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Showing papers on "Symmetry (physics) published in 1999"


Journal ArticleDOI
TL;DR: In this paper, the authors presented an identity relating the partition function of N = 4 supersymmetric QED to that of its dual under mirror symmetry, which is a generalized Fourier transform.
Abstract: We present an identity relating the partition function of N = 4 supersymmetric QED to that of its dual under mirror symmetry. The identity is a generalized Fourier transform. Many known properties of abelian theories can be derived from this formula, including the mirror transforms for more general gauge and matter content. We show that N = 3 Chern-Simons QED and N = 4 QED with BF-type couplings are conformal field theories with exactly marginal couplings. Mirror symmetry acts on these theories as strong-weak coupling duality. After identifying the mirror of the gauge coupling (sometimes called the "magnetic coupling") we construct a theory which is exactly mirror - at all scales - to N = 4 SQED. We also study vortex-creation operators in the large N-f limit.

381 citations


Journal ArticleDOI
TL;DR: In this paper, a new method of representing non-spherical, smooth-surfaced, axi-symmetrical particles in discrete element (DE) simulation using model particles comprising overlapping spheres of arbitrary size whose centres are fixed in position relative to each other along the major axis of symmetry of the particle is presented.
Abstract: A new method of representing non‐spherical, smooth‐surfaced, axi‐symmetrical particles in discrete element (DE) simulation using model particles comprising overlapping spheres of arbitrary size whose centres are fixed in position relative to each other along the major axis of symmetry of the particle is presented. Contact detection and calculation of force‐deformation and particle movement is achieved using standard DE techniques modified to integrate the behaviour of each element sphere with that of the multi‐element particle to which it belongs. The method enables the dynamic behaviour of particles of high aspect ratio and irregular curvature (in two dimensions) to be modelled. The use of spheres to represent a particle takes advantage of the computational speed and accuracy of contact detection for spheres, which should make the method comparable in computational efficiency to alternative schemes for representing non‐spherical particles.

344 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that a system of self-propelled particles exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions.
Abstract: We demonstrate that a system of self-propelled particles exhibits spontaneous symmetry breaking and self-organization in one dimension, in contrast with previous analytical predictions. To explain this surprising result we derive a new continuum theory that can account for the development of the symmetry broken state and belongs to the same universality class as the discrete self-propelled particle model.

264 citations


Journal ArticleDOI
TL;DR: In this article, the full symmetry groups for all single-wall and multi-wall carbon nanotubes are found, and the optical activity is studied within this framework, and a detailed classification of the possible nanotube-based optical devices is given.
Abstract: The full symmetry groups for all single-wall and multiwall carbon nanotubes are found. As for the single-wall tubes, the symmetries form non-Abelian nonsymorphic line groups, enlarging the groups reported in the literature. In the multiwall case, any type of line and axial point groups can be obtained, depending on single-wall constituents and their relative position. The isogonal symmetry is related to the macroscopic tensor properties of the nanotubes. The optical activity is studied within this framework, and a detailed classification of the possible nanotube-based optical devices is given. At the microscopic level, full symmetry is used to find general forms of the characteristic functions of the nanotubes. In particular, the stability of the double-wall configurations and the possibility of chiral currents are discussed. Several other consequences are discussed: quantum numbers and related selection rules, phonon spectra, etc. In particular, the bands of the zigzag and the armchair tubes are generally expected to be fourfold degenerate.

255 citations


Journal ArticleDOI
TL;DR: In this paper, a mechanism of symmetry transition upon compactification of a 5-dimensional field theory on $S^1/Z_2 was studied, where all components in a multiplet of a symmetry group have a common parity on the field theory.
Abstract: We study a mechanism of symmetry transition upon compactification of a 5-dimensional field theory on $S^1/Z_2$. The transition occurs unless all components in a multiplet of a symmetry group have a common $Z_2$ parity on $S^1/Z_2$. This mechanism is applied to a reduction of SU(5) gauge symmetry in grand unified theory, and phenomenological implications are discussed.

204 citations


Journal ArticleDOI
TL;DR: In this paper, the authors studied the large-N reduced model of D-dimensional Yang-Mills theory with special attention to dynamical aspects related to the eigenvalues of the N × N matrices, which correspond to the space-time coordinates in the IIB matrix model.

