Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

To develop a unitary quantum theory with probabilistic description for pseudo-Hermitian systems one needs to consider the theories in a different Hilbert space endowed with a positive definite metric operator. There are different approaches to find such metric operators. We compare the different approaches of calculating positive definite metric operators in pseudo-Hermitian theories with the help of several explicit examples in non-relativistic as well as in relativistic situations. Exceptional points and spontaneous symmetry breaking are also discussed in these models.

Generalized Maximum Principles and Stochastic Completeness for Pseudo-Hermitian Manifolds

In this paper,the authors establish a generalized maximum principle for pseudo-Hermitian manifolds.As corollaries,Omori-Yau type maximum principles for pseudo-Hermitian manifolds are deduced.Moreover,they prove that the stochastic completeness for the heat semigroup generated by the sub-Laplacian is equivalent to the validity of a weak form of the generalized maximum principles.Finally,they give some applications of these generalized maximum principles.

An explicit formula for the Webster torsion of a pseudo-hermitian manifold and its application to torsion-free hypersurfaces Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

This paper gives an explicit formula for calculating the Webster pseudo torsion for a strictly pseudoconvex pseudo-hermitian hypersurface. As applications, we are able to classify some pseudo torsion-free hypersurfaces, which include real ellipsoids.

CC-稳态映射的刘维尔型定理

引进了从黎曼流形到伪Hermitian流形上映射的水平泛函ΦH,这种泛函的临界映射称为CC-稳态映射.利用水平应力能量张量,得到从黎曼流形出发到伪Hermitian流形上的水平CC-稳态映射和从黎曼流形出发到Sasakian流形上的CC-稳态映射的能量单调公式及刘维尔型结果.

粒子在虚数周期磁场中的能带及其结构

为了验证满足一定对称性且具有周期性的非厄密哈密顿量具有实数能带,以在虚数周期磁场中运动的二维粒子为模型,在其哈密顿量满足PT赝厄密对称的情形下,运用数值方法和WKB方法计算能带并分析能带结构。结果表明:模型在此情形下有实数能带,且能带结构与哈密顿量具有PT对称的情形相同。由此再进行分析,得到了在周期场中,PT对称和PT赝厄密对称之间存在相位对应关系。

基于自适应重采样次数的协方差角度估计算法

针对基于Hermitian分解的协方差角度估计算法在低信噪比(SNR)时性能差的问题,提出了基于自适应重采样次数的协方差角度估计算法。该算法首先用接收信号扫描角度空间内的所有导向矢量,划定正确的角度估计区间,并给出判断角度估计结果是否可靠的标准。然后构造协方差矩阵,得到角度估计结果,接着以角度估计结果是否可靠为判断标准自适应地对原始信号进行重采样。若重采样后对应某一信号的多个角度估计结果都不可靠,则对原信号重采样并估计到达角,直到所有信号均有可靠结果为止。仿真结果表明,所提算法修正异常的角度估计结果,提高协方差角度估计算法在低信噪比时的精确度。

Classification of irreducible isoparametric submanifolds in CP^n

The classification theorem of the isoparametric submanifolds in CPn is obtained and geometry properties of them are discussed.

Trace of heat kernel,spectral zeta function and isospectral problem for sub-laplacians

In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ? n+1. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.

Adapted Metrics and Webster Curvature in Finslerian 2-Dimensional Geometry

The Webster scalar curvature is computed for the sphere bundle T_1S of a Finsler surface(S, F) subject to the Chern-Hamilton notion of adapted metrics. As an application,it is derived that in this setting(T_1S, g Sasaki) is a Sasakian manifold homothetic with a generalized Berger sphere, and that a natural Cartan structure is arising from the horizontal 1-forms and the author associates a non-Einstein pseudo-Hermitian structure. Also, one studies when the Sasaki type metric of T_1S is generally adapted to the natural co-frame provided by the Finsler structure.