A metric topology for causally continuous completions

A metric topologyH(¯M) is introduced on the causal completion¯M of a causally continuous space-timeM. This metric topology is at least as coarse as the extended Alexandrov topologyA(¯M) on¯M. In bothH(¯M) andA(¯M), the original space-timeM is an open and dense subset. From the definition ofH(¯M), it follows that the causality on¯M is continuous at boundary points. IfM admits a compact Cauchy surface, thenH(¯M) andA(¯M) are the same.     

Interionic exchange interaction in A 1−x II MxBVI systems

The superexchange interaction integral J _NN is investigated in semimagnetic semiconductors of the type A _1−x ^II M_xB^VI systems, where the Mn, Fe, and Co ions are considered as the magnetic component M. Calculations are done in the framework of Racah’s many particle theory including the ground orbital states of the M ions in a cubic crystal. The results of these calculations are compared with published experimental data and with data from a study of the temperature dependence of Faraday rotation. The superexchange mechanism can be used to explain the correlation in the critical values x* at which the interionic interaction becomes important for the Cd_1−x Mn_xTe and Cd_1−x Fe_xTe systems. Fiz. Tverd. Tela (St. Petersburg) 39, 344–348 (February 1997)     

Ab initio dynamics of the He + H+ 2 → HeH+ +H reaction: a new potential energy surface and quantum mechanical cross-sections

The reaction He + H⁺ ₂(v,j = 0) → HeH⁺(v′ = 0, j′) for v = 0, 1,2 and 3 and for scattering energies near the threshold (0.95–1.15 eV) has been studied by calculating ab initio points at MRCI level and ‘exact’ integral quantum reactive cross-sections. More than 1400 nuclear geometries have been chosen to cover the most important regions for the dynamics, an extended set of points being taken directly on a hyperspherical coordinate grid. A many-body expansion with a large number of terms permits an accurate analytical representation of the potential energy surface with a root-mean-square deviation <12meV. The hyperquantization algorithm has been extended to obtain quantum mechanical integral cross-sections which are compared with previous calculations and with experimental results.     

Coherent State Path Integral for the Harmonic Oscillator and a Spin Particle in a Constant Magnetic field

Definition and formulas for harmonic oscillator coherent states and spin coherent states are reviewed in detail. The path integral formalism and its relation with the partition function of a system are also reviewed. The harmonic oscillator coherent state path integral is evaluated exactly at the discrete level and then used to find its continuum limit using various regularizations. The computation of the path integral for a particle of spin s put in a constant magnetic field is carried out using harmonic oscillator coherent states and spin coherent states, with a careful analysis of infinitesimal terms (in 1/N where N is the number of time slices) appearing in the Lagrangian. A mapping of the spin system into a CP¹ model is shown explicitly. The theory of a spinless particle in the field of a magnetic monopole and its relation with the spin system are explained. The equivalence of these two models is established up to infinitesimal order by the introduction of an external field correction. This gives a new representation of a coherent state path integral in terms of a more familiar Feynman path integral.     

Different time slices for different degrees of freedom in Feynman path integration

A general scheme is presented for using different numbers of ‘time slices’ for different degrees of freedom in a path integral evaluation of the Boltzmann operator for a large molecular system. This will be particularly useful, for example, in evaluating the ‘quantum instanton’ rate constant [cf. W.H. Miller, Y. Zhao, M. Ceotto, S. Yang. J. Chem. Phys., 119, 1329 (2003)] for H atom transfer reactions, or any applications involving atoms with largely differing masses.     

A generalized Hadamard transformation from new entangled state

A new entangled state | eta ;theta rangle is proposed by the technique of integral within an ordered product. A generalized Hadamard transformation is derived by virtue of | eta ;theta rangle , which plays a role of Hadamard transformation for (hat a_1 sin theta - hat a_2 cos theta ) and (hat a_1 cos theta + hat a_2 sin theta ).     

