SU（2）和SU（1，1）在相空间中指数算符的正规乘积和反正规乘积的简单实现

赖云忠, 梁九卿

研究了哈密顿算符是ＳＵ（１，１）和ＳＵ（２）算子线性组合且系数显含时间量子系统的时间演化。我们发现适当选取厄密不变量，不仅可得到统一的量子态时间演化封闭解，而且可得到时间演化幺正算符。用时间演化算符我们讨论了含时双光子压缩态和ＳＵ（１，１）相干态以及ＳＵ（２）压缩态的压缩性质。

刘汉俊, 王晓芹

GU Yan, LU Zhanpeng

本文研究了由SU(1,1)和SU(2)李代数生成元所构成的含时非厄米系统的Berry相位, 其分别对应于周期驱动外场下的一维谐振子及任意参数下的单个自旋粒子模型. 具体来说, 基于广义规范变换方法,通过引入含时厄米的且非幺正的变换算符, 系统可变换为不显含时间的形式, 并可导出系统的精确解及其对应的非绝热Berry相位. 结果表明, 对于SU(2)系统, 存在奇异点Gc (ω) = Ω+ω/2, 在该点处等效本征值发散, Berry相位从实数变为复数, 对应赝厄米相的自发破缺. 而SU(1,1)系统的能谱始终保持实数,Berry相位为纯实数, 无奇异点出现. 该对比揭示了SU(1,1)非紧致群与SU(2) 紧致群结构对非厄米系统几何相位的根本性影响. 该研究结果为非厄米系统中Berry相位的理论分析提供了新的视角和理解.

王晓光, 吕原生

Alex E. Bernardini, Roldão da Rocha

Solutions of generic $SU(2)\otimes SU(2)$ Hamiltonian eigensystems are obtained through systematic manipulations of quartic polynomial equations. An {\em ansatz} for constructing separable and entangled eigenstate basis, depending on the quartic equation coefficients, is proposed. Besides the quantum concurrence for pure entangled states, the associated thermodynamic statistical ensembles, their partition function, quantum purity and quantum concurrence are shown to be straightforwardly obtained. Results are specialized to a $SU(2)\otimes SU(2)$ structure emulated by lattice-layer degrees of freedom of the Bernal stacked graphene, in a context that can be extended to several mesoscopic scale systems for which the onset from $SU(2)\otimes SU(2)$ Hamiltonians has been assumed.

田永红, 彭金生