Showing papers on "Antisymmetric relation published in 1973"

Optical switching and modulation in parallel dielectric waveguides

Abstract: Coupling of electromagnetic energy between parallel single‐mode dielectric waveguides is investigated theoretically. Expressions giving the decrease in coupling length due to an antisymmetric change in refractive index are derived. The minimum parallel‐guide path length, l, required for switching or modulation is determined from coupling length calculations. It is shown that, for large waveguide separations, Δnl=3λ/4, where λ is the free‐space wavelength and Δn is the magnitude of the antisymmetric index change. Calculations for slab and square‐cross‐section waveguide geometries indicate that antisymmetric index changes are much more effective than symmetric changes for switching or modulation.

Circularly polarized Raman spectroscopy: Direct determination of antisymmetric scattering in the resonance Raman spectrum of ferrocytochrome c

Abstract: An apparatus is described for measuring Raman backscattering with both linearly and circularly polarized light. All four polarization components, parallel, perpendicular, corotating and contrarotating, can be directly compared and used to determine the relative magnitudes of the three invariants of the non-symmetric Raman tensor for randomly oriented molecules. The method has been applied to the resonance Raman spectrum of ferrocytochrome c. Antisymmetric scattering, previously detected through anomalous depolarization ratios, has been confirmed by direct measurement of the antisymmetric tensor invariant. In addition to the four anomalously polarized bands, two bands with normal polarizations have been shown to exhibit significant antisymmetric scattering. This result implies a reduction from four-hold symmetry for the heme chromosphere.

Effect of Antisymmetric Interactions on Critical Phenomena: A System with Helical Ground State

Abstract: A classical Heisenberg Hamiltonian, to which is added single-ion anisotropy and antisymmetric Dzialoshinsky-Moriya interactions is studied with use of Wilson theory. The phase diagram is obtained; it consists of ferromagnetic, spiral, and ferromagnetic-spiral regions, with critical exponents that are Ising-like, $\mathrm{xy}$-like, and Heisenberg-like, respectively. These results lead to the conclusion that breaking of exchange symmetry does not change the nature of the phase transition. Crossover behavior is also discussed.

Geometry of the octet

Abstract: A number of formulas equivalent to those already known are demonstrated. The demonstrations presented are simpler than tension to be made to more complicated cases. SU(n) algebras which are symmetric and antisymmetric and invariant on R(n/sup 2/-1) and the geometry of the SU(3) octet are examined successively. (auth)

Perturbation theory for the surface-wave multistrip coupler

Abstract: A space-harmonic perturbation theory is presented for the multistrip coupler which does not require any adjustment parameters and which gives the dispersion relations separately for the symmetric and for the antisymmetric modes. The agreement with experimental results for different widths and spacings of the strips is very good when the number of strips per wavelength is greater than two, but is not as good for smaller values, because the effects of the reflected wave and of the radiated bulk waves have been neglected.

Matrix elements of general configuration of nonorthogonalized orbitals in state with definite spin

Abstract: The expressions for matrix elements of spin-independent operators F and G with the use of Young operators are obtained in the case of arbitrary nonorthogonalized orbital configuration, including both singly and doubly filled orbitals and corresponding to the definite value of total spin. The formulas obtained do not require a preliminary construction of linear combinations of determinants and turn into known Lowdin formulas in the particular case of fully antisymmetric spatial states.

Mathematical foundations of the atomic theory; Matematicheskie osnovy teorii atoma

Abstract: The monograph is intended for sciertific workers specializing in the area of the quantum theory of atoms, atomic spectra, and related problem s of contemporary physics. Methods for the construction of antisymmetric wave functions by means of one-electron wave functions (spin-orbital) and expressions of the matrix elements of the operators of atomic magnitudes through radial integrals are examined. For the shell of equivaience electrons the fractional parertage coefficient was used and for operators--the mathematical apparatus of irreducible tensor operators which includes both the electrostatic and the magnetic interactions. The material gave an account that can be used in cases of the consideration of correlations by the method of configuration coincidence (usuai forms or the multiconfiguration approximation) or by expanded methods of calculation. It was made possible to formulate rapidly expressions for the matrix elements of operators. (tr-auth)

Approximate solutions of the Liouville equation. II. Stationary variational principles

Abstract: Stationary variational functionals for the Laplace transform of the Liouville distribution are constructed. The value of the functional is the autocorrelation function that one wishes to compute. It is shown that the functionals may be transformed to a renormalized form. Trial functions not involving the potential explicitly give rise to time-dependent autocorrelation functions determined only by equilibrium spatial correlation functions. Another class of functionals is constructed by independently varying the parity symmetric and antisymmetric parts of the distribution function. Trial functions need only be assumed for one of these—the optimum value of the other one is given exactly. This procedure is used to improve the simplest known theories for velocity and density autocorrelation functions.

