Orbifold Hodge numbers of the wreath product orbifolds

We prove that the wreath product orbifolds studied earlier by the first author provide a large class of higher dimensional examples of orbifolds whose orbifold Hodge numbers coincide with the ordinary ones of suitable resolutions of singularities. We also make explicit conjectures on elliptic genera for the wreath product orbifolds.     

First order generalized symmetries of Maxwell's equations

The results of the calculation of first order generalized symmetries of Maxwell's equations in vacuum are summarized. The Lie algebra structure of the symmetries is also discussed.     

Resonance tunneling in superconducting junctions with different order parameter symmetries

Resonance tunneling in superconducting junctions with electrode order parameters of s and d symmetry was studied. The Green function formalism was used to derive an equation for the resonance current in junctions of arbitrary dimensionality and order parameter symmetry. A universal equation for resonance super-current was obtained for junctions of arbitrary dimensionality with isotropic electrode order parameters. A numerical analysis of resonance current transport in junctions of various types was performed for the two-dimensional model.     

Multiple gap symmetries for the order parameter of cuprate superconductors from penetration depth measurements

The temperature dependence of the London penetration depth lambda was measured for an untwinned single crystal of YBa_{2}Cu_{3}O_{7-delta} along the three principal crystallographic directions (a, b, and c). Both in-plane components (lambda_{a};{-2} and lambda_{b};{-2}) show an inflection point in their temperature dependence which is absent in the component along the c direction (lambda_{c};{-2}). The data provide convincing evidence that the in-plane superconducting order parameter is a mixture of (s+d)-wave symmetry whereas it is mainly s wave along the c direction. In conjunction with previous results it is concluded that coupled s+d-order parameters are universal and intrinsic to cuprate superconductors.     

Gradient property of low order covariants and truncated bifurcation equations for SO(N) symmetries

It is proved that the convariants of order p ≤ 3 of any irreducible representation of SO(N), and therefore the bifurcation equation truncated at order q ≤ 3 of any system with SO(N) symmetry, can be written in gradient form.     

含时滞的非保守系统动力学的Noether对称性

提出并研究含时滞的非保守系统动力学的Noether对称性与守恒量. 首先,建立含时滞的非保守系统的Hamilton原理,得到含时滞的Lagrange方程;其次,基于含时滞的Hamilton作用量在依赖于广义速度的无限小群变换下的不变性,定义系统的Noether对称变换和准对称变换,建立Noether对称性的判据;最后,研究对称性与守恒量之间的关系,建立含时滞的非保守系统的Noether理论. 文末举例说明结果的应用. 关键词： 时滞系统 非保守力学 Noether对称性 守恒量     

On a lie group of infinite order as a non-trivial coupling of intrinsic and space-time symmetries

A real Lie algebra of denumerable infinite order is derived. The algebra contains the Poincaré algebraP and the algebraSU(2) as sub-algebras. The algebra reduces to the direct sumP SU(2) in the limitM _n /M _p 1.     

Chirped photonic crystal with different symmetries for asymmetric light propagation

In the present paper, we have carried out analysis of asymmetric light propagation in a chirped photonic crystal waveguide. The designed structures have hexagonal arrangement and square arrangement of silicon rods in air substrate. Dimensions of the defect rods are tailored, so that the proposed design structure works as an optical isolator. The transmission analysis of the structure reveals that it can act as an optical diode. We have plotted the extinction ratio and transmission analysis graphs for the structure, and it has been observed that the maximum output is obtained for telecom wavelength of 1.55 μm. Dispersion curves are obtained using the plane wave expansion method, and the transmission is simulated using finite element method. The proposed structures are applicable for photonic integrated circuits due to their simple and clear operating principle.     

A method for finding Lanczos coefficients with the aid of symmetries

A set of algorithms involving the Lanczos potential and certain kinematical quantities for some arbitrary space-times, obtained using timelike vector fields, is considered. It is shown that such algorithms appear most naturally in the context of the spin coefficient formalism. Furthermore, explicit solutions are derived for the new spin coefficient algorithms.     

Tests of gravitational symmetries with radio pulsars

Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.     

两自由度弱非线性耦合系统的一阶近似Lie对称性与近似守恒量

采用变劲度系数的耦合弹簧构建一实际的两自由度弱非线性耦合系统, 用近似Lie对称性理论研究系统的一阶近似Lie对称性与近似守恒量, 得到6个一阶近似Lie对称性和一阶近似守恒量, 其中1个一阶近似守恒量实为系统的精确守恒量, 4个一阶近似守恒量为平凡的一阶近似守恒量, 只有1个一阶近似守恒量为稳定的一阶近似守恒量. 关键词： 两自由度弱非线性耦合系统 近似Lie对称性 近似守恒量     

Stochastic Loewner evolution for conformal field theories with lie group symmetries

The stochastic Loewner evolution is a recent tool in the study of two-dimensional critical systems. We extend this approach to the case of critical systems with continuous symmetries, such as SU(2) Wess-Zumino-Witten models, where domain walls carry an additional spin-1/2 degree of freedom.     

On the symmetries of integrable systems with boundaries

We employ appropriate realizations of the affine Hecke algebra and we recover previously known non-diagonal solutions of the reflection equation for the case. With the help of linear intertwining relations involving the aforementioned solutions of the reflection equation, the symmetry of the open spin chain with a particular choice of the left boundary is exhibited. The symmetry of the corresponding local Hamiltonian is also explored. Presented at the International Colloquium “Integrable Systems and Quantum Symmetries”, Prague, 16–18 June 2005.