Antisymmetric relation

About: Antisymmetric relation is a research topic. Over the lifetime, 3322 publications have been published within this topic receiving 64365 citations. The topic is also known as: antisymmetric property & anti-symmetric property.

Photonic bands of metallic systems. I. Principle of calculation and accuracy

Abstract: The dispersion relation, the field distribution, and the lifetime of the radiational eigenmodes in two-dimensional photonic crystals composed of metallic cylinders were calculated for the E polarization by means of the numerical simulation of the dipole radiation based on the finite-difference time-domain (FDTD) method. The convergence and the central processing unit time were compared with the plane-wave expansion method. The opaque frequency ranges in the transmission spectra calculated by the method of Pendry and MacKinnon corresponded quite well to the band gaps and the antisymmetric modes found in the photonic band diagram. The dispersion relation and the symmetry of the eigenmodes obtained by the numerical calculation were consistent with the prediction of the group theory and the analytical expression by the long-wavelength approximation.

Spontaneous symmetry breaking in a nonlinear double-well structure

Abstract: We propose a model of a nonlinear double-well potential (NDWP), alias a double-well pseudopotential, with the objective to study an alternative implementation of the spontaneous symmetry breaking (SSB) in Bose-Einstein condensates (BECs) and optical media, under the action of a potential with two symmetric minima. In the limit case when the NDWP structure is induced by the local nonlinearity coefficient represented by a set of two delta functions, a fully analytical solution is obtained for symmetric, antisymmetric, and asymmetric states. In this solvable model, the SSB bifurcation has a fully subcritical character. Numerical analysis, based on both direct simulations and computation of stability eigenvalues, demonstrates that, while the symmetric states are stable up to the SSB bifurcation point, both symmetric and emerging asymmetric states, as well as all antisymmetric ones, are unstable in the model with the delta functions. In the general model with a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the SSB bifurcation from the subcritical to supercritical type. Antisymmetric solutions may also get stabilized in the NDWP structure of the general type, which gives rise to a bistability between them and asymmetric states. The symmetric states require a finite norm for their existence, an explanation to which is given. A full diagram for the existence and stability of the trapped states in the model is produced. Experimental observation of the predicted effects should be possible in BEC formed by several hundred atoms.

Wave motion in an isotropic elastic layer generated by a time-harmonic point load of arbitrary direction

Abstract: Wave motion in an infinite elastic layer due to the application of a time-harmonic point load of arbitrary direction, applied either internally or on one of the faces of the layer, is expressed as a sum of four expansions in Lamb-wave modes and horizontally polarized wave modes. The point load is decomposed into components normal and parallel to the plate faces. Each of these cases is decomposed into a symmetric and an antisymmetric loading case, relative to the mid-plane of the layer. The displacement solutions for the symmetric and antisymmetric cases are expressed as expansions of symmetric and antisymmetric modes, respectively. Appropriate orthogonality relations are derived from reciprocity considerations. Elastodynamic reciprocity is also used in conjunction with dummy wave modes to obtain the coefficients in the wave-mode expansion.