Application of semiclassical collision theory to the collinear reactive H+H2 system

Semiclassical collision theory using the stationary-phase method and the near classical method was applied to the collinear H+H₂ system, in the (total) energy range E = 12·5-30 kcal/mole. It was found that although the near classical method was applicable in the near-threshold energy range of E = 13-17 kcal/mole, and both methods gave qualitatively correct results for E > 17 kcal/mole, yet there was no good quantitative agreement with the exact results.     

Resonances and chaos in the collinear collision system (He,H 2 + ) and its isotopic variants

The collinear atom-diatom collision system provides one of the simplest instances of chaotic or irregular scattering. Classically, irregular scattering is manifest in the sensitive dependence of post-collision variables on initial conditions, and quantally, in the appearance of a dense spectrum of dynamical resonances. We examine the influence of kinematic factors on such dynamical resonances in collinear (He, H ₂ ⁺ ) collisions by computing the transition state spectra for collinear (He, HD⁺) and (He, DH⁺) collisions using the time-dependent quantum mechanical approach. The nearest neighbor spacing distributionP(s) and the spectral rigidity Δ₃(L) for these resonances suggest that the dynamics is predominantlyirregular for collinear (He, HD⁺) and predominantlyregular for collinear (He, DH⁺). These findings are reinforced by a significantly larger “correlation hole” in ensemble averaged survival probability ≪P(t)≫ values for collinear (He, HD⁺) than for collinear (He,DH⁺). In addition we have also examined measures of classical chaos through the dependence of the final vibrational action,n _f, on the initial vibrational phaseφ _i of the diatom, and Poincaré surfaces-of-section. They show that (He, HD⁺) collisions are partly chaotic over the entire energy range (0–2.78 eV) while (He, DH⁺) collisions, in contrast, are highly regular at collision energies below the classical threshold for reaction. Above the threshold, the scattering remains regular for initial vibrational statesv=0 and 1 of DH⁺.     

Electronic structures of ternary iron arsenides AFe2As2 (A = Ba, Ca, or Sr)

We have studied the electronic and magnetic structures of the ternary iron arsenides AFe₂As₂ (A = Ba, Ca, or Sr) using the first-principles density functional theory. The ground states of these compounds are in a collinear antiferromagnetic order, resulting from the interplay between the nearest and the next-nearest neighbor superexchange antiferromagnetic interactions bridged by As 4p orbitals. The correction from the spin-orbit interaction to the electronic band structure is given. The pressure can reduce dramatically the magnetic moment and diminish the collinear antiferromagnetic order. Based on the calculations, we propose that the low energy dynamics of these materials can be described effectively by a t-J _H -J ₁-J ₂-type model [2008, arXiv: 0806.3526v2].     

Calculation of the Combination Scattering Spectrum of the H2O Molecule Based on the Effective Polarizability Operator

This paper presents a procedure for calculation of the combination scattering spectrum of a nonlinear molecule of the X₂Y type which is based on a transformed polarizability operator taking into account the vibration-rotation interaction in the molecule to within the second order of the perturbation theory. The matrix elements of the operator are determined and classified by molecule symmetry type. The combination scattering spectrum of the H₂O molecule is calculated in the region of the 2v ₂ band. The second derivative of the average polarizability of the H₂O molecule with respect to the normal coordinate q ₂, associated with deformation vibrations, and the vibrational dependence of the average polarizability of the H₂O molecule on the deformation quantum number v ₂ are estimated.     

Zero Temperature Phases of the Frustrated <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Antiferromagnetic Spin-1/2 Heisenberg Model on a Simple Cubic Lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J ₁ and J ₂) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Néel phase for small J ₂ (AF), and a collinear antiferromagnetic phase at large J ₂ (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, p _c =0.56 or J ₂/J ₁=0.28. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.     

On the application of group theory to spinwaves in collinear magnetic structures

The application of group theory to spinwaves in collinear magnetic structures is discussed in close analogy with similar applications made in the case of lattice vibrations. Some of the basic features pertaining to magnetic space groups are first recalled and the spinwave equations for collinear magnetic systems are set up. The details of applying group theory are then described using the multiplier-representation approach, and finally the methodology is illustrated by working through in detail the classification of spinwaves in Fe₃O₄. The relationship of the present results to those given earlier by Brinkman and Elliott for the same crystal is also pointed out.     

Exchange interactions in BaFe12O19

In the scope of the mean field approximation the nine nearest neighbour exchange interactions existing among the ferric ions in BaFe₁₂O₁₉ hexagonal ferrite have been determined from the experimental sublattice magnetizations. It is shown that these exchange interactions are well explained by means of the superexchange theory. It is also concluded that some direct exchange interaction does exist among the octahedral 4f _VI ions. The calculated magnetization, paramagnetic susceptibility, and Curie temperature are in good agreement with the corresponding experimental values. The stability of the collinear Gorter-type magnetic structure of BaFe₁₂O₁₉ is discussed as well.     

