论文标题
通过特殊点：案例研究
Passage through exceptional point: Case study
论文作者
论文摘要
猜想是，单参数级 - - - 高米特$ n $ by $ n $ matrix hamiltonian $ h（t）$的特殊点（EP）奇异性可以扮演量子相位转换界面的角色，连接一个无单位量子系统的不同动力学状态。详细描述了对EP介导的量子相变的六个实现。在初始，中级或最终阶段中考虑了任何矩阵尺寸$ n $的相当现实的Bose-Hubbard（BH）和离散的Anharmonic振荡器（AO）模型。在这种相位变化的线性代数说明中，所有成分（首先，所有过渡矩阵）均以封闭的代数，非数字形式构建。
It is conjectured that the exceptional-point (EP) singularity of a one-parametric quasi-Hermitian $N$ by $N$ matrix Hamiltonian $H(t)$ can play the role of a quantum phase-transition interface connecting different dynamical regimes of a unitary quantum system. Six realizations of the EP-mediated quantum phase transitions "of the third kind" are described in detail. Fairly realistic Bose-Hubbard (BH) and discrete anharmonic oscillator (AO) models of any matrix dimension $N$ are considered in the initial, intermediate, or final phase. In such a linear algebraic illustration of the changes of phase, all ingredients (and, first of all, all transition matrices) are constructed in closed, algebraic, non-numerical form.
