Showing papers on "Symmetry (physics) published in 1997"

Pseudospin as a relativistic symmetry

Abstract: We show that pseudospin symmetry in nuclei could arise from nucleons moving in a relativistic mean field which has an attractive scalar and repulsive vector potential nearly equal in magnitude. {copyright} {ital 1997} {ital The American Physical Society}

P-wave reflection coefficients for transversely isotropic models with vertical and horizontal axis of symmetry

Abstract: The study of P-wave reflection coefficients in anisotropic media is important for amplitude variation with offset (AVO) analysis. While numerical evaluation of the reflection coefficient is straightforward, numerical solutions do not provide analytic insight into the influence of anisotropy on the AVO signature. To overcome this difficulty, I present an improved approximation for P-wave reflection coefficients at a horizontal boundary in transversely isotropic media with vertical axis of symmetry (VTI media). This solution has the same AVO-gradient term describing the low-order angular variation of the reflection coefficient as the equations published previously, but is more accurate for large incidence angles. The refined approximation is then extended to transverse isotropy with a horizontal axis of symmetry (HTI), which is caused typically by a system of vertical cracks. Comparison of the approximate reflection coefficients for P-waves incident in the two vertical symmetry planes of HTI media indicates that the azimuthal variation of the AVO gradient is a function of the shear-wave splitting parameter y, and the anisotropy parameter describing P-wave anisotropy for nearvertical propagation in the vertical plane containing the symmetry axis.

Symmetry and Asymmetry from Local Phase

Abstract: Symmetry is an important mechanism by which we identify the structure of objects. Man-made objects, plants and animals are usually highly recognizable from the symmetry, or partial symmetries that they often exhibit. Two difficulties found in most symmetry detection algorithms are firstly, that they usually require objects to be segmented prior to any symmetry analysis, and secondly, that they do not provide any absolute measure of the degree of symmetry at any point in an image. This paper presents a new measure of symmetry that is based on the analysis of local frequency information. It is shown that points of symmetry and asymmetry give rise to easily recognized patterns of local phase. This phase information can be used to construct a contrast invariant measure of symmetry that does not require any prior recognition or segmentation of objects.

Asymptotic structure of symmetry reduced general relativity

Abstract: Gravitational waves with a space-translation Killing field are considered. Because of the symmetry, the four-dimensional Einstein vacuum equations are equivalent to the three-dimensional Einstein equations with certain matter sources. This interplay between four- and three-dimensional general relativity can be exploited effectively to analyze issues pertaining to four dimensions in terms of the three-dimensional structures. An example is provided by the asymptotic structure at null infinity: While these space-times fail to be asymptotically flat in four dimensions, they can admit a regular completion at null infinity in three dimensions. This completion is used to analyze the asymptotic symmetries, introduce the analogue of the four-dimensional Bondi energy momentum, and write down a flux formula. The analysis is also of interest from a purely three-dimensional perspective because it pertains to a diffeomorphism-invariant three-dimensional field theory with local degrees of freedom, i.e., to a midisuperspace. Furthermore, because of certain peculiarities of three dimensions, the description of null infinity has a number of features that are quite surprising because they do not arise in the Bondi-Penrose description in four dimensions.

Robust heteroclinic cycles

Abstract: One phenomenon in the dynamics of differential equations which does not typically occur in systems without symmetry is heteroclinic cycles. In symmetric systems, cycles can be robust for symmetry-preserving perturbations and stable. Cycles have been observed in a number of simulations and experiments, for example in rotating convection between two plates and for turbulent flows in a boundary layer. Theoretically the existence of robust cycles has been proved in the unfoldings of some low codimension bifurcations and in the context of forced symmetry breaking from a larger to a smaller symmetry group. In this article we review the theoretical and the applied research on robust cycles.

Breathing modes and hidden symmetry of trapped atoms in two dimensions

Abstract: Atoms confined in a harmonic potential show universal oscillations in two dimensions (2D). We point out the connection of these ``breathing'' modes to the presence of a hidden symmetry. The underlying symmetry SO(2,1), i.e., the two-dimensional Lorentz group, allows pulsating solutions to be constructed for the interacting quantum system and for the corresponding nonlinear Gross-Pitaevskii equation. We point out how this symmetry can be used as a probe for recently proposed experiments of trapped atoms in 2D.