Inverse problems of the nonlinear electrodynamics of high-T c superconductors

A method is developed for reconstructing the dependence of the surface impedance of Z _s (H) of high-T _c superconductors (HTSCs) on the amplitude of an ac magnetic field from measurements of the nonlinear radiophysical characteristics of microwave HTSC resonators. It is shown that the nonuniformity of the structure of the electromagnetic field in a resonator lead to integral equations for Z _s (H). The corresponding integral equations are obtained for certain types of resonators. The errors of the conventional methods employing algebraic relations for Z _s (H) are analyzed. The Tikhonov regularization method, developed in the theory of ill-posed inverse problems, is used to reconstruct the functions Z _s (H) from the integral equations. Numerical experiments on the reconstruction of Z _s (H) were performed, and the requirements for the accuracies and other characteristics of the experimental data were determined from them. Zh. Tekh. Fiz. 68, 78–86 (August 1998)     

A proof of part of Haldane's conjecture on spin chains

It has been argued that the spectra of infinite length, translation and U(1) invariant, anisotropic, antiferromagnetic spin s chains differ according to whether s is integral or 1/2 integral: There is a range of parameters for which there is a unique ground state with a gap above it in the integral case, but no such range exists for the 1/2 integral case. We prove the above statement for 1/2 integral spin. We also prove that for all s, finite length chains have a unique ground state for a wide range of parameters. The argument was extended to SU(n) chains, and we prove analogous results in that case as well.Work partially supported by U.S. National Science Foundation grant PHY80-19754 and by the A.P. Sloan Foundation.Work partially supported by U.S. National Science Foundation grant PHY-85-15288.     

Quantum chemical study of a new class of sensitisers: influence of the substitution of aromatic rings on the properties of copper complexes

We present a computational study of new copper complexes with potential applications as sensitisers for solar cells. The applied methodology for this study is based on the density functional theory (DFT) and time-dependent DFT, using the B3LYP, PBE0 and M06 functionals with the LANL2DZ (D95V on first row), 6-31G(d,p), 6-311G(d,p) and DZVP basis sets. Optimised molecular structure, the absorption spectra, the molecular orbitals energies and the chemical reactivity parameters that arise from conceptual DFT were calculated. Solvent effects have been taken into account by an implicit approach, namely, the polarisable continuum model (PCM), using the non-equilibrium version of the integral equation formalism of the PCM model. Interesting work for experimentalists in the dye sensitised solar cells’ field.     

First‐principles X‐ray absorption dose calculation for time‐dependent mass and optical density

A dose integral of time‐dependent X‐ray absorption under conditions of variable photon energy and changing sample mass is derived from first principles starting with the Beer–Lambert (BL) absorption model. For a given photon energy the BL dose integral D(e, t) reduces to the product of an effective time integral T(t) and a dose rate R(e). Two approximations of the time‐dependent optical density, i.e. exponential A(t) = c + aexp(?bt) for first‐order kinetics and hyperbolic A(t) = c + a/(b + t) for second‐order kinetics, were considered for BL dose evaluation. For both models three methods of evaluating the effective time integral are considered: analytical integration, approximation by a function, and calculation of the asymptotic behaviour at large times. Data for poly(methyl methacrylate) and perfluorosulfonic acid polymers measured by scanning transmission soft X‐ray microscopy were used to test the BL dose calculation. It was found that a previous method to calculate time‐dependent dose underestimates the dose in mass loss situations, depending on the applied exposure time. All these methods here show that the BL dose is proportional to the exposure time D(e, t) ? K(e)t.     

