Spontaneous symmetry breaking in a time-dependent space-time

Spontaneous symmetry breaking of a ⁴ quantum of field theory in a time-dependent space-time, de Sitter space, is discussed in the Schrödinger picture. Instead of the usual cutoff method we use an-regularization procedure to deal with the divergent integrals.     

A memristive chaotic system with offset-boostable conditional symmetry

The European Physical Journal Special Topics - Conditional symmetry is obtained in a memristive system when the function-based polarity inverse meets the new polarity balance, which produces...     

The generic quantum superintegrable system on the sphere and Racah operators

We consider the generic quantum superintegrable system on the d-sphere with potential \(V(y)=\sum _{k=1}^{d+1}\frac{b_k}{y_k^2}\), where \(b_k\) are parameters. Appropriately normalized, the symmetry operators for the Hamiltonian define a representation of the Kohno–Drinfeld Lie algebra on the space of polynomials orthogonal with respect to the Dirichlet distribution. The Gaudin subalgebras generated by Jucys–Murphy elements are diagonalized by families of Jacobi polynomials in d variables on the simplex. We define a set of generators for the symmetry algebra, and we prove that their action on the Jacobi polynomials is represented by the multivariable Racah operators introduced in Geronimo and Iliev (Constr Approx 31(3):417–457, 2010). The constructions also yield a new Lie-theoretic interpretation of the bispectral property for Tratnik’s multivariable Racah polynomials.     

引入守恒格式的自相似解进行ICF辐射驱动时变对称性分析

引入守恒格式的自相似解计算黑腔X射线能流时空分布,通过视角因子方法计算靶丸表面入射能流分布,从而进行惯性约束聚变辐射驱动时变对称性分析。分析了光斑运动、激光脉冲波形及靶丸装配偏差对靶丸辐照均匀性的影响。以二阶分量时间积分值为优化目标,最佳腔长计算值与内爆对称性调节实验结果相符,内爆腔靶组合参数扫描得到的最佳长径比与NIF目前实验值相当,模型有效性得到验证。     

An ideal optical system with double-sided symmetry

A theory of an ideal optical system possessing double-sided (or planar) symmetry is developed using the projective transformations technique. In terms of the angular eikonal theory in the paraxial approximation, the theory developed is applied to the construction of a multimodular optical system consisting of ideal, at least two-component, optical systems with double-sided symmetry.     

Hamilton系统的Mei对称性、Noether对称性和Lie对称性

研究Hamilton系统的形式不变性即Mei对称性，给出其定义和确定方程.研究Hamilton系统的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明本文结果的应用. 关键词： Hamilton系统 Mei对称性 Noether对称性 Lie对称性 守恒量     

Dynamical symmetries for superintegrable quantum systems

We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are obtained by generalizing the techniques of factorization of one-dimensional systems. We firstly obtain a pair of noncommuting Lie algebras su(2) that originate the algebra so(4). By considering three spherical coordinate systems, we get the algebra u(3) that can be enlarged by “reflexions” to so(6). The bounded eigenstates of the Hamiltonian hierarchies are associated to the irreducible unitary representations of these dynamical algebras. The text was submitted by the authors in English.     

A superintegrable discrete harmonic oscillator based on bivariate Charlier polynomials

Physics of Atomic Nuclei - A simple discrete model of the two-dimensional isotropic harmonic oscillator is presented. It is superintegrable with su(2) as its symmetry algebra. It is constructed...     

Vacco动力学方程的Mei对称性、Lie对称性和Noether对称性

研究Vacco动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Vacco动力学方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一 个例子说明结果的应用. 关键词： Vacco动力学方程 Mei对称性 Noether对称性 Lie对称性 守恒量     

Emden方程的Mei对称性、Lie对称性和Noether对称性

研究Emden动力学方程的形式不变性即Mei对称性，给出其定义和确定方程，研究Emden方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量，给出一个例子说明结果的应用. 关键词： Emden动力学方程 Mei对称性 Noether对称性 Lie对称性     

Synchrotron radiation of a system with spherical symmetry

Generalized expressions are obtained for the power of synchrotron radiation of both charged and uncharged systems with charge distribution having spherical symmetry. The distribution is considered arbitrary in the radial direction.Tomsk Polytechnic Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 12–15, September, 1993.     

Two-dimensional superintegrable metrics with one linear and one cubic integral

We describe all local Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral cubic in momenta.     

离散变质量完整系统的Noether对称性与Mei对称性

本文研究离散变质量完整系统的Noether对称性与Mei对称性.首先用差分离散变分的方法,建立起离散变质量完整系统的运动方程和能量演化方程.然后给出该系统的Noether对称性和Mei对称性的定义及离散Noether守恒量的形式.得到系统的Noether对称性与Mei对称性导致离散Noether守恒量的条件.最后举例说明结果的应用.     

Ion-beam instabilities in an accelerating system with axial symmetry

Beam instabilities in an accelerator with focusing of an axisymmetric accelerating field are considered for deviation of the field from axial symmetry. The effect is evaluated quantitatively for an accelerator with phase-variable focusing produced by a two-conductor resonator. It is shown that at the resonances the effective beam radius can increase substantially, even for a short accelerator about 1 m in length.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 10–13, December, 1987.     

变质量完整系统的共形不变性和Noether对称性及Lie对称性

研究变质量完整系统在无限小变换下的共形不变性与Noether对称性和Lie对称性.首先,给出了变质量完整系统的共形不变性的定义;其次,研究了系统的共形不变性与Noether对称性之间的关系,得到了共形不变性导致的Noether守恒量;最后,研究了系统的共形不变性与Lie对称性之间的关系,得到了共形不变性同时是Lie对称性导致的Hojman守恒量.最后举例说明了结果的应用.     

A symmetry and a conserved quantity for the Birkhoff system

A symmetry and a conserved quantity of the Birkhoff system are studied. The symmetry is called the Birkhoff symmetry. Its definition and criterion are given in this paper. A conserved quantity can be deduced by using the symmetry. An example is given to illustrate the application of the result.     

奇异系统Hamilton正则方程的Mei对称性、Noether对称性和Lie对称性

研究奇异系统Hamilton正则方程的形式不变性即Mei对称性，给出其定义、确定方程、限制方程和附加限制方程.研究奇异系统Hamilton正则方程的Mei对称性与Noether对称性、Lie对称性之间的关系，寻求系统的守恒量.给出一个例子说明结果的应用. 关键词： 奇异系统 Hamilton正则方程 约束 对称性 守恒量     

Finite-temperature effective potential of a system with spontaneously broken symmetry

A quantum-mechanical system with spontaneously broken symmetry is considered, the effective potential is determined, and it is shown that with reduction of temperature the system undergoes a phase transition of the first kind.Yaroslavl State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 111–114, June, 1995.     

A generalized Mei conserved quantity and Mei symmetry of Birkhoff system

This paper studies a new conserved quantity which can be called generalized Mei conserved quantity and directly deduced by Mei symmetry of Birkhoff system. The conditions under which the Mei symmetry can directly lead to generalized Mei conserved quantity and the form of generalized Mei conserved quantity are given. An example is given to illustrate the application of the results.     

Lagrange系统Mei对称性直接导致的一种守恒量

研究Lagrange系统的Mei对称性直接导致的一种守恒量. 给出系统的Mei对称性的定义和判据方程, 得到系统Mei对称性直接导致的一种守恒量的条件和形式,并举例说明结果的应用. 关键词： Lagrange系统 Mei对称性 守恒量