Nuclear magnetic resonance of 55Mn in the antiferromagnet CsMnBr3 in a variable longitudinal magnetic field

The spectrum and intensities of NMR lines are investigated experimentally and theoretically for excitation by an alternating magnetic field h‖ parallel to a static field H in the quasi-one-dimensional, six-sublattice antiferromagnet CsMnBr₃. According to theory, two new NMR lines, which are not excited by a transverse magnetic field h _⊥, are observed near the phase transition from triangular to collinear structure (H=H _c ) [JETP 86, 197 (1998)]. Zh. éksp. Teor. Fiz. 115, 2228–2241 (June 1999)     

Isomerization of C3H3NO isomers: ab initio study

The structures and isomerization process of C₃H₃NO species have been explored at the MP2/6–311++G(d,p) level of theory of the ab initio method. Eleven minima and four interconversion transition states have been identified. The zero-point vibrational energy corrections were made to predict reliable energies. We predict a five-membered ring-like structure to be the lowest energy isomer, which is 177.73?kcal?mol^?1 more stable than the least stable isomer X found on the potential energy surface. The transition states and minima isomers were verified by frequency calculation. Intrinsic reaction coordinate (IRC) calculations have been performed to confirm that each transition state is linked by the desired reactants and products. The isomer stabilities have been studied using the relative energies, chemical hardness and chemical potential. The MHP principle could not predict the order of stability for C₃H₃NO isomers as arrived at with the relative energies. The role of intramolecular hydrogen bonds on the equilibrium structure has been discussed. The energy barrier and reaction enthalpy have been calculated during isomerization.     

Third order nonlinear optical difference frequency generation in KH2PO4, TiO2, LiNbO3, CaCO3, ZnO and CdS

Third-order nonlinear optical susceptibilities of different crystals have been measured relative to LiNbO₃ by observing collinear phase-matched difference frequency generation ₁=2 ₂– ₄. The two incident light waves have been produced by a ruby laser ( ₂, ₂=694.3 nm) and by induced Raman scattering ( ₄, ₄=765.8 nm). With noncollinear phase-matching the number of nonlinear processes and the possibilities to determine nonlinear coefficients is much larger than in the collinear case. Therefore the theory of Raman-type third order interactions has been extended to noncollinear propagation of the interacting waves. The theory has been tested experimentally for CdS.     

Factorization and infrared properties of non-perturbative contributions to DIS structure functions

In this paper we present a new derivation of QCD factorization. We deduce the k _T and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-perturbative contributions and attributing them to the different blobs. After that the convolutions correspond to QCD factorization. Then we reduce this totally unintegrated (basic) factorization first to k _T -factorization and finally to collinear factorization. In order to yield a finite expression for the Compton amplitude, the integration over the loop momentum in the basic factorization must be free of both ultraviolet and infrared singularities. This obvious mathematical requirement leads to theoretical restrictions on the non-perturbative contributions (parton distributions) to the Compton amplitude and the DIS structure functions related to the Compton amplitude through the Optical Theorem. In particular, our analysis excludes the use of the singular factors x ^−a (with a>0) in the fits for the quark and gluon distributions because such factors contradict the integrability of the basic convolutions for the Compton amplitude. This restriction is valid for all DIS structure functions in the framework of both k _T -factorization and collinear factorization if we attribute the perturbative contributions only to the upper blob. The restrictions on the non-perturbative contributions obtained in the present paper can easily be extended to other QCD processes where the factorization is exploited.     

Anharmonic force fields of cis- and trans-S1 C2H2

We calculate second-order vibrational perturbation theory (VPT2) anharmonic force fields for the cis and trans conformers of S₁ C₂H₂, and compare the results to experiment. The vibrational assignments of recently observed levels belonging to the cis well are of particular interest. A refined estimate of the cis origin position (44,870?±?10?cm^?1) is proposed, and preliminary low-energy fits to the global J?=?K?=?0 trans level structure are also described. The performance of perturbation theory in this isomerizing system is examined, and both surprising successes and failures are encountered. We examine these and their causes, and offer practical suggestions for avoiding the pitfalls of applying perturbation theory to systems with large amplitude motions.     