Theory and simulation of electrolyte mixtures

Monte Carlo simulation and theoretical results on some aspects of thermodynamics of mixtures of electrolytes with a common species are presented. Both charge symmetric mixtures, where ions differ only in size, and charge asymmetric but size symmetric mixtures at ionic strength ranging generally from I = 10^?4 to 1.0 M, and in a few cases up to I = 2 M, are examined. The theoretical methods explored are: (i) the symmetric Poisson-Boltzmann theory, (ii) the modified Poisson-Boltzmann theory and (iii) the hypernetted-chain integral equation. The first two electrolyte mixing coefficients w ₀ and w ₁ of the various mixtures are calculated from an accurate determination of their osmotic pressure data. The theories are seen to be consistent among themselves, and with certain limiting laws in the literature, in predicting the trends of the mixing coefficients with respect to ionic strength. Some selected relevant experimental data have been analysed and compared with the theoretical and simulation trends. In addition the mean activity coefficients for a model mimicking the mixture of KC1 and KF electrolytes are calculated and hence the Harned coefficients obtained for this system. These calculations are compared with the experimental data and Monte Carlo results available in the literature. The theoretically predicted Harned coefficients are in good agreement with the simulation results for the model KC1-KF mixture.     

Theoretical investigation of magnetic parameters in two-dimensional sheets of pure organic BEDT-TTF and BETS molecules by using ab initio MO and DFT methods

The effective exchange integrals (J _ab(M)) between two cation radicals of title compounds in the Heisenberg model were calculated by ab initio molecular orbital (MO) and density functional theory (DFT) methods, together with hybrid DFT methods. The J _ab(D) values between two dimer mono-cation radicals were also estimated assuming J _ab(D) = J _ab(M)/2. It is found that the spin lattice obtained by the ab initio method is square planar and linear in BEDT-TTF and BETS planes, respectively, although other previous calculations show that spin lattice in the BEDT-TTF plane is a triangular one. The J _ab and overlap integrals (s_ab ) values by the ab initio methods were used to determine transfer integral (t_ab ) and Coulomb repulsion (U_cff ) parameters of the Hubbard model, which were compared with those of the previous results. Implications of the calculated results are discussed in relation to the spin-mediated mechanism for superconductivity.     

Trapezoidal (p,q)-Integral Inequalities Related to (η1,η2)-convex Functions with Applications

In this paper, the authors introduce the (p,q)-trapezoidal integral inequalities, which are the (p,q)-analogues of the recently introduced q-trapezoidal integral inequalities. We derive a new (p,q)-integral identity for twice (p,q)-differentiable function. Utilizing this as an auxiliary result, we establish several new (p,q)-trapezoidal type integral inequalities for the function whose absolute value of twice (p,q)-derivative is (η₁,η₂)-convex functions. Some special means of real numbers are also given. At the end, we give brief conclusion. It is expected that this method which is very useful, accurate, and versatile will open a new venue for the real-world phenomena of special relativity and quantum theory.

     

On the theory of temporal aberrations for cathode lenses

A new approach to the theory of temporal aberration for cathode lenses is given in the present paper. A definition of temporal aberration is given in which a certain initial energy of electron emission along the axial direction ε_z1 (0ε_z1ε_0max) is considered. A new method to calculate the temporal aberration coefficients of cathode lenses named “direct integral method” is also presented. The “direct integral method” gives new expressions of the temporal aberration coefficients which are expressed in integral forms. The difference between “direct integral method” and “τ-variation method” is that the “τ-variation method” needs to solve the differential equations for the three of temporal geometrical aberration coefficients of second order, while the “direct integral method” only needs to carry out the integral calculation for all of these temporal aberration coefficients of second order.All of the formulae of the temporal aberration coefficients deduced from “direct integral method” and “τ-variation method” have been verified by an electrostatic concentric spherical system model, and contrasted with the analytical solutions. Results show that these two methods have got identical solutions and the solutions of temporal aberration coefficients of the first and second order are the same as with the analytical solutions. Although some forms of the results seem different, but they can be transformed into the same form. Thus, it can be concluded these two methods given by us are equivalent and correct, but the “direct integral method” is related to solve integral equations, which is more convenient for computation and could be suggested for use in practical design.     

