$\cal PT$ -对称系统的可解膨胀模型
Solvable dilation model of $\cal PT$-symmetric systems
摘要：
膨胀方法是实验模拟非厄米量子系统，特别是$\cal PT$对称量子系统的一种实用方法。然而，依赖于时间的膨胀问题一般不能明确解决。本文提出了一个简单而非平凡的具有二维含时$\cal PT$对称哈密顿量的精确可解膨胀问题。我们的系统最初设置在不间断的$\cal PT$ -对称阶段，后来越过所谓的例外点，并进入破碎的$\cal PT$ -对称阶段。对该系统，解析地计算了$\cal PT$对称系统的扩张哈密顿量和演化。我们的结果清楚地表明，例外点没有太多的物理相关性在\textit{time-dependent}系统。
英文摘要：
The dilation method is a practical way to experimentally simulate non-Hermitian, especially $\cal PT$-symmetric quantum systems. However, the time-dependent dilation problem cannot be explicitly solved in general. In this paper, we present a simple yet non-trivial exactly solvable dilation problem with two dimensional time-dependent $\cal PT$-symmetric Hamiltonian. Our system is initially set in the unbroken $\cal PT$-symmetric phase and later goes across the so-called exceptional point and enters the broken $\cal PT$-symmetric phase. For this system, the dilated Hamiltonian and the evolution of $\cal PT$-symmetric system are analytically worked out. Our result clearly showed that the exceptional points do not have much physical relevance in a \textit{time-dependent} system.
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