Perturbative approach for strong and weakly coupled time-dependent for non-Hermitian quantum systems
Perturbative approach for strong and weakly coupled time-dependent for non-Hermitian quantum systems
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DOI：
10.1088/1402-4896/abe259
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发表时间：
2020-10
期刊：
影响因子：
2.9
通讯作者：
A. Fring;Rebecca Tenney
中科院分区：
文献类型：
--
作者：
A. Fring;Rebecca Tenney
我们提出了一种微扰方法来确定含时Dyson映射和与含时非Hermitian Hamilton算子相关的度量算子。我们将该方法应用于一对显式的时间依赖的二维谐振子，弱耦合到彼此在PT对称的方式和强耦合显式的时间依赖的负四次非谐振子势。我们证明，一旦微扰Anglomerus成立的耦合微分方程的顺序顺序，可以递归地解决建设性的方式，从而绕过需要作出任何猜测的戴森地图或度量算子。探索的模糊性的顺序顺序的微分方程的解决方案，自然会导致一整套的不等价的解决方案的戴森地图和度量运营商，这意味着不同的物理行为所表现出的期望值的时间依赖的能量运营商。
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.