Kappa-Symmetry, Supersymmetry and Intersecting Branes

Abstract: We present a new form of kappa-symmetry transformations for D-branes in which the dependence on the Born-Infeld field strength is expressed as a relative rotation on the left- and right-moving fields with opposite parameters. Then, we apply this result to investigate the supersymmetry preserved by certain intersecting brane configurations at arbitrary angles and with non-vanishing constant Born-Infeld fields. We also comment on the covariant quantization of the D-brane actions.

Monte carlo simulation of topological defects in the nematic liquid crystal matrix around a spherical colloid particle

Abstract: We use a Monte Carlo algorithm to simulate the director field around a spherical inclusion in a uniform nematic liquid crystal matrix. The resulting structure crucially depends on the relative strength of the nematic bulk elasticity and the director anchoring on the particle surface. When this anchoring is weak, the director field perturbations are small and have quadrupolar symmetry. With increasing strength of anchoring two topologically nontrivial situations are possible: a dipolar configuration with a satellite point defect (hedgehog) near the particle pole, or a quadrupolar configuration with a ``Saturn ring'' of disclination around the particle equator.

Density of Kinks after a Quench: When Symmetry Breaks, How Big are the Pieces?

Abstract: Numerical study of order parameter evolution in the course of symmetry breaking transitions with Landau-Ginzburg{endash}like dynamics shows that the density of topological defects, kinks which form during the quench, is proportional to the fourth root of its rate. This is a limited (1D) test of the more general theory of domain-size evolution in the course of symmetry breaking transformations proposed by one of us. Using these ideas, it is possible to compute the density of topological defects from the quench time scale and from the equilibrium scaling of the correlation length and relaxation time near the critical point. {copyright} {ital 1997} {ital The American Physical Society}

Optimal Control for Holonomic and Nonholonomic Mechanical Systems with Symmetry and Lagrangian Reduction

Abstract: In this paper we establish necessary conditions for optimal control using the ideas of Lagrangian reduction in the sense of reduction under a symmetry group. The techniques developed here are designed for Lagrangian mechanical control systems with symmetry. The benefit of such an approach is that it makes use of the special structure of the system, especially its symmetry structure, and thus it leads rather directly to the desired conclusions for such systems. Lagrangian reduction can do in one step what one can alternatively do by applying the Pontryagin maximum principle followed by an application of Poisson reduction. The idea of using Lagrangian reduction in the sense of symmetry reduction was also obtained by Bloch and Crouch [Proc. 33rd CDC, IEEE, 1994, pp. 2584--2590] in a somewhat different context, and the general idea is closely related to those in Montgomery [Comm. Math. Phys., 128 (1990), pp. 565--592] and Vershik and Gershkovich [Dynamical Systems VII, V. Arnold and S. P. Novikov, eds., Springer-Verlag, 1994]. Here we develop this idea further and apply it to some known examples, such as optimal control on Lie groups and principal bundles (such as the ball and plate problem) and reorientation examples with zero angular momentum (such as the satellite with moveable masses). However, one of our main goals is to extend the method to the case of nonholonomic systems with a nontrivial momentum equation in the context of the work of Bloch, Krishnaprasad, Marsden, and Murray [Arch. Rational Mech. Anal., (1996), to appear]. The snakeboard is used to illustrate the method.

Consistent Interactions Between Gauge Fields: The Cohomological Approach

Abstract: The cohomological approach to the problem of consistent interactions between fields with a gauge freedom is reviewed. The role played by the BRST symmetry is explained. Applications to massless vector fields and 2-form gauge fields are surveyed.

Symmetries and decay of the generalized Kadomtsev-Petviashvili solitary waves

Abstract: We prove that the solitary waves of the generalized Kadomtsev--Petviashvili equations, when they exist, are cylindrical with respect to the transverse variables and decay with an optimal algebraic rate.

