高斯积分在量子表象理论中的应用

首先证明了真空投影算符的正规乘积形式,然后结合有序算符内积分技术,把数学上的高斯积分推广到量子算符的积分形式.通过表象的完备性与对称性,进一步给出了坐标表象、动量表象、中介表象和相干态表象的具体形式.     

Evolution of Number State to Density Operator of Binomial Distribution in the Amplitude Dissipative Channel

We show that passing through the amplitude dissipative channel the initial pure number state density operator is evolved into the density operator of binomial distribution （a mixed state）, and the binomial distribution parameter is just equal to e^-2kt, where k is the dissipative parameter of the channel. We solve the corresponding master equation to obtain the operator-sum representation of the density operator by virtue of the entangled state representation, which seems to be a convenient approach.     

Photonic band structures of two-dimensional photonic crystals with deformed lattices

Using the plane-wave expansion method, we have calculated and analysed the changes of photonic band structures arising from two kinds of deformed lattices, including the stretching and shrinking of lattices. The square lattice with square air holes and the triangular lattice with circular air holes are both studied. Calculated results show that the change of lattice size in some special ranges can enlarge the band gap, which depends strongly on the filling factor of air holes in photonic crystals; and besides, the asymmetric band edges will appear with the broken symmetry of lattices.     

基于坐标表象的脊波变换研究

在小波变换量子力学机制的启发下, 通过采用Fock空间里双模坐标本征态改写经典Ridgelet变换, 定义了量子光学态的Ridgelet变换. 然后利用IWOP技术给出不对称积分算符的显式, 并推导出了两个有用的双模算符正规乘积公式. 在此基础上, 通过选取双模“墨西哥帽”母小波函数, 分析了相干态、特殊压缩相干态、中介纠缠态表象的Ridgelet变换. 关键词： IWOP技术 Ridgelet变换 相干态     

量子光学态的Ridgelet变换

利用有序算符内积分技术推导出一个有用的双模算符正规乘积公式. 然后在量子力学框架下, 计算出相干态、特殊压缩相干态、中介纠缠态表象的Radon变换. 在此基础上, 通过选取“墨西哥帽”母小波函数, 分别分析了以上三种量子光学态的Ridgelet变换. 关键词： 有序算符内积分技术 Radon变换 Ridgelet变换     

基于算符正规乘积的若干厄米多项式关系式证明

主要利用量子力学的方法证明了厄米多项式的递推关系.另外,根据厄米多项式的表达式,得出了两个与厄米多项式有关的积分公式.     

光子晶体在半导体激光器中的应用

激光的发明，将人类带入光通信、光存储、光显示的高科技文明中，随着高科技的不断发展、进步和应用范围的不断扩大，对激光的要求更高，例如低阈值、高效率、高亮度、高速、小体积、好的模式特性等，这些要求在现有的传统激光器理论及技术中是难以达到的。但是当人们将光子晶体的理论与现有激光物理和技术相结合时，则有望突破传统激光器的性能瓶颈。例如，提高自发辐射速率，同时获得更高的自发辐射向受激辐射的耦合效率，实现激光器的无阈值工作；利用光子晶体对光子态的调制作用，可以获得比传统激光器大几个数量级的光学腔品质因子，大幅度提高激光的亮度、单色性；结合光子晶体微腔及其显著增加的光学腔品质因子，可以提高激光器的调制速率等，因此，人们预期光子晶体科学与技术将成为未来光电子领域发展的核心之一。文章介绍了光子晶体在半导体激光器中的应用，指出光子晶体科学技术引入发展了几十年的半导体激光器中，使半导体激光器展现出更加优异的性能。最后文章作者展望了光子晶体激光器的未来发展和应用的方向。     

利用扫描电镜和原子力显微镜测量纳米微孔阳极氧化铝膜

利用多孔型阳极氧化铝膜（PAA）制备纳米材料是近年来研究的热点之,对PAA的形貌进行准确的表征具有重要的意义,文章首先分析了传统扫描电镜（SEM）观测方法中镀膜工艺对样品和测量结果的影响,并提出了对镀膜过渡区进行观测的方案,然后着重研究了利用原子力显微镜（AFM）对PAA进行无损测量的方法,比较了不同测量模式下的测量结果,并利用Reiss模型对“针尖-样品卷积效应”进行了有效的修正,文章的研究结果不仅适用于多孔型阳极氧化铝膜这一研究领域,对于纳米多孔材料的测量也有普遍的参考价值。     

Modeling walking behavior of pedestrian groups with floor field cellular automaton approach

Walking in groups is very common in a realistic walking environment. An extended floor field cellular automaton(CA)model is therefore proposed to describe the walking behavior of pedestrian groups. This model represents the motion of pedestrian groups in a realistic way. The simulation results reveal that the walking behavior of groups has an important but negative influence on pedestrian flow dynamics, especially when the density is at a high level. The presence of pedestrian groups retards the emergence of lane formation and increases the instability of operation of pedestrian flow. Moreover,the average velocity and volume of pedestrian flow are significantly reduced due to the group motion. Meanwhile, the parameter-sensitive analysis suggests that pedestrian groups should make a compromise between efficient movement and staying coherent with a certain spatial structure when walking in a dense crowd.