S矩阵的有效哈密顿量与酉性
Effective Hamiltonian and unitarity of the S matrix
摘要：
有效哈密顿量${\cal H}$可以很好地描述开放量子系统的性质，它由两部分组成：具有离散本征态的封闭系统的哈密顿量$H$和离散态与连续态之间的耦合矩阵$W$. ${\cal H}$的特征值决定了$S$矩阵的极点。${\cal H}$的本征态$k$和连续谱之间的耦合矩阵元$\tilde W_k^{cc'}$可以与$H$的本征态和连续谱之间的耦合矩阵元$W_k^{cc'}$非常不同。由于$S$矩阵的么正性，$\TW_k^{cc'}$以一种非平凡的方式依赖于能量，这与重叠区域中某些反应方法的假设相冲突。给出了共振态的波函数及其相位的显式表达式，分别在复平面中避免的能级交叉和$S$矩阵的双极点附近。
英文摘要：
The properties of open quantum systems are described well by an effective Hamiltonian ${\cal H}$ that consists of two parts: the Hamiltonian $H$ of the closed system with discrete eigenstates and the coupling matrix $W$ between discrete states and continuum. The eigenvalues of ${\cal H}$ determine the poles of the $S$ matrix. The coupling matrix elements $\tilde W_k^{cc'}$ between the eigenstates $k$ of ${\cal H}$ and the continuum may be very different from the coupling matrix elements $W_k^{cc'}$ between the eigenstates of $H$ and the continuum. Due to the unitarity of the $S$ matrix, the $\TW_k^{cc'}$ depend on energy in a non-trivial manner, that conflicts with the assumptions of some approaches to reactions in the overlapping regime. Explicit expressions for the wave functions of the resonance states and for their phases in the neighbourhood of, respectively, avoided level crossings in the complex plane and double poles of the $S$ matrix are given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