171 citations


Journal ArticleDOI
TL;DR: In this article, a p-adic expression for the Parisi replica matrix is given and moreover, in the case of spontaneous symmetry breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of padic fractional differentiation.
Abstract: Methods of p-adic analysis are applied to the investigation of spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the Parisi replica matrix is given and, moreover, the Parisi replica matrix in models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also, the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) is investigated using p-adic analysis.

170 citations


Journal ArticleDOI
TL;DR: In this article, the authors generalize the (p,q) 5-brane web construction of five-dimensional field theories by introducing 7-branes, and apply this construction to theories with a one-dimensional Coulomb branch.
Abstract: We generalize the (p,q) 5-brane web construction of five-dimensional field theories by introducing (p,q) 7-branes, and apply this construction to theories with a one-dimensional Coulomb branch. The 7-branes render the exceptional global symmetry of these theories manifest. Additionally, 7-branes allow the construction of all En theories up to n = 8, previously not possible in 5-brane configurations. The exceptional global symmetry in the field theory is a subalgebra of an affine symmetry on the 7-branes, which is necessary for the existence of the system. We explicitly determine the quantum numbers of the BPS states of all En theories using two simple geometrical constraints.

170 citations


Journal ArticleDOI
TL;DR: Using supersymmetry, the corresponding network model is mapped to a classical loop model, whose boundary critical behavior was recently determined exactly, and predictions of the exact solution are verified by extensive numerical simulations.
Abstract: We consider the spin quantum Hall transition which may occur in disordered superconductors with unbroken SU(2) spin-rotation symmetry but broken time-reversal symmetry. Using supersymmetry, we map a model for this transition onto the two-dimensional percolation problem. The anisotropic limit is an sl(2|1) supersymmetric spin chain. The mapping gives exact values for critical exponents associated with disorder-averages of several observables in good agreement with recent numerical results.

161 citations


Journal ArticleDOI
TL;DR: In this article, a comprehensive review is given on experimental studies of small particles with fivefold symmetry accompanied by an in-depth theoretical description of their characteristics and computer modeling, including the cases of uniform and nonuniform deformations (disclination model), stability and relaxation of elastic stresses in pentagonal particles and needle-like crystals.
Abstract: A comprehensive review is given on experimental studies of small particles with fivefold symmetry accompanied by an in-depth theoretical description of their characteristics and computer modeling. The cases of uniform and nonuniform deformations (disclination model), stability and relaxation of elastic stresses in pentagonal particles and needle-like crystals, models of their formation are discussed.

150 citations


Journal ArticleDOI
TL;DR: In this article, a robust algorithm is presented that determines the symmetries present in an atomic configuration and idealizes the cell parameters according to the crystal system suggested by the detected symmetry.
Abstract: A robust algorithm is presented that determines the symmetries present in an atomic configuration and idealizes the cell parameters according to the crystal system suggested by the symmetries detected. No information besides the coordinates of the atoms within some arbitrary unit cell of the crystal is required.

Journal ArticleDOI
TL;DR: In this article, a p-adic expression for the replica matrix is given and moreover, a replica matrix in the models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of padic fractional differentiation.
Abstract: Methods of p-adic analysis are applied to the investigation of the spontaneous symmetry breaking in the models of spin glasses. A p-adic expression for the replica matrix is given and moreover the replica matrix in the models of spontaneous breaking of the replica symmetry in the simplest case is expressed in the form of the Vladimirov operator of p-adic fractional differentiation. Also the model of hierarchical diffusion (that was proposed to describe relaxation of spin glasses) investigated using p-adic analysis.

Journal ArticleDOI
TL;DR: In this paper, a new exactly solvable PT invariance model for complex potentials with real symmetry with imaginary antisymmetry was proposed. But the model is not deterministic.

Journal ArticleDOI
TL;DR: In this article, it was shown that the nonlinear diffusion equation can be reduced to Fujita's equation if it admits a class of generalized conditional symmetry, and some new exact solutions for a number of important non-linear diffusion equations are obtained.
Abstract: In this paper, we discuss the reduction to Fujita's equation for the nonlinear diffusion equation under certain types of generalized conditional symmetry. It is shown that the nonlinear diffusion equation can be reduced to Fujita's equation if it admits a class of generalized conditional symmetry. As the results, some new exact solutions for a number of important nonlinear diffusion equations are obtained. Many of the solutions obtained here are illustrated graphically with particular reference to the phenomena of extinction, periodic property, blow-up and asymptotical behaviour.