Pattern formation in weakly damped parametric surface waves

Abstract: We present a theoretical study of nonlinear pattern formation in parametric surface waves for fluids of low viscosity, and in the limit of large aspect ratio. The analysis is based on a quasi-potential approximation to the equations governing fluid motion, followed by a multiscale asymptotic expansion in the distance away from threshold. Close to onset, the asymptotic expansion yields an amplitude equation which is of gradient form, and allows the explicit calculation of the functional form of the cubic nonlinearities. In particular, we find that three-wave resonant interactions contribute significantly to the nonlinear terms, and therefore are important for pattern selection. Minimization of the associated Lyapunov functional predicts a primary bifurcation to a standing wave pattern of square symmetry for capillary-dominated surface waves, in agreement with experiments. In addition, we find that patterns of hexagonal and quasi-crystalline symmetry can be stabilized in certain mixed capillary-gravity waves, even in this case of single-frequency forcing. Quasi-crystalline patterns are predicted in a region of parameters readily accessible experimentally.

Molecular symmetry and group theory

Abstract: Fundamental Concepts. Representations of Groups. Techniques and Relationships for Chemical Applications. Symmetry and Chemical Bonding. Equations for Wave Functions. Vibrational Spectroscopy. Transition Metal Complexes. Appendices. Index.

Effect of surface anisotropy on the exchange resonance modes

Abstract: Exchange resonance modes in small ferromagnetic spheres were first predicted for the case of a cylindrical symmetry of the magnetization configurations. It is shown here that when the constraint of this symmetry is removed, other modes are also possible, but their lowest resonance frequency is very nearly the same as that of one of the cylindrically symmetric modes. Therefore, new resonances may only be sought at higher frequencies than those observed in the most recent experiment. It is also shown that the dependence on the particle size observed in that experiment may be accounted for by assuming a rather strong surface anisotropy in the measured spheres. The original prediction of an R−2 dependence, typical for the curling mode, may still be reached if either the particle size or the surface anisotropy is considerably reduced.

Dirac symmetry operators from conformal Killing - Yano tensors

Abstract: We show how, for all dimensions and signatures, a symmetry operator for the massless Dirac equation can be constructed from a conformal Killing - Yano tensor of arbitrary degree.

Pure d x 2 - y 2 order-parameter symmetry in the tetragonal superconductor TI 2 Ba 2 CuO 6+δ

Abstract: Crucial to the successful development of a theoretical model for high-temperature superconductivity is knowledge of the symmetry of the order parameter (or wavefunction) that describes the pairing of electrons in the superconducting state. Several experimental studies1–8provide convincing evidence for an anisotropic order parameter, consistent with a symmetry. But none of these earlier experiments could rule out unambiguously an additional contribution from isotropic s-wave pairing; these experiments either involved superconductors with an orthorhombic crystal structure (for which a mixed s + d state is becoming increasingly recognized as a likely consequence9,10), or their interpretation required detailed modelling of the uncertain effects of disorder and defects. Here we report the results of an experiment designed to circumvent these difficulties: the material studied is the single-layer tetragonal superconductor Tl2Ba2CuO6+δ, and the experimental configuration is such that the interpretation of the results relies solely on symmetry considerations. Our results indicate that this material has pure pairing symmetry, so providing a starting point for understanding the more complex mixed s + d state that appears to characterize other high-temperature superconductors.

General symmetry selection rules for the photoionization of polyatomic molecules

Abstract: General rovibronic symmetry selection rules, which are applicable to any molecular symmetry, have been obtained for the photoionization of polyatomic molecules. The use of the molecular symmetry groups leads to a particularly transparent derivation. The photoelectron is characterized by a partial wave expansion in the orbital angular momentum quantum number l. For a given value of l, one-photon electric dipole transitions can only occur between neutral and ionic states that obey the rovibronic symmetry conditions Γrve (neutral) ⊗ Γrve (ion) ⊃ Γ* for l even and Γrve(neutral) ⊗ Γrve(ion) ⊃ Γ(s) for l odd, where Γ(s) and Γ* represent the totally symmetric and the antisymmetric representations, respectively. Combined with the wellknown angular momentum conservation selection rule Δ J = J + - J = l + , l + ½,…, l - ½, l - [EQUATION](where J + and J represent the total angular momentum quantum number of the ionic and the neutral state between which the photoelectronic transition occurs), these symmetry selectio...

Nöther Symmetries in Bianchi Universes

Abstract: We use our Nother Symmetry Approach to study the Einstein equations minimally coupled with a scalar field, in the case of Bianchi universes of class A and B. Possible cases, when such symmetries exist, are found and two examples of exact integration of the equations of motion are given in the cases of Bianchi AI and BV.

