共轭线性对称性及其对PT-对称量子理论的应用

传统量子系统的哈密顿是自伴算子,哈密顿的自伴性不仅保证系统遵循酉演化和保持概率守恒,而且也保证了它自身具有实的能量本征值,这类系统称为自伴量子系统.然而,确实存在一些物理系统(如PT-对称量子系统),其哈密顿不是自伴的,这类系统称为非自伴量子系统.为了深入研究PT-对称量子系统,并考虑到算子PT的共轭线性性,首先讨论了共轭线性算子的一些性质,包括它们的矩阵表示和谱结构等;其次,分别研究了具有共轭线性对称性和完整共轭线性对称性的线性算子,通过它们的矩阵表示,给出了共轭线性对称性和完整共轭线性对称性的等价刻画;作为应用,得到了关于PT-对称及完整PT-对称算子的一些有趣性质,并通过一些具体例子,说明了完整PT-对称性对张量积运算不具有封闭性,同时说明了完整PT-对称性既不是哈密顿算子在某个正定内积下自伴的充分条件,也不是必要条件.     

Water contact angles on charged surfaces in aerosols

Interactions between water and solid substrates are of fundamental importance to various processes in nature and industry. Electric control is widely used to modify interfacial water, where the influence of surface charges is inevitable. Here we obtain positively and negatively charged surfaces using LiTaO₃ crystals and observe that a large net surface charge up to 0.1 C/m² can nominally change the contact angles of pure water droplets comparing to the same uncharged surface. However, even a small amount of surface charge can efficiently increase the water contact angle in the presence of aerosols. Our results indicate that such surface charges can hardly affect the structure of interfacial water molecular layers and the morphology of the macroscopic droplet, while adsorption of a small amount of organic contaminants from aerosols with the help of Coulomb attraction can notably decrease the wettability of solid surface. Our results not only provide a fundamental understanding of the interactions between charged surfaces and water, but also help to develop new techniques on electric control of wettability and microfluidics in real aerosol environments.     

伪自伴量子系统的酉演化与绝热定理

经典量子系统的哈密尔顿是自伴算子.哈密尔顿算符的自伴性不仅确保了系统遵循酉演化,而且也保证了它自身具有实的能量本征值.但是,确实有一些物理系统,其哈密尔顿是非自伴的,但也具有实的能量本征值,这种具有非自伴哈密尔顿的系统就是非自伴量子系统.具有伪自伴哈密尔顿的系统是一类特殊的非自伴量子系统,其哈密尔顿相似于一个自伴算子.本文研究伪自伴量子系统的酉演化与绝热定理.首先,给出了伪自伴算子定义及其等价刻画;其次,对于伪自伴哈密尔顿系统,通过构造新内积,证明了伪自伴哈密尔顿在新内积下是自伴的,并给出了系统在新内积下为酉演化的充分必要条件.最后,建立了伪自伴量子系统的绝热演化定理及与绝热逼近定理.     

一种平板显示无缝拼接技术的研究

针对平板显示技术最新进展和技术特点,提出利用光学移像技术实现平板显示屏无缝拼接显示的方法。采用隔行/隔列或分时显示技术,在平板显示屏邻近边框区域设置重叠显示区显示2幅图像,借用偏振光旋转装置与偏振反射膜,实现图像的分离。通过斜方棱镜将分离出的图像引导至显示器件边框位置覆盖边框,将原来36mm宽的拼接缝减小至3条不到0.5mm宽的棱镜拼接缝,实现了平板显示屏的无缝拼接。