Journal ArticleDOI
TL;DR: In this article, a 3-dimensional Cartesian (x,y,z) coordinate grid is used to simulate axisymmetric systems about the z axis, which avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity.
Abstract: We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3+1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x,y,z) coordinate grid which covers (say) the y=0 plane, but is only one finite-difference-molecule--width thick in the y direction. The field variables in the central y=0 grid plane can be updated using normal (x,y,z)--coordinate finite differencing, while those in the y eq 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3+1 numerical general relativity, involving both black holes and collapsing gravitational waves.

Book
30 Jun 1999
TL;DR: The Petrov Classification of symmetry inheritance is presented in this paper, where the authors define symmetry inheritance as the inheritance of symmetry groups and symmetries of some geometric structures, such as Semi-Riemannian Manifolds, Hypersurfaces, Lie Derivatives and Symmetry Groups.
Abstract: Dedication. Preface. 1. Preliminaries. 2. Semi-Riemannian Manifolds and Hypersurfaces. 3. Lie Derivatives and Symmetry Groups. 4. Spacetimes of General Relativity. 5. Killing and Affine Killing Vector Fields. 6. Homothetic and Conformal Symmetries. 7. Connection and Curvature Symmetries. 8. Symmetry Inheritance. 9. Symmetries of Some Geometric Structures. A: The Petrov Classification. Bibliography. Index.

Journal ArticleDOI
TL;DR: In this paper, the conformal Einstein equations for polytropic perfect fluid cosmologies admit an isotropic singularity, and it is shown that the Cauchy problem for these equations is wellposed, that solutions exist, are unique, and depend smoothly on the data, with data consisting of simply the 3metric of the singularity.

Journal ArticleDOI
TL;DR: In this article, the pairing state due to the usual BCS mechanism in substances of cubic and hexagonal symmetry where the Fermi surface forms pockets around several points of high symmetry is considered.
Abstract: We consider the pairing state due to the usual BCS mechanism in substances of cubic and hexagonal symmetry where the Fermi surface forms pockets around several points of high symmetry. We find that the symmetry imposed on the multiple pocket positions could give rise to a multidimensional nontrivial superconducting order parameter. The time-reversal symmetry in the pairing state is broken. We suggest several candidate substances where such ordering may appear, and discuss means by which such a phase may be identified.

Journal ArticleDOI
TL;DR: In this paper, a quantum kinetic equation describing both boson and fermion pair production was analyzed and the solution of the non-Markovian kinetic equation was explored analytically and numerically.
Abstract: We analyze a quantum kinetic equation describing both boson and fermion pair production and explore analytically and numerically the solution of the non-Markovian kinetic equation. In the low density limit of the kinetic equation we find an analytical solution for the single particle distribution function of bosons and fermions. The numerical investigation for a homogeneous, constant electric field shows an enhancement (bosons) or a suppression (fermions) of the pair creation rate according to the symmetry character of the produced particles. For strong fields non-Markovian effects are important while they disappear for weak fields. Hence it is sufficient to apply the low density limit for weak fields but necessary to take into account memory effects for strong fields.

Journal ArticleDOI
TL;DR: In this paper, the volume spectrum of a loop quantum theory of cosmological models with rotational symmetry has been calculated and its implications for quantum cosmology have been discussed; it is observed that the stronger the symmetry conditions are, the smaller the spectrum, which can be interpreted as level splitting due to broken symmetry.
Abstract: Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly. It is observed that the stronger the symmetry conditions are the smaller is the volume spectrum, which can be interpreted as level splitting due to broken symmetries. Some implications for quantum cosmology are presented.

Journal ArticleDOI
TL;DR: In this article, a symmetry reduction method is proposed, implemented and studied to stabilize topology design formulations, with the added benefit of greatly simplified design sensitivity analysis of non-simple repeated vibrational eigenvalues which occur in many symmetrical structures.

Journal ArticleDOI
TL;DR: In this paper, the amplitude for exchange of massless gauge bosons between pairs of massive scalar fields in anti-de Sitter space was studied and a concise, covariant, Y2K compatible derivation of the gauge boson propagator in AdS d + 1 was given.

Journal ArticleDOI
TL;DR: The role of potential symmetry is studied in a three-field reaction-diffusion system presenting bistability by means of a two-state theory for stochastic resonance in general asymmetric systems, indicating that it is this feature which governs the optimization of the system's response to periodic signals.
Abstract: We study the role of potential symmetry in a three-field reaction-diffusion system presenting bistability by means of a two-state theory for stochastic resonance in general asymmetric systems. By analyzing the influence of different parameters in the optimization of the signal-to-noise ratio, we observe that this magnitude always increases with the symmetry of the system's potential, indicating that it is this feature which governs the optimization of the system's response to periodic signals.

