Invariant forms and Hamiltonian systems: A geometrical setting

A geometric proof is given of Lee Hwa Chung's theorem for regular Hamiltonian systems, which identifies all the possible differential forms left invariant by the dynamics. Applications of this theorem in the area of canonical transformations are also remarked in a purely geometrical context.     

On the nature of the geometrical symmetry groups in the quantum intramolecular dynamics

A hypothesis for the nature of the geometrical symmetry groups that are used in the quantum intramolecular dynamics in the Born-Oppenheimer approximation is considered. It is assumed that they are the dynamic symmetry groups of a more rigorous problem of intramolecular motion. On this basis, the contradictions in the concept of geometrical symmetry groups are removed and a number of new conclusions concerning the general properties of molecular systems are made.     

Hamilton’s theory of turns and a new geometrical representation for polarization optics

Hamilton’s theory of turns for the group SU(2) is exploited to develop a new geometrical representation for polarization optics. While pure polarization states are represented by points on the Poincaré sphere, linear intensity preserving optical systems are represented by great circle arcs on another sphere. Composition of systems, and their action on polarization states, are both reduced to geometrical operations. Several synthesis problems, especially in relation to the Pancharatnam-Berry-Aharonov-Anandan geometrical phase, are clarified with the new representation. The general relation between the geometrical phase, and the solid angle on the Poincaré sphere, is established.     

Geometrical optical modeling of femtosecond setups having angular dispersion

A reliable and efficient method based on a geometrical optical approach is presented to model the propagation of ultrashort pulses in optical systems. It is shown that the commonly used method to determine the group delay of the spectral components of a pulse from their geometrical optical path lengths is only correct for aberration-free optical systems. In the case of systems with angular dispersion and imaging errors, a correction to the path values obtained from ray-tracing calculations must be applied, since for specific systems neglect of the correction causes significant errors. A technique for performing this correction is presented. Two optical arrangements used for the generation and detection of tunable THz radiation by the femtosecond tilted-pulse-front excitation technique are analyzed to demonstrate the indispensability of the correction. Received: 29 July 2002 / Revised version: 22 October 2002 / Published online: 29 January 2003 RID="*" ID="*"Corresponding author. Fax: +36-72/501-571, E-mail: kozma@fizika.ttk.pte.hu     

T-shaped dielectric slot waveguides for efficient control of birefringence and polarization independent directional coupling

A novel dielectric slot waveguide supporting strongly confined field in a T-shaped low-index slot region for both TE and TM polarizations is proposed and analyzed. Numerical simulations have demonstrated that quite different birefringent modal properties are achievable with tight optical confinement in the slot by tuning key geometrical parameters of the waveguide. Based on such a slot structure, the characteristics of directional couplers are investigated and the conditions for polarization independent coupling are also given. The presented T-shaped slot waveguide might be employed in integrated photonic systems as important building blocks enabling a number of potential applications.     

The doorknob transformer

The three-dimensional vector boundary-value problem for doorknob transformers is solved by the method of partial problems. systems of equations are obtained for calculation of the cylindrical-harmonic transformation ratios at the coaxial-radial junction. The numerical stability of these systems as a function of the collocation-point distribution is investigated. A six-terminal equivalent circuit is constructed and the behavior of its parameters as a function of the geometrical dimensions and wavelength is studied.     

面对称光学系统的初级波像差理论研究

非旋转轴对称光学系统波像差理论的建立有利于理解旋转 轴对称光学系统的装调误差和离轴三反射光学系统等非旋转轴对称光学系统的选型设计. 本文利用旋转轴对称球面光学系统的全口径初级波像差理论推导了子孔径面对称光学系统的初级波像差分布公式, 证明了面对称光学系统中的节点像差理论, 即除球差外的所有初级像差的零值节点偏离视场中心, 而不再是视场的旋转对称函数; 并首次阐述了多零值节点初级非对称像差产生的根源和变化特性. 该理论可以有效指导非对称光学系统初始结构的选择和优化设计过程. 关键词： 面对称 像差 几何光学     

