Showing papers on "Symmetry (physics) published in 2000"

Pairing symmetry in cuprate superconductors

Abstract: Pairing symmetry in the cuprate superconductors is an important and controversial topic. The recent development of phase-sensitive tests, combined with the refinement of several other symmetry-sensitive techniques, has for the most part settled this controversy in favor of predominantly $d$-wave symmetry for a number of optimally hole- and electron-doped cuprates. This paper begins by reviewing the concepts of the order parameter, symmetry breaking, and symmetry classification in the context of the cuprates. After a brief survey of some of the key non-phase-sensitive tests of pairing symmetry, the authors extensively review the phase-sensitive methods, which use the half-integer flux-quantum effect as an unambiguous signature for $d$-wave pairing symmetry. A number of related symmetry-sensitive experiments are described. The paper concludes with a brief discussion of the implications, both fundamental and applied, of the predominantly $d$-wave pairing symmetry in the cuprates.

Hierarchies without symmetries from extra dimensions

Abstract: It is commonly thought that small couplings in a low-energy theory, such as those needed for the fermion mass hierarchy or proton stability, must originate from symmetries in a high-energy theory. We show that this expectation is violated in theories where the standard model fields are confined to a thick wall in extra dimensions, with the fermions ''stuck'' at different points in the wall. Couplings between them are then suppressed due to the exponentially small overlaps of their wave functions. This provides a framework for understanding both the fermion mass hierarchy and proton stability without imposing symmetries, but rather in terms of higher dimensional geography. A model independent prediction of this scenario is non-universal couplings of the standard model fermions to the ''Kaluza-Klein'' excitations of the gauge fields. This allows a measurement of the fermion locations in the extra dimensions at the CERN LHC or NLC if the wall thickness is close to the TeV scale. (c) 2000 The American Physical Society.

Controlled Lagrangians and the stabilization of mechanical systems. I. The first matching theorem

Abstract: We develop a method for the stabilization of mechanical systems with symmetry based on the technique of controlled Lagrangians. The procedure involves making structured modifications to the Lagrangian for the uncontrolled system, thereby constructing the controlled Lagrangian. The Euler-Lagrange equations derived from the controlled Lagrangian describe the closed-loop system, where new terms in these equations are identified with control forces. Since the controlled system is Lagrangian by construction, energy methods can be used to find control gains that yield closed-loop stability. We use kinetic shaping to preserve symmetry and only stabilize systems module the symmetry group. The procedure is demonstrated for several underactuated balance problems, including the stabilization of an inverted planar pendulum on a cart moving on a line and an inverted spherical pendulum on a cart moving in the plane.

Numerical investigation of transitional and weak turbulent flow past a sphere

Abstract: This work reports results of numerical simulations of viscous incompressible flow past a sphere. The primary objective is to identify transitions that occur with increasing Reynolds number, as well as their underlying physical mechanisms. The numerical method used is a mixed spectral element/Fourier spectral method developed for applications involving both Cartesian and cylindrical coordinates. In cylindrical coordinates, a formulation, based on special Jacobi-type polynomials, is used close to the axis of symmetry for the efficient treatment of the ‘pole’ problem. Spectral convergence and accuracy of the numerical formulation are verified. Many of the computations reported here were performed on parallel computers. It was found that the first transition of the flow past a sphere is a linear one and leads to a three-dimensional steady flow field with planar symmetry, i.e. it is of the ‘exchange of stability’ type, consistent with experimental observations on falling spheres and linear stability analysis results. The second transition leads to a single-frequency periodic flow with vortex shedding, which maintains the planar symmetry observed at lower Reynolds number. As the Reynolds number increases further, the planar symmetry is lost and the flow reaches a chaotic state. Small scales are first introduced in the flow by Kelvin–Helmholtz instability of the separating cylindrical shear layer; this shear layer instability is present even after the wake is rendered turbulent.

Directed Current due to Broken Time-Space Symmetry.

Abstract: We consider the classical dynamics of a particle in a one-dimensional space-periodic potential U(X) = U(X+2pi) under the influence of a time-periodic space-homogeneous external field E(t) = E(t+T). If E(t) is neither a symmetric function of t nor antisymmetric under time shifts E(t+/-T/2) not equal-E(t), an ensemble of trajectories with zero current at t = 0 yields a nonzero finite current as t-->infinity. We explain this effect using symmetry considerations and perturbation theory. Finally we add dissipation (friction) and demonstrate that the resulting set of attractors keeps the broken symmetry property in the basins of attraction and leads to directed currents as well.