Phase‐velocity relation for an acoustic wedge guide mode

Abstract: A variational analysis is presented for the phase velocity of an acoustic wave guided by the apex of an infinitely tall wedge. The lowest‐order antisymmetric flexural mode is considered. It is demonstrated that rather simple approximations to the particle displacements lead to an accurate prediction of the mode phase velocity as a function of the apex angle. An analytic expression is obtained for phase velocity in the limit of small apex angles.

Application of Kraichnan's direct interaction approximation to kinematic dynamo theory. II. Incompressible, helical velocity turbulence and a pair of coupled, singular, nonlinear integral equations

Abstract: Using Kraichnan's direct interaction approximation, we set up the equations governing the normal modes of the ensemble average magnetic field under incompressible, nonmirror symmetric velocity turbulence We show that (i) the Green's stress tensor enjoys equipartition of its symmetric and antisymmetric parts at the normal mode frequencies of the ensemble average field, (ii) for static velocity turbulence, including helicity, there are no growing modes, (iii) the commonly used first order smoothing theory approximation is invalid when compared to the Kraichnan equations, for the Kraichnan equations do not satisfy Hammerstein's theorem while first order smoothing theory requires the satisfaction of Hammerstein's theorem, (iv) if there is to be any growth of the ensemble average magnetic field it must come from time dependent velocity turbulence, and when the velocity turbulence is time dependent we have so far been unable to solve the Kraichnan equations We have done these calculations for two reasons First to illustrate, by exact solution, the manner in which the normal modes of the ensemble average magnetic field depend on the helicity and Reynolds number of the turbulent velocity field Second to show that approximate treatments of the hydromagnetic equation (like first order smoothing theory), rather than exact solution, are liable to give rise to substantial error in view of the fact that the Kraichnan equations do not satisfy Hammerstein's theorem

Antisymmetric problems in shock diffraction theory

Abstract: Various aspects of the diffraction of plane shock waves by moving antisymmetric thin bodies are examined A method is presented for removing the inhomogeneity in the shock condition This is done without knowledge of the explicit form of the solution, and is applicable to both symmetric and antisymmetric problems With this reduction, explicit solutions have been previously obtained for symmetric bodies For the antisymmetric case, the problem has been previously reduced to a complicated set of integrodifferential equations In the cases where the flow field exhibits conical properties or when the body is slender, solutions may be obtained without recourse to solving the governing integral equations In this paper it is shown that two-dimensional conical solutions are obtainable for moving antisymmetric wings only in the restricted case of the wing Mach numbers relative to the stream ahead of and behind the shock being the same An analytical solution is presented for the above problem In the case of slender bodies, it is shown that the classical steady slender body theory may be extended to shock diffraction problems and again analytical solutions are presented It is shown that for general slender bodies, the lift and moment coefficients, and therefore the center of lift is influenced by the shock wave only through the Mach number change across the shock Results are presented for the pressure distribution on the body, the lift and moment coefficients, and the center of lift for various slender body configurations at angle of attack

On Zeta-Functions of Infinite-Dimensional Representations

Abstract: In this paper we consider the group of similitudes of a nondegenerate symmetric or antisymmetric bilinear form over a global field.For representations of this group, realized as functions on the factor-space of the adeles of this group modulo the principal adeles, we construct certain zeta-functions possessing an Euler product and a meromorphic continuation.Bibliography: 7 items.

Duality of the scattering amplitude in the complex energy plane

Abstract: By use of the ordinary dispersion relations evaluated for complex argument, the behaviour of the antisymmetric forward pion-nucleon scattering amplitude in the complex ϑ-plane is exhaustively studied. It is found that duality is better verified off the real axis than for physical energies, and that it holds rather well both for the real and imaginary parts down to |ϑ|∼(2÷3) GeV. The connection of this result with the known finite-energy sum rules is investigated, and a new type of sum rules based on the duality requirement is presented. It is also shown that the subtraction of the Born term improves the agreement between the scattering amplitude and its asymptotic expression over the whole region of interest in the complex ϑ-plane. Finally, the parameters of the amplitude zeros are determined, and the possibility that there might be a connection between such zeros and duality breakdown at low energies is hinted.

Antisymmetric bosons in nuclear structure

Abstract: The concept of an ideal space of bosons and ideal particles is applied directiy to systems of ordinary particles with a transcription of the particle into that ideal space that preserves both the Pauli principle and the transformation properties of the one- and two-body operators. Systems up to four particles are treated. (auth)

Stability of plane-parallel MHD flows in transverse magnetic field

Abstract: We study within the framework of linear theory the stability of plane-parallel flows of a viscous, electrically conducting fluid in a transverse magnetic field. The magnetic Reynolds numbers are assumed small. The critical Reynolds number as a function of the Hartmann number is obtained over the entire range of variation of the latter. The small perturbation spectrum is studied in detail on the example of Hartmann flow. Neutral curves are constructed for symmetric and antisymmetric disturbances. The destablizing effect of a magnetic field is studied in the case of modified Couette flow. The results obtained agree with the calculations of Lock and Kakutani (where they meet) and are at variance with the results of Pavlov.