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.

PT symmetry with a system of three-level atoms.

Abstract: We show that a vapor of multilevel atoms driven by far-off-resonant laser beams, with the possibility of interference of two Raman resonances, is highly efficient for creating parity-time symmetric profiles of the probe-field refractive index, whose real part is symmetric and imaginary part is antisymmetric in space. The spatial modulation of the probe-field susceptibility is achieved by a proper combination of standing-wave strong control fields and of Stark shifts induced by far-off-resonance laser fields. As particular examples we explore a mixture of isotopes of rubidium atoms and design a parity-time symmetric lattice and a parabolic refractive index with a linear imaginary part.

Analytical models for bistable cylindrical shells

Abstract: Thin cylindrical shell structures can show interesting bistable behaviour. If made unstressed from isotropic materials they are only stable in the initial configuration, but if made from fibre-reinforced composites they may also have a second, stable configuration. If the layup of the composite is antisymmetric, this alternative stable configuration forms a tight coil; if the layup is symmetric the alternative stable configuration is helical. A simple two-parameter model for these structure is presented that is able to distinguish between these different behaviours.

Superpolynomials for toric knots from evolution induced by cut-and-join operators

Abstract: The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R-matrix and ends up with a trivially-looking split W representation familiar from character calculus applications to matrix models and Hurwitz theory. Substitution of MacDonald polynomials for characters in these formulas provides a very simple description of "superpolynomials", much simpler than the recently studied alternative which deforms relation to the WZNW theory and explicitly involves the Littlewood-Richardson coefficients. A lot of explicit expressions are presented for different representations (Young diagrams), many of them new. In particular, we provide the superpolynomial P_[1]^[m,km\pm 1] for arbitrary m and k. The procedure is not restricted to the fundamental (all antisymmetric) representations and the torus knots, still in these cases some subtleties persist.