Journal ArticleDOI
TL;DR: The classical n-dimensional Calogero-Moser system is a maximally superintegrable system endowed with a rich variety of symmetries and constants of motion as discussed by the authors.
Abstract: The classical n-dimensional Calogero–Moser system is a maximally superintegrable system endowed with a rich variety of symmetries and constants of motion. In the first part of the article some properties related with the existence of several families of constants of motion are analyzed. In the second part, the master symmetries and the time-dependent symmetries of this system are studied.

Journal ArticleDOI
TL;DR: In this article, the authors transform the spinning C-metric into Weyl coordinates and analyze some of its properties as Killing vectors and curvature invariants, and then a transformation is found which brings the metric into the canonical form of the radiative spacetimes with the boost-rotation symmetry.
Abstract: The spinning C-metric was discovered by Plebanski and Demianski as a generalization of the standard C-metric which is known to represent uniformly accelerated non-rotating black holes. We first transform the spinning C-metric into Weyl coordinates and analyze some of its properties as Killing vectors and curvature invariants. A transformation is then found which brings the metric into the canonical form of the radiative spacetimes with the boost-rotation symmetry. By analytically continuing the metric across "acceleration horizons", two new regions of the spacetime arise in which both Killing vectors are spacelike. We show that this metric can represent two uniformly accelerated, spinning black holes, either connected by a conical singularity, or with conical singularities extending from each of them to infinity. The radiative character of the metric is briefly discussed.

Journal ArticleDOI
TL;DR: In this paper, a near-horizon limit is found in which the quantum mechanics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes.
Abstract: Quantum mechanics on the moduli space of N supersymmetric Reissner-Nordstrom black holes is shown to admit 4 supersymmetries using an unconventional supermultiplet which contains 3N bosons and 4N fermions. A near-horizon limit is found in which the quantum mechanics of widely separated black holes decouples from that of strongly-interacting, near-coincident black holes. This near-horizon theory is shown to have an enhanced D(2,1;0) superconformal symmetry. The bosonic symmetries are SL(2,R) conformal symmetry and SU(2)xSU(2) R-symmetry arising from spatial rotations and the R-symmetry of N=2 supergravity.

Journal ArticleDOI
TL;DR: In this article, the existence and symmetry property of multi-bump solutions of −Δv+λV(x)v=vp,v>0,inRN was studied and conditions were given to assure that the multibump solutions obtained have prescribed subgroups of O(N) as their exact symmetry.

Proceedings ArticleDOI
01 Dec 1999
TL;DR: In this paper, the authors extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems, which complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables.
Abstract: We extend the method of controlled Lagrangians to include potential shaping for complete state-space stabilization of mechanical systems. The method of controlled Lagrangians deals with mechanical systems with symmetry and provides symmetry-preserving kinetic shaping and feedback-controlled dissipation for state-space stabilization in all but the symmetry variables. Potential shaping complements the kinetic shaping by breaking symmetry and stabilizing the remaining state variables. The approach also extends the method of controlled Lagrangians to include a class of mechanical systems without symmetry such as the inverted pendulum on a cart that travels along an incline.

Journal ArticleDOI
TL;DR: In this paper, the standard definition of cylindrical symmetry in general relativity is reviewed, and it is argued that the requirement of orthogonal transitivity of the isometry group should be dropped.
Abstract: The standard definition of cylindrical symmetry in general relativity is reviewed. Taking the view that axial symmetry is an essential prerequisite for cylindrical symmetry, it is argued that the requirement of orthogonal transitivity of the isometry group should be dropped, this leading to a new, more general definition of cylindrical symmetry. Stationarity and staticity in cylindrically symmetric spacetimes are then defined, and these issues are analysed in connection with orthogonal transitivity, thus proving some new results on the structure of the isometry group for this class of spacetimes.

Journal ArticleDOI
TL;DR: In this paper, the authors use group representation theory to identify the symmetry properties of any states of self-stress or mechanisms present in a symmetric structure, and show that in some cases, this linear analysis, combined with symmetry arguments, can show that particular mechanisms of an asymmetric structure must be finite.