Showing papers on "Antisymmetric relation published in 1984"

Nonlinear Faraday resonance

Abstract: A cylinder containing liquid with a free surface is subjected to a vertical oscillation of amplitude eg/ω2 and frequency 2ω, where ω is within O(eω) of the natural frequency of a particular (primary) mode in the surface-wave spectrum and 0 δ, where δ is the damping ratio (actual/critical) of the primary mode, is a necessary condition for subharmonic response of that mode. Explicit results are given for the dominant axisymmetric and antisymmetric modes in a circular cylinder. Internal resonance, in which a pair of modes have frequencies that approximate ω and 2ω, is discussed separately, and the fixed points and their stability for the special case ω2 = 2ω1 are determined. Internal resonance for ω2 = ω1 is discussed in an appendix.

Clarification of the electronic asymmetry in Π‐state Λ doublets with some implications for molecular collisions

Abstract: The asymmetry of the orbital part of the electronic wave functions and electronic charge distributions in 1Π, 2Π, and 3Π Λ doublets is carefully examined, to clear up considerable past confusion on this subject. The results are: (1) For 1Π and 3ΠΩ=1 states the electronic wave function in the e Λ‐doublet levels is symmetric with respect to reflection in the plane of rotation of the molecule and, in the f levels, antisymmetric. (2) For 2Π and 3Π0,2 states, in the Hund’s case (a) limit the electronic distributions in both Λ‐doublet levels are cylindrically symmetric. (3) As the case (b) limit is approached, the F1 e and F2 f wave functions of a 2Π state acquire an increasing degree of symmetric character with respect to reflection in the plane of rotation, while the F1 f and F2 e levels acquire antisymmetric character. In a 2Σ+–2Π radiative transition, the main branch P and R lines probe 2Π levels which are symmetric with respect to reflection in the plane of rotation while the main branch Q lines probe leve...

The density matrix, density, and Fermi hole in Hartree-Fock theory

Abstract: In density matrix and density functional theory, one is concerned with methods that bypass explicit calculation of antisymmetric wave functions but nevertheless take full account of the Fermionic nature of the problem. The purpose of this paper is to examine two quite different approaches which achieve this aim. The first of these involves general many‐electron theory and subsequent closure yielding an integrodifferential equation for the density matrix. Despite the interesting nature of this equation, analytical progress is hampered by its nonlinearity. Hence we have considered an alternative more practical variational procedure which, for some simpler systems, has the additional merit of yielding closed differential equations for the density.

p-Polarized Nonlinear Surface Waves in Symmetric Layered Structures

Abstract: An exact solution of Maxwell's equations is found, corresponding to a p-polarized nonlinear surface wave propagating in a symmetric layered structure. The system under consideration consists of a layer with a linear dielectric constant 1 bounded at two sides by a nonlinear medium characterized by the diagonal dielectric tensor 11 = 22 = ⊥ + α(|E1|2 +|E2|2), 33 = ||. It is shown that besides symmetric and antisymmetric modes there exist asymmetric modes at power flows exceeding some certain minimal value. We have found also bistable states of p-polarized nonlinear surface waves provided that the power flow in the wave is the control parameter.

Modal gain in coupled-stripe lasers

Abstract: Using an effective index model, we calculate the eigenvalue equation for a large array of evanescent-wave-coupled multistripe lasers. The special cases of symmetric and antisymmetric modes for both the index- and gain-guided lasers are treated in detail. The main findings are 1) weak index-guided coupling, with small differences in optical confinement factors, and 2) stronger gain-guided coupling, with parameter-dependent selection of the mode symmetry having higher gain.

Unitary group approach to the many-electron problem. II. Adjoint tensor operators for U(n)

Abstract: In this paper we present a derivation of the U(n) adjoint coupling coefficients for the representations appropriate to many-electron systems. Since the states of a many-fermion system are to comprise the totally antisymmetric Nth rank tensor representation of U(2n), the work of this paper enables the matrix elements of the U(2n) generators to be evaluated directly in the U(n) × U(2) (i.e., spin orbit) basis using their transformation properties as adjoint tensor operators. A connection between the adjoint coupling coefficients, as derived in this paper, and the matrix elements of certain (spin independent) two-body operators is also presented. This indicates that in CI calculations, one may obtain the matrix elements of spin-dependent operators from the known matrix elements of certain spin-independent two-body operators. In particular this implies a segment-level formula for the matrix elements of the U(2n) generators in the spin-orbit basis.

Antisymmetric Spin Interaction in Metals

Abstract: The bilinear term of the spin-polarization density in the spin-dependent energy of metals is separated into the terms of the symmetric spin interaction (SSI) and of the antisymmetric spin interaction (ASI), whose properties are first investigated phenomenologically. A microscopic derivation of the SSI and ASI is given for a metal which has no inversion center. It is shown that the spin-orbit coupling which splits electronic bands in the absence of inversion center produces an antisymmetric component of the wave-vector-dependent susceptibility and the ASI is proportional to the antisymmetric component to the first order of the latter quantity. The obtained ASI energy is concluded to be not always small compared with the SSI energy.

Parametrization of molecular orbital transformations

Abstract: It is proved that any orthogonal matrix U can be represented in the form U=eX U where X is real, antisymmetric, and block off‐diagonal, and U is orthogonal and block diagonal with arbitrary block structure. The unique elements of X constitute the orbital rotation subset of a larger set (p, q, X) of independent perturbational and variational parameters. These provide a convenient separation of variables for orbital optimization and for analytic computation of derivative properties of variational wave functions.