Temporally stable coherent states for infinite well and P\"oschl-Teller potentials

Abstract: This paper is a direct illustration of a construction of coherent states which has been recently proposed by two of us (JPG and JK). We have chosen the example of a particle trapped in an infinite square-well and also in Poschl-Teller potentials of the trigonometric type. In the construction of the corresponding coherent states, we take advantage of the simplicity of the solutions, which ultimately stems from the fact they share a common SU(1,1) symmetry a la Barut--Girardello. Many properties of these states are then studied, both from mathematical and from physical points of view.

The Geometry of¶(Super) Conformal Quantum Mechanics

Abstract: N-particle quantum mechanics described by a sigma model with an N-dimensional target space with torsion is considered. It is shown that an SL(2,ℝ) conformal symmetry exists if and only if the geometry admits a homothetic Killing vector D a δ a whose associated one-form D a dX a is closed. Further, the SL(2,ℝ) can always be extended to Osp(1|2) superconformal symmetry, with a suitable choice of torsion, by the addition of N real fermions. Extension to SU(1,1|1) requires a complex structure I and a holomorphic U(1) isometry D a I a b δ b . Conditions for extension to the superconformal group D(2,1;α), which involve a triplet of complex structures and SU(2)×SU(2) isometries, are derived. Examples are given.

How massless are massless fields in $AdS_d$

Abstract: Massless fields of generic Young symmetry type in $AdS_d$ space are analyzed. It is demonstrated that in contrast to massless fields in Minkowski space whose physical degrees of freedom transform in irreps of $o(d-2)$ algebra, $AdS$ massless mixed symmetry fields reduce to a number of irreps of $o(d-2)$ algebra. From the field theory perspective this means that not every massless field in flat space admits a deformation to $AdS_d$ with the same number of degrees of freedom, because it is impossible to keep all of the flat space gauge symmetries unbroken in the AdS space. An equivalent statement is that, generic irreducible AdS massless fields reduce to certain reducible sets of massless fields in the flat limit. A conjecture on the general pattern of the flat space limit of a general $AdS_d$ massless field is made. The example of the three-cell ``hook'' Young diagram is discussed in detail. In particular, it is shown that only a combination of the three-cell flat-space field with a graviton-like field admits a smooth deformation to $AdS_d$.

Symmetry Analysis of Differential Equations with Mathematica

Abstract: We will discuss three different methods for finding symmetry solutions based on the Frechet derivative common to each procedure. The methods discussed are Lie's standard procedure of symmetry analysis, the nonclassical method, and the derivation of potential symmetries. A ferromagnet in a strong external field represented by a nonlinear telegraph equation serves as an example describing the application of all three methods. The symmetry methods discussed are realized in a Mathematica package called MathLie performing all of the required calculations.

Reduction theory and the Lagrange-Routh equations

Abstract: Reduction theory for mechanical systems with symmetry has its roots in the classical works in mechanics of Euler, Jacobi, Lagrange, Hamilton, Routh, Poincare, and others. The modern vision of mechanics includes, besides the traditional mechanics of particles and rigid bodies, field theories such as electromagnetism, fluid mechanics, plasma physics, solid mechanics as well as quantum mechanics, and relativistic theories, including gravity. Symmetries in these theories vary from obvious translational and rotational symmetries to less obvious particle relabeling symmetries in fluids and plasmas, to subtle symmetries underlying integrable systems. Reduction theory concerns the removal of symmetries and their associated conservation laws. Variational principles, along with symplectic and Poisson geometry, provide fundamental tools for this endeavor. Reduction theory has been extremely useful in a wide variety of areas, from a deeper understanding of many physical theories, including new variational and Poisson structures, to stability theory, integrable systems, as well as geometric phases. This paper surveys progress in selected topics in reduction theory, especially those of the last few decades as well as presenting new results on non-Abelian Routh reduction. We develop the geometry of the associated Lagrange–Routh equations in some detail. The paper puts the new results in the general context of reduction theory and discusses some future directions.

Strings in AdS_3 and SL(2,R) WZW Model : I

Abstract: In this paper we study the spectrum of bosonic string theory on AdS_3. We study classical solutions of the SL(2,R) WZW model, including solutions for long strings with non-zero winding number. We show that the model has a symmetry relating string configurations with different winding numbers. We then study the Hilbert space of the WZW model, including all states related by the above symmetry. This leads to a precise description of long strings. We prove a no-ghost theorem for all the representations that are involved and discuss the scattering of the long string.

