torus. We link the two formulas by showing directly the equality between the above-mentioned Wess–Zumino amplitude and the Berry phase, as well as between their square roots. An essential tool of independent interest is an equivariant version of the adjoint Polyakov–Wiegmann formula for fields \(\mathbb {T}^2 \rightarrow U(N)\), of which we provide a proof employing only basic homotopy theory and circumventing the language of bundle gerbes.     

Two-, three-, and four-bond N–F spin–spin coupling constants in fluoroazines

Ab initio EOM-CCSD calculations have been performed to investigate 2-, 3- and 4-bond ¹⁵N–¹⁹F coupling constants in mono-, di-, and trifluoroazines. ²J(N–F) values are negative and are dominated by the Fermi-contact (FC) term. Absolute values of ²J(N–F) tend to decrease as the number of N atoms in the ring increases, and may also be influenced by the number and positions of C–F bonds. ³J(N–F) values are positive with three exceptions, are usually dominated by the FC term, and also tend to decrease as the number of N atoms increases. The three molecules which have negative values of ³J(N–F) have dominant negative paramagnetic-spin orbit (PSO) terms, and are structurally similar insofar as they have an intervening C–F bond between the N and the coupled F. ⁴J(N–F) values are negative because the PSO, FC, and spin-dipole (SD) terms are negative, with only one exception. Four molecules have significantly greater values of ⁴J(N–F). These are structurally similar with the coupled N bonded to two other N atoms. The computed EOM-CCSD ⁿJ(N–F) coupling constants are in good agreement with the few experimental values that are available.     

Fomenko–Mischenko Theory, Hessenberg Varieties, and Polarizations

The symmetric algebra ${S(\mathfrak{g})}$ over a Lie algebra ${\mathfrak{g}}$ has the structure of a Poisson algebra. Assume ${\mathfrak{g}}$ is complex semisimple. Then results of Fomenko–Mischenko (translation of invariants) and Tarasov construct a polynomial subalgebra ${{\mathcal {H}} = {\mathbb C}[q_1,\ldots,q_b]}$ of ${S(\mathfrak{g})}$ which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of ${\mathfrak{g}}$ . Let G be the adjoint group of ${\mathfrak{g}}$ and let ? = rank ${\mathfrak{g}}$ . Using the Killing form, identify ${\mathfrak{g}}$ with its dual so that any G-orbit O in ${\mathfrak{g}}$ has the structure (KKS) of a symplectic manifold and ${S(\mathfrak{g})}$ can be identified with the affine algebra of ${\mathfrak{g}}$ . An element ${x\in \mathfrak{g}}$ will be called strongly regular if ${\{({\rm d}q_i)_x\},\,i=1,\ldots,b}$ , are linearly independent. Then the set ${\mathfrak{g}^{\rm{sreg}}}$ of all strongly regular elements is Zariski open and dense in ${\mathfrak{g}}$ and also ${\mathfrak{g}^{\rm{sreg}}\subset \mathfrak{g}^{\rm{ reg}}}$ where ${\mathfrak{g}^{\rm{reg}}}$ is the set of all regular elements in ${\mathfrak{g}}$ . A Hessenberg variety is the b-dimensional affine plane in ${\mathfrak{g}}$ , obtained by translating a Borel subalgebra by a suitable principal nilpotent element. Such a variety was introduced in Kostant (Am J Math 85:327–404, 1963). Defining Hess to be a particular Hessenberg variety, Tarasov has shown that ${{\rm{Hess}}\subset \mathfrak{g}^{\rm{sreg}}}$ . Let R be the set of all regular G-orbits in ${\mathfrak{g}}$ . Thus if ${O\in R}$ , then O is a symplectic manifold of dimension 2n where n = b ? ?. For any ${O\in R}$ let ${O^{\rm{sreg}} = \mathfrak{g}^{\rm{sreg}} \cap O}$ . One shows that O ^sreg is Zariski open and dense in O so that O ^sreg is again a symplectic manifold of dimension 2n. For any ${O\in R}$ let ${{\rm{Hess}}(O) = {\rm{Hess}}\cap O}$ . One proves that Hess(O) is a Lagrangian submanifold of O ^sreg and that $${\rm{Hess}} = \sqcup_{O\in R}{\rm{Hess}}(O).$$ The main result of this paper is to show that there exists simultaneously over all ${O\in R}$ , an explicit polarization (i.e., a “fibration” by Lagrangian submanifolds) of O ^sreg which makes O ^sreg simulate, in some sense, the cotangent bundle of Hess(O).     

