论文标题
来自二维点转换的PT对称耦合振荡器的Lewis-Riesenfeld不变式振荡器和谎言代数膨胀
Lewis-Riesenfeld invariants for PT-symmetrically coupled oscillators from two dimensional point transformations and Lie algebraic expansions
论文作者
论文摘要
我们从二维点转换中构造了刘易斯 - 里森菲尔德的不变式，以以pt-smoretical和时间依赖性的方式在空间中相互耦合的两个振荡器。该模型的非热汉密尔顿人以符号$ sp（4）$ lie代数的生成器方面方便地表达。这允许采用另一种系统的方法来查找Lewis-Riesenfeld不变性，从而导致一组耦合的微分方程，我们通过使用时间订购的指数来解决。我们还证明，可以利用点转换来直接构建参考系统中各自独立的对应物的时间依赖性dyson映射。
We construct Lewis-Riesenfeld invariants from two dimensional point transformations for two oscillators that are coupled to each other in space in a PT-symmetrical and time-dependent fashion. The non-Hermitian Hamiltonian of the model is conveniently expressed in terms of generators of the symplectic $sp(4)$ Lie algebra. This allows for an alternative systematic approach to find Lewis-Riesenfeld invariants leading to a set of coupled differential equations that we solve by using time-ordered exponentials. We also demonstrate that point transformations may be utilized to directly construct time-dependent Dyson maps from their respective time-independent counterparts in the reference system.
