arXiv 1206.60002012-06-26quant-phmath-phmath.MP

量子灾变：一个案例研究

Quantum catastrophes: a case study

Miloslav Znojil

备注：: 23 pp
发表信息：: J. Phys. A: Math. Theor. 45 (2012) 444036
DOI：: 10.1088/1751-8113/45/44/444036

摘要：

假设哈密顿量H的束缚态谱在参数的物理值的非空域D中是实的。这意味着对于这些参数，H可以被称为隐埃尔米特，即，经由量子束缚态的物理希尔伯特空间中的内积的{ \it adhoc}选择而使其成为厄米特（即，经由所谓的度量的{ \it adhoc}构造）。量子灾难的名称然后被分配给N元组异常点交叉，即，到的情况下，我们离开域D沿着这样一条路径，在边界D，一个N的束缚态能量退化，随后，复杂化。在任何固定的$N \geq 2$，该过程通过N × N基准有效矩阵哈密顿量H来模拟。最后，它被分配这样一个封闭形式的度量，这是唯一的通过N-外推友好的要求。

英文摘要：

The bound-state spectrum of a Hamiltonian H is assumed real in a non-empty domain D of physical values of parameters. This means that for these parameters, H may be called crypto-Hermitian, i.e., made Hermitian via an {\it ad hoc} choice of the inner product in the physical Hilbert space of quantum bound states (i.e., via an {\it ad hoc} construction of the so called metric). The name of quantum catastrophe is then assigned to the N-tuple-exceptional-point crossing, i.e., to the scenario in which we leave domain D along such a path that at the boundary of D, an N-plet of bound state energies degenerates and, subsequently, complexifies. At any fixed $N \geq 2$, this process is simulated via an N by N benchmark effective matrix Hamiltonian H. Finally, it is being assigned such a closed-form metric which is made unique via an N-extrapolation-friendliness requirement.

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