Mixed Models and Reduction Techniques for Large-Rotation, Nonlinear Analysis of Shells of Revolution with Application to Tires

Abstract: An effective computational strategy is presented for the large-rotation, nonlinear axisymmetric analysis of shells of revolution. The three key elements of the computational strategy are: (1) use of mixed finite-element models with discontinuous stress resultants at the element interfaces; (2) substantial reduction in the total number of degrees of freedom through the use of a multiple-parameter reduction technique; and (3) reduction in the size of the analysis model through the decomposition of asymmetric loads into symmetric and antisymmetric components coupled with the use of the multiple-parameter reduction technique. The potential of the proposed computational strategy is discussed. Numerical results are presented to demonstrate the high accuracy of the mixed models developed and to show the potential of using the proposed computational strategy for the analysis of tires.

Low-temperature thermoelastic effects in glasses

Abstract: Thermoeiastic effects have been studied in vitreous silica and in polymethyl methacrylate (PMMA) by measuring the temperature response of a sample subjected to strain. Both ramp and sinusoidal strains were used, the latter covering the frequency range 0·01 to 10 Hz, in the temperature range 0·5 to 10 K. The temperature changes induced by applying and removing the strain over a time interval Δt, typically 0·1 s (the ramp strains), were analysed into sunn and difference terms, representing the symmetric and antisymmetric responses respectively. Antisymmetric changes give values of the Gruneisen function y which agree well with values derived from thermal-expansion experiments in silica above 4 K and in PMMA above 2 K. At lower temperatures, the antisymmetric response is swamped by the symmetric term which measures irreversible processes. The magnitude of the losses increases with decreasing Δt, but, by assuming a microscopic model based on two-level states, this behaviour can be explained, and lead...

The solution of the one-dimensional sign problem for Fourier transforms

Abstract: An iterative procedure for the determination of the signs of scattering amplitudes is considered. It is assumed that the scattering density is a one-dimensional antisymmetric function with a limited range of definition. The convergence of the method to a rigorous solution is proved. The stability of the procedure with respect to various experimental errors is shown in model examples. The proof can be generalized for a one-dimensional phase determination of a continuous intensity distribution.

Symmetry breaking patterns for third-rank totally antisymmetric representations of unitary groups

Abstract: Some possible symmetry breaking patterns for unitary group gauge theoretic models based on Higgs scalars in the third-rank totally antisymmetric tensor representations of U(n) are studied. The critical points are expressed in terms of a single parameter xi such that 1/n or=9, and remarks are made concerning a conjecture of Michel (1979).

Classroom simulation of the coupled motion of piano strings

Abstract: The movement of doubled strings is simulated on a device, described in the paper, which permits the main features of the motion to be seen in the classroom. When the strings move up and down together, the motion is heavily damped. For antisymmetric motion the damping rate is much smaller (the Weinreich mechanism). A simple model of the mechanism is discussed as it applies to the simulator. A less restricted solution of the coupled equations of motion is given in the Appendix.

New class of antisymmetrized optical potentials

Abstract: This paper is mainly concerned with the construction and various properties of a new class of antisymmetric, two-fragment, elastic scattering optical potentials. The construction is based directly on the wave function formulation of $N$-particle collision theories, which are antisymmetrized herein using the method of Adhikari and Gl\"ockle. Those theories which are label transforming are considered first. For such theories, the resulting optical potentials are asymmetric but nevertheless real for energies below the inelastic threshold ${E}_{\mathrm{inel}}$, and are asymmetric and absorptive for $E\ensuremath{\ge}{E}_{\mathrm{inel}}$. This unusual feature of asymmetry is a consequence of working directly with $N$-particle collision theories, almost all of which are expressed in non-Hermitian matrix form, and arguments are presented as to why asymmetry is not a practical problem. Not only are the new class of optical potentials asymmetric, it is also found that exchange effects generally enter them in an extremely simple fashion. These latter two features distinguish the members of the new class from the optical potential developed recently by Goldflam and Kowalski. Examples of label-transforming theories producing such potentials are the extended Faddeev theory of Levin, the precursor form of the Bencze, Redish, Sloan theory, and the wave function component theory of L'Huillier, Redish, and Tandy. Their existence establishes that formalisms other than those based on the Alt, Grassberger, Sandhas transition operator lead to symmetrized optical potentials free of elastic unitarity cuts, albeit potentials which are not Hermitian analytic. In addition to the above theories, a new, symmetrized form of the equations of the channel permuting array theory is developed.

Symmetric and antisymmetric solutions for nonlinear wave modulations in plasmas

Abstract: The existence of symmetric and antisymmetric stationary localized solutions for nonlinear amplitude‐modulated Langmuir waves and circularly polarized electromagnetic waves in plasmas is considered. It is shown that the antisymmetric Langmuir solitons exist in the entire range of the Mach number, namely, 0

Cooperative and interference effects in the resonance fluorescence of two identical three-level atoms at high photon densities II. Numerical results

Abstract: Numerical calculations are presented for the excitation spectrum of two identical three-level atoms interacting with a strong resonant laser field. The atoms interact through their dipole-dipole interaction and radiate to each other as well. The spectrum of the symmetric and antisymmetric modes due to the radiative decay from the higher to the lower excited state of the interacting atoms is considered without and with taking into account the effects of the strong pumping process. In the absence of strong pumping, the dipole-dipole interaction in the spectrum of the symmetric modes gives rise to an asymmetric doublet whose ratio of intensities is 2:1, while the spectrum of the antisymmetric modes consists of two peaks one of which represents a stable mode indicating the trapping of a photon between the atoms and a radiative one which has a lifetime one-half that of the isolated atom. In the presence of strong pumping, asymmetries due to the dipole-dipole interaction arise enhancing certain peaks while diminishing the intensity of others and a new pair of sidebands is induced as well. The computed spectra are presented graphically for different values of the Rabi frequencies and the dipole-dipole interaction, respectively.