论文标题
通过矢量化方法中非热系统中的保守数量
Conserved quantities in non-Hermitian systems via vectorization method
论文作者
论文摘要
在过去的二十年中，开放的古典和量子系统引起了极大的兴趣。其中包括具有平等时间$（\ Mathcal {pt}）$对称性的非热汉密尔顿人所描述的系统，这些系统最能理解为具有平衡，分离的增益和损失的系统。在这里，我们提出了一种在这样的开放系统中表征和得出保守数量或交织操作员的另一种方法。结果，我们还获得了非高级或遗传运营商的期望值显示单个指数时间依赖性。通过使用$ \ Mathcal {pt} $ - 在两个不同的物理实现中产生的对称二聚体的简单示例，我们演示了我们的静态哈密顿量的过程，并将其推广到时间周期（floquet）案例，其中相互交织的操作员在频道上保留了频繁的操作员。受lindblad密度矩阵方程式的启发，我们的方法为表征非炎症系统中时间不变的良好方法提供了有用的补充。
Open classical and quantum systems have attracted great interest in the past two decades. These include systems described by non-Hermitian Hamiltonians with parity-time $(\mathcal{PT})$ symmetry that are best understood as systems with balanced, separated gain and loss. Here, we present an alternative way to characterize and derive conserved quantities, or intertwining operators, in such open systems. As a consequence, we also obtain non-Hermitian or Hermitian operators whose expectations values show single exponential time dependence. By using a simple example of a $\mathcal{PT}$-symmetric dimer that arises in two distinct physical realizations, we demonstrate our procedure for static Hamiltonians and generalize it to time-periodic (Floquet) cases where intertwining operators are stroboscopically conserved. Inspired by the Lindblad density matrix equation, our approach provides a useful addition to the well-established methods for characterizing time-invariants in non-Hermitian systems.
