论文标题
$ \ MATHCAL {PT} $ - 在紧凑的相位空间中的对称性线性汉密尔顿
$\mathcal{PT}$-symmetry in compact phase space for a linear Hamiltonian
论文作者
论文摘要
我们研究了相关的相位空间紧凑的PT对称，非铁量子系统的时间演变。我们专注于这种哈密顿量的最简单的非平凡示例，该例子是在角动量操作员中线性的。为了描述系统的演化，我们使用了进化算子的特定解剖分解，即使在特殊点的附近，也在数值上仍然是准确的。然后，我们分析了哈密顿量的非富米特部分如何影响两个原型量子状态，相干和迪克状态的时间演变。为此，我们计算Husimi分布或Q功能，并研究其在相空间中的演变。对于相干状态，Husimi函数的演化方程的特征与相应的角动量期望值的轨迹一致。这允许将这些曲线视为经典系统的轨迹。对于其他类型的量子状态，例如迪克说，丢失了特征和期望值轨迹的等效性。
We study the time evolution of a PT-symmetric, non-Hermitian quantum system for which the associated phase space is compact. We focus on the simplest non-trivial example of such a Hamiltonian, which is linear in the angular momentum operators. In order to describe the evolution of the system, we use a particular disentangling decomposition of the evolution operator, which remains numerically accurate even in the vicinity of the Exceptional Point. We then analyze how the non-Hermitian part of the Hamiltonian affects the time evolution of two archetypical quantum states, coherent and Dicke states. For that purpose we calculate the Husimi distribution or Q function and study its evolution in phase space. For coherent states, the characteristics of the evolution equation of the Husimi function agree with the trajectories of the corresponding angular momentum expectation values. This allows to consider these curves as the trajectories of a classical system. For other types of quantum states, e.g. Dicke states, the equivalence of characteristics and trajectories of expectation values is lost.
