论文标题
非官方二次汉密尔顿人的代数分析
Algebraic analysis of non-Hermitian quadratic Hamiltonians
论文作者
论文摘要
我们研究了一般的单模非二次二次汉密尔顿，该二次二次汉密尔顿人不表现出$ \ Mathcal {pt} $ - 对称性。通过代数方法，我们确定存在真实特征值以及特殊点的位置的条件。我们还提出了广义Bogoliubov转换的代数替代方案，使人们可以将二次操作员转换为更简单的形式，以原始的创建和an灭操作员。我们对两个模式振荡器进行了类似的分析，该分析由两个相同的单式振荡器组成，该振荡器由二次术语耦合。
We study a general one-mode non-Hermitian quadratic Hamiltonian that does not exhibit $\mathcal{PT}$-symmetry. By means of an algebraic method we determine the conditions for the existence of real eigenvalues as well as the location of the exceptional points. We also put forward an algebraic alternative to the generalized Bogoliubov transformation that enables one to convert the quadratic operator into a simpler form in terms of the original creation and annihilation operators. We carry out a similar analysis of a two-mode oscillator that consists of two identical one-mode oscillators coupled by a quadratic term.