Magnetic properties of strongly frustrated and correlated systems

While consequences of frustration of magnetic interactions are much studied in localized spin systems, much less studies have been performed on frustrated metallic systems. However, several effects of strong geometrical frustration in metallic correlated system have also been experimentally observed in rare-earth or transition metal compounds: coexistence of magnetic and non-magnetic sites in ordered magnetic structure, heavy fermion behaviour and anomalous Hall effect due to spin chirality are consequences of frustration. An overview of the experimental observations and of the proposed models is given. Other interesting effects due to magnetic frustration in metallic systems, which have been predicted theoretically, are also reviewed.     

Dislocations and torsion in graphene and related systems

A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the torsion tensor and uses the technique of quantum field theory in curved space. When applied to two-dimensional systems with Dirac points like graphene we find that dislocations couple in the form of vector gauge fields similar to these arising from curvature or elastic strain. We also describe the ways to couple dislocations to normal metals with a Fermi surface.     

Geometric Constructions of Toda and Periodic Toda Chains

A geometrical and neat framework is established to derive both Toda and periodic Toda systems from the geodesics of symmetric spaces. The counterpart of the Iwasawa decomposition of a semisimple Cie group in the case of a loop group is also derived. By these, we get a Lie su balgebra with Lie bracket [,]R, and the corresponding Poisson bracket {,}R gives the Hamiltonian form of the periodic Toda chains.     

Experimental study of color percolation in disordered macrosystems

The concentration dependence of the bulk resistivity for a dielectric-semiconductor-conductor three-component model system is studied. A geometrical technique for finding a percolation point in multi-component systems is suggested.     

The aberration theory of a combined electron focusing–deflection system with a rotating deflection field following the rotation of the electrons

A new type of combined magnetic focusing–electrostatic deflection systems whose orientation of deflection field is rotated synchronously with the beam electrons is proposed. This rotation deflection field can be formed by twistification of tube wall electrode (TWE) deflectors. Formulae are derived for the first-order optical properties, third-order geometrical aberrations and first-order chromatic aberrations of this system. A program was written in FORTRAN for numerical computation. An example is given; the computation results show that compared to the conventional systems, the proposed new system has lower deflection aberration coefficients.     

Symplectic quantization with higher derivatives

We show that systems with higher derivatives can also be consistently quantized by means of a geometrical procedure.     

阻尼Jaynes-Cummings模型中两原子的量子关联动力学

几何量子失协 (geometrical quantum discord, GQD)是目前度量量子体系中量子关联的一种行之有效的方法, 本文利用几何量子失协考察了有阻尼存在的Jaynes-Cumming (J-C)模型中两原子的量子关联动力学. 给出了几何量子失协在原子和光场发生共振和非共振耦合两种情况下的动力学演化行为, 尤其揭示了阻尼耗散对几何量子失协的影响. 关键词： 阻尼Jaynes-Cummings(J-C) 模型 量子关联 几何量子失协 (GQD)     

介观物理的粒子自旋轨道耦合和量子几何相位

本文较系统地但并非全面地讨论粒子的自旋轨道耦合。从基本概念到在介观物理的一些应用,特别着重讨论了自旋轨道耦合和量子几何相位的关系,也从作者的观点评论现代文献的一些有关问题和概述作者及其研究合作者的一些工作。本文讨论很大部分内容并不局限在介观尺度,而是相当普通的,可供物理各个领域研究参考。     

介观物理的粒子自旋轨道耦合和量子几何相位

本文较系统地但并非全面地讨论粒子的自旋轨道耦合。从基本概念到在介观物理的一些应用,特别着重讨论了自旋轨道耦合和量子几何相位的关系,也从作者的观点评论现代文献的一些有关问题和概述作者及其研究合作者的一些工作。本文讨论很大部分内容并不局限在介观尺度,而是相当普通的,可供物理各个领域研究参考。