论文标题
统治参数依赖的非赫米特汉顿汉密尔顿的动态的运动方程
Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians
论文作者
论文摘要
我们研究了非赫米特汉密尔顿$ \ hat {h}（λ，δ）$的异常点（EPS），其参数为$λ\ in {\ mathbb c} $ in {\ mathbb c} $和$Δ\ in {\ mathbb r} $。随着实际控制参数$δ$的变化，$ k $ -th ep（或$ k $ - th的同时存在EPS的群集）为$ \ hat {h}（λ，δ）$沿连续轨迹的$λ$的复杂平面移动，$λ_k（δ）$。我们为轨迹$λ_K（δ）$的自我包含的运动方程（EOM）提供，同时将$δ$解释为传播时间。每当一个人希望研究相关哈密顿官对外部扰动或连续参数变化的响应时，这种EOM就会成为感兴趣的。例如，〜从赫尔米尼曲线交叉/脱色器中发出的EPS的情况（当Hamiltonian参数持续变化时，它们会变成避免的交叉/接近级别）。所提出的EOM不仅具有其理论优点，而且还具有实质性的实际相关性。也就是说，即使是一种有效的数值方法，也可以将刚刚提出的方法视为有效的方法，可用于为原子，核和凝结物理学中遇到的一类广泛的复杂量子系统生成EPS。这种方法的性能在此处在简单但非平凡的玩具模型上进行数值测试。
We study exceptional points (EPs) of a nonhermitian Hamiltonian $\hat{H}(λ,δ)$ whose parameters $λ\in {\mathbb C}$ and $δ\in {\mathbb R}$. As the real control parameter $δ$ is varied, the $k$-th EP (or $k$-th cluster of simultaneously existing EPs) of $\hat{H}(λ,δ)$ moves in the complex plane of $λ$ along a continuous trajectory, $λ_k(δ)$. We derive a self contained set of equations of motion (EOM) for the trajectory $λ_k(δ)$, while interpreting $δ$ as the propagation time. Such EOM become of interest whenever one wishes to study the response of EPs to external perturbations or continuous parametric changes of the pertinent Hamiltonian. This is e.g.~the case of EPs emanating from hermitian curve crossings/degeneracies (which turn into avoided crossings/near-degeneracies when the Hamiltonian parameters are continuously varied). The presented EOM for EPs have not only their theoretical merits, they possess also a substantial practical relevance. Namely, the just presented approach can be regarded even as an efficient numerical method, useful for generating EPs for a broad class of complex quantum systems encountered in atomic, nuclear and condensed matter physics. Performance of such a method is tested here numerically on a simple yet nontrivial toy model.