Universal symmetry property of point defects in crystals

Abstract: Point defects (vacancies, solute atoms, and disorder) are ubiquitous in crystalline solids. With in situ transmission electron microscopy we find clear evidence for the existence of a universal symmetry property of point defects; i.e., the symmetry of short-range order of point defects follows the crystal symmetry when in equilibrium. We further show that this symmetry-conforming property can lead to various interesting effects including ``aging-induced microstructure memory'' and the associated ``time-dependent two-way shape memory.''

Relativistic Symmetry Suppresses Quark Spin-Orbit Splitting

Abstract: Experimental data indicate small spin-orbit splittings in hadrons. For heavy-light mesons we identify a relativistic symmetry that suppresses these splittings. We suggest an experimental test in electron-positron annihilation. Furthermore, we argue that the dynamics necessary for this symmetry are possible in QCD.

Do secondary orbital interactions really exist

Abstract: A revision of the most typical examples used to illustrate the existence of secondary orbital interactions (SOI) has been achieved. However, our analysis indicates that no conclusive evidence can be obtained from these cases. All five examples proposed by Woodward and Hoffmann in The Conservation of Orbital Symmetry have been revisited. A combination of well-known mechanisms (such as solvent effects, steric interactions, hydrogen bonds, electrostatic forces, and others) can be invoked instead to justify the endo/exo selectivity of Diels−Alder reactions.

Higher-Order Corrections to the Effective Gravitational Action from Noether Symmetry Approach

Abstract: Higher-order corrections of the Einstein–Hilbert action of general relativity can be recovered by imposing the existence of a Noether symmetry to a class of theories of gravity where the Ricci scalar R and its d'Alembertian □ R are present. In several cases, it is possible to get exact cosmological solutions or, at least, to simplify the dynamics by recovering constants of motion. The main result is that a Noether vector seems to rule the presence of higher-order corrections of gravity.

Fine structure of defects in radial nematic droplets

Abstract: We investigate the structure of defects in nematic liquid crystals confined in spherical droplets and subject to radial strong anchoring. Equilibrium configurations of the order-parameter tensor field in a Landau--de Gennes free energy are numerically modeled using a finite-element package. Within the class of axially symmetric fields, we find three distinct solutions: the familiar radial hedgehog, the small ring (or loop) disclination predicted by Penzenstadler and Trebin, and a solution that consists of a short disclination line segment along the rotational symmetry axis terminating in isotropic end points. Phase and bifurcation diagrams are constructed to illustrate how the three competing configurations are related. They confirm that the transition from the hedgehog to the ring structure is first order. The third configuration is metastable (in our symmetry class) and forms an alternate solution branch bifurcating off the radial hedgehog branch at the temperature below which the hedgehog ceases to be metastable. Dependence on temperature, droplet size, and elastic constants is investigated, and comparisons with other studies are made.

Theory of fabric-reinforced viscous fluids

Abstract: Constitutive equation are formulated for flow of fabric-reinforced composite materials which show viscous response at the forming temperature. It is shown that in general the characterization for linear viscous response involves five viscosity coefficients, but this number may be reduced as a result of material symmetry of the fabric. In the case in which the material is a plane sheet, the rheological behaviour is described by a single function of the current angle between the fibre directions. The theory is applied to the analysis of the ‘picture-frame’ experiment, and it is shown that this experiment provides a method of measuring the response function. The effect of symmetry of the fabric architecture is considered, and it is found that for some fabric symmetries the theory allows the possibility of different responses to in-plane shearing in different shearing directions, as has been observed in picture-frame experiments. The general theory for nonlinear viscosity is also formulated, and specialized to the analysis of plane sheets, and in particular to the case of a power law fluid. In this case also, it is shown that the material can be characterized by a single response function of the rate-of deformation and the angle between the fibre directions.

Selection Rules in Minisuperspace Quantum Cosmology

Abstract: The existence of a Noether symmetry for a given minisuperspace cosmological model is a sort of selection rule to recover classical behaviours in cosmic evolution since oscillatory regimes for the wave function of the universe come out. The so-called Hartle criterion to select correlated regions in the configuration space of dynamical variables can be directly connected to the presence of a Noether symmetry and we show that such a statement works for generic extended theories of gravity in the framework of minisuperspace approximation. Examples and exact cosmological solutions are given for nonminimally coupled and higher-order theories.

Continuous rearrangement and symmetry of solutions of elliptic problems

Abstract: This work presents new results and applications for the continuous Steiner symmetrization. There are proved some functional inequalities, e.g. for Dirichlet-type integrals and convolutions and also continuity properties in Sobolev spaces W 1; p . Further it is shown that the local minimizers of some variational problems and the nonnegative solutions of some semilinear elliptic problems in symmetric domains satisfy a weak, 'local' kind of symmetry.