Topic
Symmetry (physics)
About: Symmetry (physics) is a research topic. Over the lifetime, 26435 publications have been published within this topic receiving 500189 citations. The topic is also known as: symmetry (physics) & physical symmetry.
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TL;DR: In this article, a detailed analysis of finite energy solitary waves in two-and three-dimensional nonlinear periodic structures exhibiting a complete photonic band gap is presented, where the important physical features such as the size, shape, peak intensity, and total energy of the solitary waves are derived using a variational method.
Abstract: We present a detailed analysis of finite energy solitary waves in two- and three-dimensional nonlinear periodic structures exhibiting a complete photonic band gap. Solitary waves in photonic crystals with a two-dimensional (2D) square and triangular symmetry group as well as a 3D fcc symmetry group are described in terms of an effective nonlinear Dirac equation derived using the slowly varying envelope approximation for the electromagnetic field. Unlike one-dimensional Bragg solitons, the multiple symmetry points of the 2D and 3D Brillouin zones give rise to two distinct classes of solitary wave solutions. Solutions associated with a higher order symmetry point of the crystal exist for both positive and negative Kerr nonlinearities, whereas solutions associated with a twofold symmetry point occur only for positive Kerr coefficient. Using a variational method we derive the important physical features such as the size, shape, peak intensity, and total energy of the solitary waves. This is then confirmed numerically using the finite element Ritz-Galerkin method. It is shown that the initial variational method and the finite element numerical method are in good agreement. We discuss the stability of these solitary waves with respect to small perturbations. It is suggested that an analytical stability criterion for spinor fields satisfying the nonlinear Dirac type of equation may exist, similar to the well known stability criterion for solitary waves in the nonlinear Schr\"odinger equation. Our stability criterion correctly reproduces the stability conditions of other nonlinear Dirac type of equations which have been studied numerically. Our study suggests that for an ideal Kerr medium, two-dimensional solitary waves in a band gap are stable, whereas three-dimensional ones are stable only in certain regions of the gap.
110 citations
TL;DR: The symmetry algebra of an integrable dispersive long-wave equation in two space dimensions is shown to be infinite-dimensional and to have a Kac-Moody-Virasoro structure.
110 citations
TL;DR: In this paper, translations of the scales of the Lu-Fano plots are introduced phenomenologically to bring out the symmetry of two-channel coupling, which leads to a phase renormalisation of the Coulomb basis wavefunctions of QDT, which eliminates the diagonal elements of Seaton's reactance matrix.
Abstract: Translations of the scales of the Lu-Fano plots are introduced phenomenologically to bring out the symmetry of two-channel coupling. These shifts in the ( nu i) space amount to a phase renormalisation of the Coulomb basis wavefunctions of QDT, which eliminates the diagonal elements of Seaton's reactance matrix. The off-diagonal element of the resulting matrix measures the effective coupling strength and the new origins of the Lu-Fano plot axes mark the extrema of channel admixture. In the continuous energy range, the parameters ( mu i, xi ) provide a compact expression of the cross section for any two-channel (one open and one closed) process, including the whole series of resonances due to the discrete states in the closed channel. A similar generalisation of the Beutler-Fano resonance formula has been previously achieved by Dubau and Seaton (1984).
110 citations
TL;DR: In this paper, it was shown that the full spurionic symmetry of Galilean invariant field theories can be deduced when those theories are the limits of relativistic parents, and that the non-relativistic daughter couples to Newton-Cartan geometry together with all of the symmetries advocated in previous work.
Abstract: We show that the full spurionic symmetry of Galilean-invariant field theories can be deduced when those theories are the limits of relativistic parents. Under the limit, the non-relativistic daughter couples to Newton-Cartan geometry together with all of the symmetries advocated in previous work, including the recently revived Milne boosts. Our limit is a covariant version of the usual one, where we start with a gapped relativistic theory with a conserved charge, turn on a chemical potential equal to the rest mass of the lightest charged state, and then zoom in to the low energy sector. This procedure gives a simple physical interpretation for the Milne boosts. Our methods even apply when there is a magnetic moment, which is known to modify the non-relativistic symmetry transformations. We focus on two examples. Free scalars are used to demonstrate the basic procedure, whereas hydrodynamics is used in order to exhibit the power of this approach in a fully dynamical setting, correcting several inaccuracies in the existing literature.
110 citations
110 citations