平衡标架揭示了无源系统的PT对称性
Equilibrium frame reveals hidden PT symmetry of passive systems
摘要：
我们讨论了如何引入一个平衡框架，其中一个给定的哈密顿具有平衡的损失和增益项，可以揭示PT对称性隐藏在非厄米哈密顿耗散系统。被动PT对称哈密顿，其中只有损失和增益是不存在的，也可以显示例外点，就像PT对称系统，因此被广泛研究。我们证明了非厄米哈密顿量，它可以分为一个PT对称项和一个长期与哈密顿量交换，具有隐藏的PT对称性。这些对称性在平衡框架中变得明显。我们还表明，在例外点具有相同值的本征态的数目通常是在初始框架比在平衡框架中更小。这个性质与哈密顿量的第二部分有关。
英文摘要：
We discuss how introducing an equilibrium frame, in which a given Hamiltonian has balanced loss and gain terms, can reveal PT symmetry hidden in non-Hermitian Hamiltonians of dissipative systems. Passive PT-symmetric Hamiltonians, in which only loss is present and gain is absent, can also display exceptional points, just like PT-symmetric systems, and therefore are extensively investigated. We demonstrate that non-Hermitian Hamiltonians, which can be divided into a PT-symmetric term and a term commuting with the Hamiltonian, possess hidden PT symmetries. These symmetries become apparent in the equilibrium frame. We also show that the number of eigenstates having the same value in an exceptional point is usually smaller in the initial frame than in the equilibrium frame. This property is associated with the second part of the Hamiltonian.
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