Showing papers on "Symmetry (physics) published in 1989"

Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth

Abstract: On etudie les solutions regulieres non negatives de l'equation conformement invariante −Δu=u (n+2)/(n−2) , u>0 dans une boule perforee, B 1 (0)\{0}⊂R n , n≥3, avec une singularite isolee a l'origine

Gravitational Field of a Global Monopole

Abstract: We present an approximate solution of the Einstein equations for the metric outside a monopole resulting from the breaking of a global O(3) symmetry. The monopole exerts practically no gravitational force on nonrelativistic matter, but the space around it has a deficit solid angle, and all light rays are deflected by the same angle, independent of the impact parameter.

The Boundary and Crosscap States in Conformal Field Theories

Abstract: A method to obtain the boundary states and the crosscap states explicitly in various conformal field theories, is presented. This makes it possible to construct and analyse open string theories in several closed string backgrounds. We discuss the construction of such theories in the case of the backgrounds corresponding to the conformal field theories with SU(2) current algebra symmetry.

Gapless fermions and gauge fields in dielectrics.

Abstract: To study the nonmagnetic dielectric state and Mott transitions we consider an example of a two-dimensional modified Hubbard model with a large number of colors Low-energy excitations in this phase are fermionic excitations and Bose excitations described by gauge fields of the U(1) group The transition into the metal state has little effect on the fermionic spectrum, but it results in the local U(1) symmetry being broken and fermions becoming able to transfer charge excitations Apart from the half-filling, scalar Bose excitations also appear Due to the presence of additional gauge fields the physical conductivity is determined by the lowest conductivity of the Fermi or Bose subsystems

Gauged Q balls

Abstract: Classical non-topological soliton configurations are considered within the theory of a complex scalar field with a gauged U symmetry Their existence and stability against dispersion are demonstrated and some of their properties are investigated analytically and numerically The soliton configuration is such that inside the soliton the local U symmetry is broken, the gauge field becomes massive and for a range of values of the coupling constants the soliton becomes a superconductor pushing the charge to the surface Furthermore, because of the repulsive Coulomb force, there is a maximum size for these objects, making impossible the existence of Q-matter in bulk form Also briefly discussed are solitons with fermions in a U gauge theory

Least-squares finite element method for fluid dynamics

Abstract: An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Surface wave mode interactions: effects of symmetry and degeneracy

Abstract: Parametrically excited surface wave modes on a fluid layer driven by vertical forcing can interact with each other when more than one spatial mode is excited. We have investigated the dynamics of the interaction of two modes that are degenerate in a square layer, but non-degenerate in a rectangular one. Novel experimental techniques were developed for this purpose, including the real-time measurement of all relevant slowly varying mode amplitudes, investigation of the phase-space structure by means of transient studies starting from a variety of initial conditions, and automated determination of stability boundaries as a function of driving amplitude and frequency. These methods allowed both stable and unstable fixed points (sinks, sources, and saddles) to be determined, and the nature of the bifurcation sequences to be clearly established. In most of the dynamical regimes, multiple attractors and repellers (up to 16) were found, including both pure and mixed modes. We found that the symmetry of the fluid cell has dramatic effects on the dynamics. The fully degenerate case (square cell) yields no time-dependent patterns, and is qualitatively understood in terms of third-order amplitude equations whose basic structure follows from symmetry arguments. In a slightly rectangular cell, where the two modes are separated in frequency by a small amount (about 1%), mode competition produces both periodic and chaotic states organized around unstable pure and mixed-state fixed points.

Asymptotically flat radiative space-times with boost-rotation symmetry: The general structure

Abstract: This paper deals for the first time with boost-rotation-symmetric space-times from a unified point of view. Boost-rotation-symmetric space-times are the only explicitly known exact solutions of the Einstein vacuum field equations which describe moving singularities or black holes, are radiative and asymptotically flat in the sense that they admit global, though not complete, smooth null infinity, as well as spacelike and timelike infinities. They very likely represent the exterior fields of uniformly accelerated sources in general relativity and may serve as tests of various approximation methods, as nontrivial illustrations of the theory of the asymptotic structure of radiative space-times, and as test beds in numerical relativity. Examples are the {ital C}-metric or the solutions of Bonnor and Swaminarayan. The space-times are defined in a geometrical manner and their global properties are studied in detail, in particular their asymptotic structure. It is demonstrated how one can construct any asymptotically flat boost-rotation-symmetric space-time starting from the boost-rotation-symmetric solution of the flat-space wave equation. The problem of uniformly accelerated sources in special relativity is also discussed. The radiative properties and specific examples of the boost-rotation-symmetric space-times will be analyzed in a following paper.

Symmetry-breaking bifurcations in resonant surface waves

Abstract: Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

Cosmology of biased discrete symmetry breaking

Abstract: The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.

Broken symmetry in an unconventional superconductor: a model for the double transition in UPt3

Abstract: The authors present a model for the superconducting states of UPt3 in which a two-dimensional order parameter couples to a field that breaks the hexagonal symmetry of the crystal. This symmetry-breaking field (SBF) splits the superconducting transition, leading to two superconducting phases in zero field. The high-temperature superconducting phase exhibits the broken hexagonal symmetry of the SBF, while the low-temperature phase spontaneously breaks time-reversal symmetry. The authors calculate the specific heat jumps at both transitions and compare with the recent measurements by Fisher et al. They find that sizeable strong-coupling corrections are needed to explain the magnitude of the heat capacity jumps and the splitting of the transition. They show that a kink in the upper critical field occurs for fields in the basal plane. Comparison of the discontinuity in the slope of Hc2(T) with the data of Taillefer et al. (on a different UPt3 crystal) is in qualitative agreement with the heat capacity data. They also predict a change in slope of Hcl(T) at the temperature of the second peak in the heat capacity, for all field orientations. Observation of all three features in the same single crystal would provide convincing evidence for unconventional pairing in UPt3 and would be a stringent test of the model presented.

