论文标题
强且弱耦合时间依赖的非量子量子系统的扰动方法
Perturbative approach for strong and weakly coupled time-dependent non-Hermitian quantum systems
论文作者
论文摘要
我们提出了一种扰动方法，以确定时间依赖性的戴森图和与时间依赖的非富米汉顿人相关的度量算子。我们将该方法应用于一对明确的时间依赖性的二维谐波振荡器，这些谐波振荡器以PT对称的方式彼此弱耦合，并将其强烈耦合的明确依赖性的负Quarty Quartic Quartic Anharmonic振荡器电位。我们证明，一旦设置了扰动的ANSATZ，就可以以建设性的方式递归地解决订单的耦合微分方程，从而绕过对Dyson Map或Metric Operator进行任何猜测的需求。通过顺序微分方程自然探索顺序解决方案中的歧义性，从而为dyson地图和公制操作员提供了一组不等的解决方案，暗示了不同的身体行为，这表明了时间依赖的能量运算符的期望值。
We propose a perturbative approach to determine the time-dependent Dyson map and the metric operator associated with time-dependent non-Hermitian Hamiltonians. We apply the method to a pair of explicitly time-dependent two dimensional harmonic oscillators that are weakly coupled to each other in a PT-symmetric fashion and to the strongly coupled explicitly time-dependent negative quartic anharmonic oscillator potential. We demonstrate that once the perturbative Ansatz is set up the coupled differential equations resulting order by order may be solved recursively in a constructive manner, thus bypassing the need for making any guess for the Dyson map or the metric operator. Exploring the ambiguities in the solutions of the order by order differential equations naturally leads to a whole set of inequivalent solutions for the Dyson maps and metric operators implying different physical behaviour as demonstrated for the expectation values of the time-dependent energy operator.
