一维势中能级的合并与聚并
Coalescing versus merging of energy levels in one-dimensional potentials
摘要：
当阱间距（$a$）缓慢增加时，一维对称双阱的能级的子势垒对会合并为一对.双峰合并的能量是独立阱的基态本征值（$ε_0$）。我们证明了当双势阱受到复PT对称势的微扰时，在特殊点$a=a_*$处能级的合并将变为两能级的合并。对于$a>a_*$，复共轭特征值的实部再次与$ε_0$重合。这是一个有趣的和罕见的两个领域的两种现象之间的联系：厄米性和复杂的PT对称性。
英文摘要：
The sub-barrier pairs of energy levels of a Hermitian one-dimensional symmetric double well potential are known to merge into one, if the inter-well distance ($a$) is increased slowly. The energy at which the doublets merge are the ground state eigenvalues of independent wells ($ε_0$). We show that if the double well is perturbed mildly by a complex PT-symmetric potential the merging of levels turns into the coalescing of two levels at an exceptional point $a=a_*$. For $a>a_*$, the real part of complex-conjugate eigenvalues coincides with $ε_0$ again. This is an interesting and rare connection between the two phenomena in two domains: Hermiticity and complex PT-symmetry.
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。
