Showing papers on "Antisymmetric relation published in 1981"

A new look at correlations in atomic and molecular systems. I. Application of fermion monte carlo variational method

Abstract: Results of research directed towrad the development of compact and accurate correlation functions for many-electron systems are reported. The computational tool used is the variational method in which the many-electron integrals are calculated by Monte Carlo using the fermion Metropolis sampling algorithm. That is, a many-fermion system is simulated by sampling the square of a correlated antisymmetric wave function. The principal advantage of the method is that interelectronic distance r/sub ij/ may be included directly in the wave function without adding significant computational complexity. In addition, other quantities of physical and theoretical interest such as electron correlation functions and representations of Coulomb and Fermi holes are very easily obtained. Preliminary results are reported for He, H/sub 2/, and Li/sub 2/.

The symmetric group: branching rules, products and plethysms for spin representations

Abstract: It is shown that the symmetric group Sn may be usefully embedded in the orthogonal group On, and that this embedding leads directly to an n-independent 'reduced' notation for both the spin and ordinary representations of Sn. Making use of this embedding, together with the properties of Q-functions (or Hall-Littlewood functions), branching rules for On (spin down) Sn are developed and the general rule for the decomposition of spin representations under Sn (spin down) Sn-1 is obtained. Simple methods are given for calculating all possible Kronecker products involving the spin and ordinary representations of Sn and the resolution of Kronecker squares into their symmetric and antisymmetric parts. The spin representations of Sn are systematically classified as to their orthogonal, symplectic or complex characters. The emphasis throughout is on obtaining results that obviate the need for explicit character tables and presenting results in an n-independent manner as much as possible.

Antisymmetric product of geminals in the context of the method of moments

Abstract: A scheme for obtaining approximate solutions of the electronic Schrodinger equation is formulated within the context of the method of moments. The flexibility of the method of moments is utilized in the construction of a model based on an antisymmetric product of geminals (APG). This APG model is compared with a model based on an antisymmetric product of strongly orthogonal geminals (APSG). As a test example the advocated APG model is applied to the ground state of ammonia. Our best APG function recovers 37% of the total molecular correlation energy to be compared with an estimated 31% for the best APSG function.

Expansion coefficient of heat kernel of Laplacian operator in Riemann-Cartan space

Abstract: The method of determining the coefficient in the asymptotic expansion of the heat kernel of the Laplacian operator in a Riemann-Cartan space is discussed. In the context of SO(4) gravity with totally antisymmetric torsion tensor, the method of coincidence limits of De Witt (1965) is equivalent to that of the algorithm of 't Hooft (1974). As an example, the axial current divergence due to the spin-1/2 field is given.

Symmetry Properties of Reduced Density Matrices

Abstract: Publisher Summary This chapter describes the symmetry properties of reduced density matrices (RDM) and their eigen functions. The chapter proposes a unified rigorous approach to the study of the symmetry properties of RDM. In the RDM approach, there arises the problem of finding the integral of motion and discrete symmetries for the density matrix D p Ψ and their relation with the motion integrals for the wave function Ψ. This problem is more general and profound than the so-called N-representability problem, which consists of finding a complete set of characteristics of RDM arising from the contraction of either antisymmetric or symmetric wave functions. A more complex problem is to find the symmetry properties of the transition density matrices from the known symmetry properties of the wave functions that determine it. The chapter reviews that the known RDM symmetry allows the simplification of the calculation of matrix elements, to quasi-diagonalize a secular problem. It is important to note that the symmetry can be recovered in two ways: either by assembly averaging over all densities of a complete set of degenerated states or by averaging the density for a certain state over the whole symmetry group of a system. These procedures are absolutely equivalent and give the invariant part of RDM.

The alternating group: branching rules, products and plethysms for ordinary and spin representations

Abstract: Practical algorithms are given for calculating all possible Kronecker products involving the spin and ordinary representations of the alternating group An and for the resolution of Kronecker squares into their symmetric and antisymmetric parts. The representations of An are classified as to their orthogonal, symplectic or complex characters. Branching rules for Sn spin down An and An spin down An-1 are given. Throughout, the emphasis is on obtaining results that obviate the need for explicit character tables and on presenting the results in an n-independent manner.

Stability of a quadruple vortex street

Abstract: The stability of a quadruple vortex street, i.e. a pair of double vortex streets in a perfect fluid is investigated for small disturbances. Permanent configurations are first determined; two of which are then examined in their stability–one is a symmetric arrangement of a pair of staggered (Karman-type) double streets and the other is an antisymmetric arrangement of the pair. The stability curves are obtained for several values of ratio of the distance 2 b 0 between the double streets to the spacing a between consecutive vorticies in a row. It is found that both types are neutrally stable for most of disturbances except unstable disturbances in very narrow ranges of a parameter specifying the disturbances mode, provided that \(b_{0}/a \gtrsim 0.5\) and b / a is taken to be about 0.28, where b is the breadth of the double street. The symmetric type is more stable than the antisymmetric one.

Solution of Transcendental and Algebraic Equations with Application to Wave Propagation in Elastic Plates.

Abstract: : A numerical method is described by which theoretical formulas governing the propagation of symmetric and antisymmetric waves in elastic plate theory may be evaluated. Vital to evaluating the formulas is the availability of a means for solving transcendental equations. A generalized iterative rootfinder that was developed for this purpose is described. This rootfinder provides the investigator having access to computing facilities with a reliable means for solving transcendental equations. Dispersion curves for both the flexural and extensional waves in rubber, steel, and beryllium plates are calculated and plotted. These curves approach a real value k for the ratio of the Rayleigh to shear wave speeds. Values of this quantity calculated from the exact elasticity theory were compared with those obtained from an approximate formula given by Victorov. In addition, the inflection and the maximum points of the strain distribution throughout a free plate were calculated. It was found that inflection points in the strain distribution do not exist at all frequencies. In addition to a description and flow chart of the iterative rootfinder method, the significant graphs, equations, and computer programs that arose when computing the dispersion curve calculations are included. (Author)

Acoustic radiation from fluid‐loaded elastic plates I. Antisymmetric modes

Abstract: The Timoshenko–Mindlin plate equation of motion is modified in order to simultaneously specify the precise cutoff and asymptotic behavior of both antisymmetric modes of plate vibration described by it. A mathematical method for extending equations of motion to include higher order antisymmetric modes is presented. This method is illustrated by the development of an equation of motion for the first four antisymmetric modes of plate vibration.

Imaging And Coupling In Parallel Multimode Dielectric Slab Waveguides

Abstract: An extension of a recently developed hybrid technique for computing beam propagation in multimode dielectric waveguides is used to treat coupling between two identical parallel slab waveguides. Propagation on these slabs can be described by system (or normal) modes, which are symmetric or antisymmetric combinations of single slab modes. These two groups of modes possess slightly different self-imaging properties which can eventually result in virtually complete power transfer from one guide to the other. Whether or not the resulting beam in the second guide is well-focused depends on the relation of the coupling distance to the self-imaging distance, as well as the properties of the beam itself.© (1981) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

The vibrational spectra of some 1,3-dimethyl-1,3-diaza-2-boracyclopentanes

Abstract: A detailed vibrational assignment is proposed for 1,3-dimethyl-1,3-diaza-2-boracyclopentanes: where X = Cl, Br or NMe 2 . The assignments are generally in accord with C 2v symmetry, but there is some evidence for a slight breakdown, as some A 2 modes appear in the IR. The BN 2 stretches are near 1500 cm −1 , (antisymmetric) and 1300 cm −1 (symmetric), consistent with a large degree of π-bonding.