A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrdinger Equations with Multiply Components

Considering the coupled nonlinear Schr¨odinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations.Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

空间中的胶体自组装现象

实践十号卫星上即将开展的空间胶体自组装实验,旨在阐明重力在胶体组装过程中的作用,进一步理解胶体自组装现象,为制作大面积高质量的胶体晶体提供理论支持,以期未来制备出具有实用价值的光子晶体器件.空间胶体自组装实验的大量创新性设计,将为未来空间实验的开展提供新的思路.     

限位液滴瞬时失重自激振荡

为探索重力瞬变引起的约束液滴自激振荡机理, 本文利用落塔装置模拟短时微重力环境并借助高速CCD记录圆形限位基片上液滴整个过程的运动情况. 自激振荡是微重力下液滴形态的重整恢复过程, 边界的限位作用使得液滴在整个运动过程接触线钉扎不变, 具体可分为两个阶段: 首先是振荡的高低点位置高度渐进上升的液滴形态变化阶段, 与重力环境渐进变化有关; 而后是平衡位置附近的阻尼衰减振荡阶段, 此时振荡的频率恒定, 振幅衰减类似孤立黏性液滴的指数衰减过程. 对于第二阶段, 在高低点等位置处存在高度不变过程, 高度起伏变化时液滴振荡模式类似自由液滴二阶振荡, 高度不变时振荡模式类似自由液滴三阶振荡. 此外, 对于本实验体系的恒定接触面积的钉扎约束, 液滴的体积量不同时, 内驱振荡的阶段和模式不变, 但具体的振荡过程有所不同. 对于大体积液滴, 会在初始振荡的中间位置出现高度不变现象, 并且随振荡逐渐消失; 而小液滴中间位置则不存在此现象, 波形较一致; 第二阶段小体积液滴振幅衰减的阻尼率更大, 无量纲频率也更高.     

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

Considering the coupled nonlinear Schrodinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

Berry phase in a generalized nonlinear two-level system

In this paper, we investigate the behaviour of the geometric phase of a more generalized nonlinear system composed of an effective two-level system interacting with a single-mode quantized cavity field. Both the field nonlinearity and the atom-field coupling nonlinearity are considered. We find that the geometric phase depends on whether the index k is an odd number or an even number in the resonant case. In addition, we also find that the geometric phase may be easily observed when the field nonlinearity is not considered. The fractional statistical phenomenon appears in this system if the strong nonlinear atom-field coupling is considered. We have also investigated the geometric phase of an effective two-level system interacting with a two-mode quantized cavity field.     

The spatial properties of atomic Raman--Nath diffraction

This paper obtains the exact analytical solution of atomic Raman--Nath diffraction in the coordinate representation and discusses the influence of different initial conditions and detunings on the atomic spatial population distribution. The phase difference between the dipole matrix element and initial atomic population may influence the atomic spatial population distribution after diffraction, which has never been discussed before as far as we know. It offers a method to measure the phase by the spatial population distribution, which is interesting in the study of quantum optics.     

Possible Realization of Cluster States and Quantum Information Transfer in Cavity QED via Raman Transition

We present a scheme to generate cluster states with many scheme, no transfer of quantum information between the atoms in cavity QED via Raman transition. In this atoms and cavities is required, the cavity fields are only virtually excited and thus the cavity decay is suppressed during the generation of cluster states. The atoms are always populated in the two ground states. Therefore, the scheme is insensitive to the atomic spontaneous emission and cavity decay. We also show how to transfer quantum information from one atom to another.     

受限胶体液滴蒸发过程中胶体颗粒沉积过程观察

亲水玻璃基片在掩模板的保护下, 通过喷涂超疏水层, 得到了被疏水层包围的圆形亲水区域. 胶体液滴在这一区域被很好地限制, 并且液滴体积可以在较大范围内变化, 体积的变化可以改变液滴与基片的表观接触角. 通过显微观察手段原位观察了表观接触角为疏水的受限胶体液滴蒸发过程中粒子沉积行为. 在整个蒸发过程中, 受限液滴边界被钉扎在亲疏水交界处. 粒子沉积过程中, 驱动粒子的液滴内部流动会发生变化. 粒子沉积图案形成过程由三种流体行为控制, 最初, Marangoni效应占主导作用, 驱动粒子在液滴表面聚集, 随之沉积到液滴边缘; 随着蒸发进行, 当接触角变小(<60°)时, 由于边界蒸发速度更快导致的毛细补偿流使得粒子直接向边界沉积. 在干燥的最后阶段, 亲水区域内的液层变得很薄, 只有一单层粒子存在于这一薄液层中, 蒸发继续进行时, 薄液层发生失稳使得粒子迅速聚集而形成网络化图案, 由于粒子间距变小, 球间的液桥毛细力也会参与到这一聚集过程中.     

Efficient Scheme for Greenberger-Horne-Zeilinger State and Cluster State with Trapped Ions

We propose a scheme to generate the Greenberger-Horne-Zeilinger （GHZ） states and the cluster states of many trapped ions. In the scheme, the ion is illuminated by a single laser tuned to the first lower vibrational sideband. The scheme only requires resonant interactions. Thus the scheme is very simple and the quantum dynamics operation can be realized at a high speed, which is important in view of decoherence.     

Explicit multi-symplectic method for the Zakharov—Kuznetsov equation

We propose an explicit multi-symplectic method to solve the two-dimensional Zakharov-Kuznetsov equation. The method combines the multi-symplectic Fourier pseudospectral method for spatial discretization and the Euler method for temporal discretization. It is verified that the proposed method has corresponding discrete multi-symplectic conservation laws. Numerical simulations indicate that the proposed scheme is characterized by excellent conservation.