On edge states in superconductors with time inversion symmetry breaking

Abstract: Superconducting states with different internal topology are discussed for the layered high-T c materials. If the time inversion symmetry is broken, the superconductivity is determined not only by the symmetry of the superconducting state but also by the topology of the ground state. The latter is determined by the integer-valued momentum-space topological invariant N. The current carrying boundary between domains with different N (N 2≠N 1) is considered. The current is produced by fermion zero modes, the number of which per layer is 2(N 2−2N 1).

Dynamics of a ring of pulse-coupled oscillators : group theoretic approach

Abstract: The dynamics of coupled oscillator arrays has been the subject of much recent experimental and theoretical interest. Example systems include Josephson junctions [1,2], lasers [3], oscillatory chemical reactions [4], heart pacemaker cells [5], central pattern generators [6], and cortical neural oscillators [7]. In many applications the oscillators are identical, dissipative, and the coupling is symmetric. Under such circumstances one can exploit the symmetry of the system to determine generic features of the dynamics such as the emergence of certain classes of solutions due to symmetry breaking bifurcations. Group-theoretic methods have been used to study both small amplitude oscillators on a ring near a Hopf bifurcation [8], and weakly coupled oscillators under phase averaging [9]. Symmetry arguments have also been used to construct central pattern generators for animal gaits [10] and to establish the existence of periodic orbits in Josephson junction series arrays [11]. Most work to date on the role of symmetry in coupled oscillator arrays has assumed that the interactions between elements of the array are smooth. On the other hand, many biological oscillators communicate with impulses as exemplified by the so-called integrate-and-fire model [12]. This latter model has recently sparked interest within the physics community due to connections with stick-slip models and self-organized criticality [13]. In Ref. [12], it was rigorously proved that globally coupled integrate-and-fire oscillators always synchronize in the presence of excitatory coupling. However, more biologically realistic models have spatially structured patterns of excitatory or inhibitory connections, and delayed couplings. It is an important issue to determine how the dynamics of pulse-coupled oscillators depends on the distribution of delays and the range of interactions. As we shall show here, the analysis of such systems is considerably facilitated by exploiting the underlying symmetries of the system. In this Letter we use group-theoretic methods to analyze the dynamics of a ring of N identical integrate-andfire oscillators with delayed interactions. In particular, we derive conditions for the existence of periodic, phaselocked solutions in which every oscillator fires with the same frequency; the latter is determined self-consistently. This set of conditions is invariant under the action of the spatiotemporal symmetry group DN 3 S 1 , where DN is the group of cyclic permutations and reflections in the ring and S 1 represents constant phase shifts in the direction of the flow. We classify the symmetries of the periodic solutions and indicate how this may be used to construct bifurcation diagrams. We also show how our results reduce to those of a corresponding phase-coupled model in the weak coupling regime. Consider a circular array of N identical pulse-coupled integrate-and-fire oscillators labeled n › 1, ... , N. Let Unstd denote the state of the nth oscillator at time t. Suppose that Unstd satisfies the set of coupled equations dUnstd

Improving flavor symmetry in the Kogut-Susskind hadron spectrum

Abstract: We study the effect of modifying the coupling of Kogut-Susskind quarks to the gauge field by replacing the link matrix in the quark action by a ``fat link,'' or sum of link plus three-link paths. Flavor symmetry breaking, determined by the mass difference between the Goldstone and non-Goldstone local pions, is reduced by approximately a factor of 2 by this modification.

Matrix Hamiltonians: SUSY approach to hidden symmetries

Abstract: A new supersymmetric approach to dynamical symmetries for matrix quantum systems is explored. In contrast to standard one-dimensional quantum mechanics where there is no role for an additional symmetry due to nondegeneracy, matrix Hamiltonians allow nontrivial residual symmetries. This approach is based on a generalization of the intertwining relations familiar in SUSY quantum mechanics. The corresponding matrix supercharges, of first or of second order in derivatives, lead to an algebra which incorporates an additional block diagonal differential matrix operator (referred to as a `hidden' symmetry operator) found to commute with the super-Hamiltonian. We discuss some physical interpretations of such dynamical systems in terms of spin particle in a magnetic field or in terms of coupled channel problem. Particular attention is paid to the case of transparent matrix potentials.