We investigate the transition probabilities for the “flavor” eigenstates in the two-level quantum system, which is described by a non-Hermitian Hamiltonian with the parity and time-reversal (PT) symmetry. Particularly, we concentrate on the so-called PT-broken phase, where two eigenvalues of the non-Hermitian Hamiltonian turn out to be a complex-conjugate pair. In this case, we find that the transition probabilities will be unbounded in the limit of infinite time t → +∞. However, after performing a connection between a non-Hermitian system, which exhibits passive PT symmetry and global decay, and the neutral-meson system in particle physics, we observe that the diverging behavior of the transition probabilities is actually applicable to the gauge-transformed neutral-meson states, whereas the transition probabilities for physical states are exponentially suppressed by the global decay. We also present a brief review on the situation at the so-called exceptional point, where both the eigenvalues and eigenvectors of the Hamiltonian coalesce.

中文翻译：

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PT断裂相中非Hermitian哈密顿量的风味本征态的跃迁概率

我们研究了两级量子系统中“风味”本征态的跃迁几率，该跃迁几率由具有奇偶校验和时间反转（PT）对称性的非Hermitian哈密顿量描述。特别地，我们集中于所谓的PT断裂相，其中非Hermitian哈密顿量的两个特征值变成复共轭对。在这种情况下，我们发现过渡概率将在无穷大的时间t →+ ∞的范围内无限制。但是，在表现出被动PT对称性和整体衰变的非厄米特系统与粒子物理学中的中子系统之间建立连接之后，我们观察到跃迁概率的发散行为实际上适用于轨距变换中性介子态，而物理态的跃迁概率被整体衰减指数级地抑制了。我们还简要介绍了所谓汉密尔顿合并的特征值和特征向量的异常情况。