Photoinduced changes in the space-modulated magnetic order of a FeBO<Subscript>3</Subscript>:Mg single crystal

An effect of nonpolarized white light on the modulated magnetic structure of a FeBO₃:Mg single crystal, which arises in this light-plane weak ferromagnet in the low temperature range during technical magnetization, has been revealed. It has been found that the degree of the light action on the magnetic state of FeBO₃:Mg depends both on its duration and on the orientation of the spontaneous magnetization vector M of the crystal during illumination. Interpretation of the results obtained has been performed in the context of the “magnetic ripple” theory on the assumption that the absorbed light induces additional uniaxial magnetic anisotropy in the easy plane of the crystal and that the anisotropy axis is collinear to the vector M during illumination.     

Antiferromagnetic resonance in NaCrS2

Antiferromagnetic resonance measurements in rhombohedral NaCrS₂ (T_N = 17 K) are reported. The data are compared with theory developed by Battles for a collinear easy-plane antiferromagnet with anisotropy in the basal plane. While there is reasonable agreement with this theory, some discrepancies occur. These are presumably related to low-temperature in-plane distortions from hexagonal symmetry, previously postulated by other workers.     

Constraints for anomalous dimensions of local light-cone operators in [ϕ 3]6 theory

Using the MS scheme, we derive in [? ³]₆ theory the collinear conformal Ward identity for the Green's functions of local light-cone operators of leading twist. The Ward identity for special collinear conformal transformations and renormalization group invariance give constraints for the off-diagonal part of the anomalous dimension matrix for the general case of β#0. We compute the anomaly of special conformal transformation in lowest loop order and obtain from the constraints the off-diagonal part of the anomalous dimension in 2-loop order.     

厄米多项式算符的新恒等式及其在量子压缩中的应用

通过发现有关厄米多项式算符H_n(X)的恒等式, 并结合有序算符内的积分技术, 得到了一些关于量子压缩的算符新恒等式, 这对于研究压缩粒子数态波函数十分有用.     

Relationship between crystalline order and melting mechanisms of solids

The mechanism for homogeneous nucleation of the liquid phase in Lennard-Jones solids is studied by combining the Landau free energy approach with some of the methodology developed to characterise transition path ensembles. The second-order bond orientational order parameter, Q ₆ which indexes the overall degree of crystalline order, is shown to provide a dynamically significant collective coordinate describing the melting process. Trajectories generated from configurations sampled in the vicinity of the maximum in the Landau free energy curve, F(Q ₆), are shown to have equal likelihood of teminating in either the solid or liquid-like free energy minima. It is also demonstrated that Q ₆ is necessary but not sufficient as a dynamical coordinate to describe melting and it is necessary to explore possiblities for additional coordinates which are critical for initiating melting. Our sudy suggests that the additional coordinates for describing the melting process would be some type of localised defect, much smaller in spatial extent than the size of the critical nucleus predicted by classical nucleation theory.      

Between general relativity and quantum theory

Some possibilities of reconciling general relativity with quantum theory are discussed. The procedure of quantization is certainly not unique, but depends upon the choice of the coordinate conditions. Most versions of quantization predict the existence of gravitons, but it is also possible to formulate a quantum theory with a classical gravity whereby the expectation values ofT _µv constitute the sources of the classical metric field.     

Non-adiabatic potentials for H2 +

In principle exact non-adiabatic pseudo-potentials for H₂ ⁺ and D₂ ⁺ are formulated in terms of the theory of conditional probability amplitudes in wave mechanics. Numerical results for the v = 0 and v = 1 (J = 0) states of H₂ ⁺ are derived from previously computed accurate non-adiabatic wave-functions. These results indicate that the non-adiabatic pseudo-potentials only differ from the adiabatic potential by small energies of the same magnitude as the non-adiabatic corrections to the adiabatic energy levels.     

Drell–Yan production at small qT, transverse parton distributions and the collinear anomaly

Using methods from effective field theory, an exact all-order expression for the Drell–Yan cross section at small transverse momentum is derived directly in q _T space, in which all large logarithms are resummed. The anomalous dimensions and matching coefficients necessary for resummation at NNLL order are given explicitly. The precise relation between our result and the Collins–Soper–Sterman formula is discussed, and as a by-product the previously unknown three-loop coefficient A ⁽³⁾ is obtained. The naive factorization of the cross section at small transverse momentum is broken by a collinear anomaly, which prevents a process-independent definition of x _T -dependent parton distribution functions. A factorization theorem is derived for the product of two such functions, in which the dependence on the hard momentum transfer is separated out. The remainder factors into a product of two functions of longitudinal momentum variables and x_T²x_{T}^{2}, whose renormalization-group evolution is derived and solved in closed form. The matching of these functions at small x _T onto standard parton distributions is calculated at O(a_s)\mathcal{O}(\alpha_{s}), while their anomalous dimensions are known to three loops.