Direct molecular-level Monte Carlo simulation of Joule—Thomson processes

We present an application of the recently developed constant enthalpy-constant pressure Monte Carlo method [SMITH, W. R., and LÍSAL, M., 2002, Phys. Rev. E, 66, 01114] for the direct simulation of Joule-Thomson expansion processes using a molecular-level system model. For the alternative refrigerant HFC-32 (CH_{2F 2}), we perform direct simulations of the isenthalpic integral Joule-Thomson effect (temperature drop) resulting from Joule-Thomson expansion from an initial pressure to the representative final pressure of 1 bar. We consider representative expansions from single-phase states yielding final states in both single-phase and two-phase regions. We also predict the dependence of T(P, h) and of the Joule-Thomson coefficient, μ (P, h), on pressure along several representative isenthalps, as well as points on the Joule-Thomson inversion curve. HFC-32 is modelled using a five-site potential taken from the literature, with parameters derived from ab initio calculations and vapour-liquid equilibrium data. The simulated results show excellent agreement with those calculated from an international standard equation of state.     

Analytic solution of the RISM equation for symmetric diatomics with Yukawa closure

We present the site-site direct correlation function c(r) for a fluid of hard diatomic symmetric molecules obtained from Monte Carlo simulation data via the RISM integral equation. This c(r) ensures that the site-site correlation function given by the RISM equation is exact, and thus provides a basis for critically examining the usual closure for the RISM equation. As an example of an improved closure we present the analytic solution of the RISM integral equation with a Yukawa closure for c(r).     

Elastic scattering of low-energy electrons by NO

We report elastic integral, momentum transfer and differential cross sections for electron scattering by N₂O for energies up to 50 eV. These results were obtained at the static-exchange approximation with the Schwinger Multichannel Method with Pseudopotentials [M.H.F. Bettega, L.G. Ferreira and M.A.P. Lima, Phys. Rev. A 47, 1111 (1993)]. In general our results show good agreement with experimental data and with other theoretical results but some discrepancies are found. We have also found a shape resonance around 4 eV in agreement with previous calculations using the R-matrix Method of Sarpal et al. [J. Phys. B 29, 857 (1996)]. On the other hand, the existence of a resonance at about 13 eV, clearly seen by the Schwinger Variational Iterative Method [Michelin et al., J. Phys. B 29, 2115 (1996)], can not be confirmed by our calculations. At this energy, our cross sections show a broad bump with no clear resonant behavior given by the eigenphase sum. Received: 13 November 1997 / Revised: 13 March 1998 / Accepted: 9 April 1998     

Influence of ro-vibrational and isotope effects on the dynamics of the C(3 P)+ OD(X 2Π) → CO(X 1 Σ+) + D(2 S) reaction

The C(³ P)+OD(X ²Π) reaction has been studied by means of quantum mechanical real wave packet (RWP) and quasiclassical trajectory (QCT) methodologies on the ground potential energy surface of Zanchet et al. [J. Phys. Chem. A 110, 12017 (2006)]. Initial state selected total reaction probabilities at J?=?0 total angular momentum have been calculated for a wide range of collision energies. Product state-resolved integral cross-sections at selected collision energies and excitation functions have been determined from the RWP calculations using the J-shifting approximation and from QCT calculations. State-specific and thermal rate coefficients have been calculated using both methodologies up to 500 K. The effect of reagent rotational excitation on the dynamics for the C(³ P)+OH(X ²Π) and C(³ P)+OD(X ²Π) reactions has been investigated and interesting discrepancies between the QCT and RWP results have been found. The RWP results are found to be in an overall good agreement with the corresponding QCT results, although the QCT integral cross-section and rate coefficients are slightly smaller than those obtained from the RWP calculations.     

On the Ricci Curvature of Compact Spacelike Hypersurfaces in Einstein Conformally Stationary-Closed Spacetimes

In this paper we develop an integral formula involving the Ricci and scalar curvatures of a compact spacelike hypersurface M in a spacetime equipped with a timelike closed conformal vector field K (in short, conformally stationary-closed spacetime), and we apply it, when is Einstein, in order to establish sufficient conditions for M to be a leaf of the foliation determined by K and to obtain some non-existence results. We also get some interesting consequences for the particular case when is a generalized Robertson-Walker spacetime.