On conformally flat and type N pure radiation metrics

We study pure radiation spacetimes of algebraic types O and N with a possible cosmological constant. In particular, we present explicit transformations which put these metrics, that were recently re-derived by Edgar, Vickers and Machado Ramos, into a general Ozsváth–Robinson–Rózga form. By putting all such metrics into the unified coordinate system we confirm that their derivation based on the GIF formalism is correct. We identify only few trivial differences.     

Currents on locally conformally Kähler manifolds

We characterize the existence of a locally conformally Kähler metric on a compact complex manifold in terms of currents, adapting the celebrated result of Harvey and Lawson for Kähler metrics.     

Noether symmetries and conserved quantities for spaces with a section of zero curvature

In an earlier paper (Feroze, 2010 [21]), the existence of new conserved quantities (Noether invariants) for spaces of different curvatures was discussed. There, it was conjectured that the number of new conserved quantities for spaces with an m$m$-dimensional section of zero curvature is m$m$. Here, along with the proof of this conjecture, the form of the new conserved quantities is also presented. For the illustration of the theorem, an example of conformally flat spacetime is constructed which also demonstrates that the conformal Killing vectors (CKVs), in general, are not symmetries of the Lagrangian for the geodesic equation.     

Constant gravitational fields and redshift of light

The solutions of Einsteins's equations in a constant energy-momentum tensor field are Ricci curvature homogeneous. Convenient perturbations of a Lorentz solvmanifold yield such curvature homogeneous metrics, prescribing redshift of light and singularities.     

一种二维不稳定流形的新算法及其应用

提出了连续时间系统二维(不)稳定流形的一种新数值算法,不但可以快速地求得流形的直观图像,而且能够准确地获取流形上各点的位置、时间、轨道距离等丰富的信息,从而有利于人们从几何上去研究系统的全局行为,如边界特征、演化过程、奇异环等等.本算法首先通过解初值问题求出均匀分布的相邻轨道,然后连接这些轨道既得流形面.Lorenz系统原点的稳定流形的计算表明本算法快速有效.此外,通过试着寻找异宿轨道,还研究了一个三维神经网络中的混沌产生机理.     

锥束CT平板探测器成像的余晖建模与校正方法

锥束CT具有高效率和高精度的显著特点, 在医学成像与工业无损检测等领域已得到广泛应用, 但余晖的存在降低了CT图像的质量. 本文借鉴余晖多指数衰减模型的思想, 结合平板探测器输出信号的实际衰减规律, 提出了一种新的基于多指数拟合的余晖衰减建模及校正方法. 首先进行了基于平板探测器的锥束CT成像实验, 结果表明平板探测器各像素的余晖衰减规律具有良好的一致性, 且余晖衰减规律与初始灰度的大小无关; 其后根据建立的余晖衰减模型实现了余晖的快速校正, 并分析比较了余晖校正前后投影图像和切片图像质量, 表明余晖校正后的零件轮廓清晰度得到了显著提升. 该方法无需获取探测器闪烁体成分及其衰减时间常数, 便于实际锥束CT成像系统的余晖检测与校正. 关键词： 余晖 平板探测器 锥束CT 多指数衰减     

Geometrical aspects and quantum brachistochrone problem for a collection of N spin-s system with long-range Ising-type interaction

We consider a physical system of N interacting qudits consisting of N spin-s particles coupled via the long-range interaction of Ising-type. We investigate the corresponding dynamics, define the associated quantum state manifold and we give the related Fubini-Study metric. We derive the Gaussian curvature and using the Gauss-Bonnet theorem, we show that the dynamics happen on a two-parametric manifold of spherical topology. We examine the geometrical phase acquired by the system under arbitrary and cyclic evolutions. Further, we study the quantum brachistochrone problem concerning the determination of the smallest possible time to realize a time-optimal evolution. By restricting our study to a two-qubit system under the Ising interaction, a detailed analysis is performed for the Fubini-Study metric, the Gaussian curvature, the geometrical phase and the optimal time in relation with the entanglement of the two qubits.     

Exact analytical results for density profile in Fourier space and elastic scattering function of a rotating harmonically confined ultra-cold Fermi gas

In this paper, the system dealt with consisting of an ultra-cold neutral spin-polarized Fermi gas undergoing rotation (or in the so-called synthetic magnetic field) trapped by an anisotropic harmonic potential in a two and three-dimensional space at zero temperature. Using the so-called Bloch propagator as a tool, we derive exact closed-form expressions for particle density in Fourier space which are valid for an arbitrary particle number confined by a two and three-dimensional rotating anisotropic harmonic trap. Numerical illustrations and discussions are presented. The results can be easily generalized at finite temperatures. The crossover from two-dimensional to the one-dimensional regime is shown to be reflected in the shape of the density distribution in Fourier space at very fast rotating velocity (or at strong synthetic magnetic field). In addition, an exact analytical expression of the elastic scattering factor is found, a quantity of interest used to probe the spatial distribution of the quantum gases.