Proton–proton,anti-proton–anti-proton,proton–anti-proton correlations in Au + Au collisions measured by STAR at RHIC

The analysis of two-particle correlations provides a powerful tool to study the properties of hot and dense matter created in heavy-ion collisions at ultra-relativistic energies. Applied to identical and non-identical hadron pairs, it makes the study of space-time evolution of the source in femtoscopic scale possible. Baryon femtoscopy allows extraction of the radii of produced sources which can be compared to those deduced from identical pion studies, providing complete information about the source characteristics. In this paper we present the correlation functions obtained for identical and non-identical baryon pairs of protons and anti-protons. The data were collected recently in Au+Au collisions at  =62 GeV and  =200 GeV by the STAR detector at the RHIC accelerator. We introduce corrections to the baryon–baryon correlations taking into account: residual correlations from weak decays, particle identification probability and the fraction of primary baryons. Finally we compare our results to theoretical predictions. PACS 25.75.-q; 25.75.Gz     

Chern–Simons,Wess–Zumino and other cocycles from Kashiwara–Vergne and associators

Descent equations play an important role in the theory of characteristic classes and find applications in theoretical physics, e.g., in the Chern–Simons field theory and in the theory of anomalies. The second Chern class (the first Pontrjagin class) is defined as \(p= \langle F, F\rangle \) where F is the curvature 2-form and \(\langle \cdot , \cdot \rangle \) is an invariant scalar product on the corresponding Lie algebra \(\mathfrak g\). The descent for p gives rise to an element \(\omega =\omega _3+\omega _2+\omega _1+\omega _0\) of mixed degree. The 3-form part \(\omega _3\) is the Chern–Simons form. The 2-form part \(\omega _2\) is known as the Wess–Zumino action in physics. The 1-form component \(\omega _1\) is related to the canonical central extension of the loop group LG. In this paper, we give a new interpretation of the low degree components \(\omega _1\) and \(\omega _0\). Our main tool is the universal differential calculus on free Lie algebras due to Kontsevich. We establish a correspondence between solutions of the first Kashiwara–Vergne equation in Lie theory and universal solutions of the descent equation for the second Chern class p. In more detail, we define a 1-cocycle C which maps automorphisms of the free Lie algebra to one forms. A solution of the Kashiwara–Vergne equation F is mapped to \(\omega _1=C(F)\). Furthermore, the component \(\omega _0\) is related to the associator \(\Phi \) corresponding to F. It is surprising that while F and \(\Phi \) satisfy the highly nonlinear twist and pentagon equations, the elements \(\omega _1\) and \(\omega _0\) solve the linear descent equation.     

Frustrated magnetic interactions,giant magneto–elastic coupling,and magnetic phonons in iron–pnictides

We present a detailed first-principles study of Fe-pnictides with particular emphasis on competing magnetic interactions, structural phase transition, giant magneto–elastic coupling and its effect on phonons. The exchange interactions J_i,j(R) are calculated up to ≈12 Å from two different approaches based on direct spin-flip and infinitesimal spin-rotation. We find that J_i,j(R) has an oscillatory character with an envelop decaying as 1/R³ along the stripe-direction while it is very short range along the diagonal direction and antiferromagnetic. A brief discussion of the neutron scattering determination of these exchange constants from a single crystal sample with orthorhombic-twinning is given. The lattice parameter dependence of the exchange constants, dJ_i,j/da are calculated for a simple spin-Peierls like model to explain the fine details of the tetragonal–orthorhombic phase transition. We then discuss giant magneto–elastic effects in these systems. We show that when the Fe-spin is turned off the optimized c-values are shorter than experimental values by 1.4 Å for CaFe₂As₂, by 0.4 Å for BaFe₂As₂, and by 0.13 Å for LaOFeAs. We explain this strange behavior by unraveling surprisingly strong interactions between arsenic ions, the strength of which is controlled by the Fe-spin state through Fe–As hybridization. Reducing the Fe-magnetic moment, weakens the Fe–As bonding, and in turn, increases As–As interactions, causing a giant reduction in the c-axis. These findings also explain why the Fe-moment is so tightly coupled to the As-z position. Finally, we show that Fe-spin is also required to obtain the right phonon energies, in particular As c-polarized and Fe–Fe in-plane modes that have been recently observed by inelastic X-ray and neutron scattering but cannot be explained based on non-magnetic phonon calculations. Since treating iron as magnetic ion always gives much better results than non-magnetic ones and since there is no large c-axis reduction during the normal to superconducting phase transition, the iron magnetic moment should be present in Fe-pnictides at all times. We discuss the implications of our results on the mechanism of superconductivity in these fascinating Fe-pnictide systems.