双模相位问题

在双模空间，给出两种模式下厄密的cosine和sine算符．由于它们互相对易，就可构造出它们的共同本征态．讨论了这些相位算符和本征态矢的性质．研究了在P-B相位表示下这些算符的期望值 关键词：     

Hopf Bifurcations for the Recently Proposed Smooth-and-Discontinuous Oscillator

We investigate the Hopf bifurcations of the recently proposed smooth-and-discontinuous （SD） oscillator which exhibits both smooth and discontinuous dynamics depending on the value of a parameter a. The nonlinearity presented in this system characterizes irrationality and piecewise linearity for smooth and discontinuous cases, respectively, which could not meet the requirements of the conventional methods due to the barrier of Taylor expansion. Introducing a series of new kinds of elliptic integrals of the first and second kind to the perturbed oscillator, we obtain the Poincare-Birchoff normal forms of Hopf bifurcations for both smooth and discontinuous regimes. We also demonstrate the criteria for the occurrence of Hopf bifurcations, the stability of periodic solutions bifurcating from the equilibria and the excellent agreement between the theoretical and numerical results.     

Theoretical and experimental study of Chen chaotic system with notch filter feedback control

Since the past two decades, the time delay feedback control method has attracted more and more attention in chaos control studies because of its simplicity and efficiency compared with other chaos control schemes. Recently, it has been proposed to suppress low-dimensional chaos with the notch filter feedback control method, which can be implemented in a laser system. In this work, we have analytically determined the controllable conditions for notch filter feedback controlling of Chen chaotic system in terms of the Hopf bifurcation theory. The conditions for notch filter feedback controlled Chen chaoitc system having a stable limit cycle solution are given. Meanwhile, we also analysed the Hopf bifurcation direction, which is very important for parameter settings in notch filter feedback control applications. Finally, we apply the notch filter feedback control methods to the electronic circuit experiments and numerical simulations based on the theoretical analysis. The controlling results of notch filter feedback control method well prove the feasibility and reliability of the theoretical analysis.     

双模场与V型三能级原子玻色-爱因斯坦凝聚体相互作用系统的光场压缩效应

研究了V型三能级原子玻色-爱因斯坦凝聚体与双模压缩相干态光场相互作用系统中的光场压缩的特性.数值计算结果表明:光场的正交分量呈现周期性压缩,其周期与原子间相互作用密切相关,而最大压缩量与持续时间与初始光场的压缩因子有关.     

Bell态原子与双模纠缠相干光场双光子相互作用的原子布居数演化特性

运用全量子理论研究了Bell态原子与双模纠缠相干光场双光子相互作用过程中的原子粒子布居差的时间演化规律.结果表明:原子初始处于|β11＞时,原子粒子布居差恒为零;原子初始处于其他三个Bell态时,随着初始光场平均光子数的增加,原子粒子数布居差时间演化曲线的振荡频率明显增大,振荡幅度明显减小;双模光场纠缠程度的大小对曲线的振荡频率及整体曲线的位置都没有影响.随着原子间偶极相互作用的增强,当原子初态处在|β01＞时,曲线的Rabi振荡频率明显增大;而两原子初始处于|β10＞或|β00＞态时,曲线的崩塌-回复现象逐渐消失.     

Bell态原子与双模纠缠相干光场双光子相互作用系统的量子纠缠

运用全量子理论和数值计算的方法,借助于原子的量子约化熵研究了初始处于Bell态|β00>和| β10>的两原子与双模纠缠相干光场双光子相互作用系统中两原子与双模光场之间纠缠的演化特性.分析了光场强度、光场纠缠度及原子间相互作用强度对原子熵演化特性的影响.结果表明:随着双模光场的平均光子数的增大,原子熵的时间演化曲线逐渐变为规则振荡;增大原子间的相互作用强度,原子熵的振荡频率和振幅都减小;改变双模光场的纠缠度,原子熵的振荡频率和振幅都不发生改变.     

一类时滞捕食系统的Hopf分支

研究了一类具有修正的Leslie-Gower和Holling-IV类功能性反应函数的时滞捕食系统,讨论了该系统的局部稳定性和Hopf分支存在性, 并利用中心流形定理和规范型理论确定了Hopf分支的方向和分支周期解的稳定性.仿真实例证明了理论分析结果的正确性.     

基于BDS/GPS和百度地图的现代有轨电车监控系统的设计

为实现对现代有轨电车车辆的位置及运行状态进行实时监控,设计了一个基于BDS/GPS和百度地图的现代有轨电车监控系统;定位终端以具有我国自主知识产权的BDS/GPS双模定位模块为主,RFID系统作为辅助定位手段;数据通过HTTP的GET方法提交至服务器,由服务器端的PHP页面自动处理后存储到MySQL数据库,中心管理平台显示页面调用百度地图API,将数据显示在百度地图上;最终该系统可以实时获取并存储列车的位置坐标、速度、时间等信息,并在百度地图上以点、线和图表的形式显示出车辆的坐标和运行轨迹等;测试结果表明,该系统运行稳定,定位精度高,获取数据准确、时延小,能够满足应用需求。     

双模压缩真空场作用下二能级原子的偶极压缩与相干俘获

运用全量子理论研究了双模压缩真空场与二能级原子双光子作用过程中原子的量子行为,论证了原子发生相干俘获的条件,讨论了压缩参数对原子偶极压缩的影响. 关键词：     

辫子范畴中的bi-Frobenius代数

在辫子范畴中考察Doi的关于bi-Frobenius代数的结果.证明了辫子bi-Frobenius代数的同态基本定理.