Special conformal Killing vector space‐times and symmetry inheritance

Abstract: Viscous heat‐conducting fluid and anisotropic fluid space‐times admitting a special conformal Killing vector (SCKV) are studied and some general theorems concerning the inheritance of the symmetry associated with the SCKV are proved. In particular, for viscous fluid space‐times it is shown that (i) if the SCKV maps fluid flow lines into fluid flow lines, then all physical components of the energy‐momentum tensor inherit the SCKV symmetry; or (ii) if the Lie derivative along a SCKV of the shear viscosity term ησab is zero then, again, we have symmetry inheritance. All space‐times admitting a SCKV and satisfying the dominant energy condition are found. Apart from the vacuum pp‐wave solutions, which are the only vacuum solutions that can admit a SCKV, the energy‐momentum tensor associated with these space‐times is shown to admit at least one null eigenvector and can represent either a viscous fluid with heat conduction or an anisotropic fluid. No perfect fluid space‐times can admit a SCKV. These SCKV space‐t...

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

Abstract: Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

Discrete symmetries in periodic-orbit theory

Abstract: The application of periodic-orbit theory to systems which possess a discrete symmetry is considered. A semiclassical expression for the symmetry-projected Green's function is obtained; it involves a sum over classical periodic orbits on a symmetry-reduced phase space, weighted by characters of the symmetry group. These periodic orbits correspond to trajectories on the full phase space which are not necessarily periodic, but whose end points are related by symmetry. If the symmetry-projected Green's functions are summed, the contributions of the unperiodic orbits cancel, and one recovers the usual periodic-orbit sum for the full Green's function. Several examples are considered, including the stadium billiard, a particle in a periodic potential, the Sinai billiard, the quartic oscillator, and the rotational spectrum of ${\mathrm{SF}}_{6}$. .AE

Linearised R+R 2 gravity: a new gauge and new solutions

Abstract: The author studies the linearised fourth-order field equations for gravitational theories with Lagrangians L=-g(R+1/2aR2+bRmu nu Rmu nu )- kappa Lm. He shows that a suitable choice of coordinate conditions involving third derivatives of the potentials leads directly to the general solution of these equations. He states appropriate junction conditions across a timelike (or spacelike) hypersurface of discontinuity. Using these junction conditions, and assuming the metric to be asymptotically flat at spatial infinity, he determines the potentials of an isolated static body in the case 3a+2b or=0. The new gauge yields the corresponding metric in a spatially isotropic form. These results are applied to a static spherically symmetric body: the potentials are obtained in a simple integral form when the rest-mass density of matter depends upon the distance from the centre. The results previously obtained for a pointlike distribution of matter and for a homogeneous sphere become trivial consequences of the general method.

Strings at superplanckian energies: in search of the string symmetry

Abstract: The characteristic energy scale of superstring theory, which attempts to unify all the interactions of matter with gravity, is the Planck energy of 10$^{28}$ eV. Although this energy is 16 orders of magnitude higher than currently accessible energies, it is important to consider the nature of string physics in this region since it could shed light on the non-perturbative physics at the Planck scale, which determines the structure of the vacuum. In this paper I review some recent attempts to explore this domain. In particular, I discuss string scattering at very high energies, the indications of the existence of a large symmetry that is restored at short distances and the possible breakdown of our concepts of space-time at these energies.

Atomic quantum states with maximum localization on classical elliptical orbits.

Abstract: We show how to build atomic states that mimic the classical Bohr-Sommerfeld elliptic orbits with minimum quantum fluctuations. These elliptic states are uniquely defined from symmetry considerations. They are the coherent states of the SO(4) symmetry group of the Coulomb interaction in three dimensions and are superpositions of the usual spherical states with well-defined weights and phases. They can be experimentally produced from laser excitation of Rydberg atoms in crossed electric and magnetic fields. We finally indicate how to build Coulomb wave packets localized both in space and time.

Gravitational fields of straight and circular cosmic strings: Relation between gravitational mass, angular deficit, and internal structure.

Abstract: The first part of the paper formulates general conditions (independent of a particular gauge-theoretic model) under which a cylindrical distribution of matter can be joined to a vacuum exterior with a conical geometry and exhibits the relation between angular deficit and internal structure. To bring out the relation to gravitational mass, the second part is devoted to a detailed study of solutions of the initial-value problem for circular loops of string at a moment of time symmetry.

Generalized Gaussian beam solutions of paraxial optics and their connection to a hidden symmetry

Abstract: It is shown that the Hermite–Gauss- and Laguerre–Gauss-type solutions of paraxial optics whose corresponding Hermite and Laguerre polynomials have complex arguments are closely related to a hidden symmetry in the parabolic equation. These solutions are generated from the fundamental Gaussian beam solution by applying the powers of the infinitesimal operators of this symmetry group. The Fourier spectrum of these solutions is obtained from the Fourier spectrum of the fundamental Gaussian beam solution in a similar manner. The Gaussian beam solutions containing Hermite polynomials with complex arguments that were derived by Siegman [ J. Opt. Soc. Am.63, 1093 ( 1973)] represent a limiting case of the more-general solutions considered here. The generalized Gaussian beam solutions show a sharp mode picture with exact zeros in the field distribution only in the focal or waist plane. Unconventional applications of the parabolic approximation in optics including focus wave modes are demonstrated.

Observable gauge transformations in the parton picture.

Abstract: The internal space-time symmetry of rapidly moving composite particles is stud- ied in terms of the little groups of the Poincare group. It is shown that Feynman's x parameter in his parton picture is a gauge transformation parameter.