基于高斯过程回归的复杂共振谱中奇异点定位方法
Gaussian-process-regression-based method for the localization of exceptional points in complex resonance spectra
AI总结：
本文提出基于高斯过程回归的机器学习方法，通过迭代添加精确本征值对来高效定位开放量子系统共振谱中的奇异点，并在氧化亚铜激子系统中验证了其有效性。
摘要：
开放量子系统中依赖于至少两个可控参数的共振可以表现出奇异点（EPs）现象，此时不仅两个或多个共振的本征值，而且它们的本征向量也会合并。在参数空间中精确确定奇异点的位置具有挑战性，尤其是在计算量子谱和共振数值上非常昂贵的系统中。我们引入了一种基于高斯过程回归（GPR）的高效机器学习算法来寻找奇异点。GPR模型使用属于某个奇异点的初始本征值对集合进行训练，并通过数值上廉价的根搜索对奇异点位置进行首次估计。随后，通过将选定的精确本征值对作为训练点添加到GPR模型中，迭代地改进该估计。基于GPR的方法在一个简单的低维矩阵模型上进行了开发和测试，然后应用于一个具有挑战性的真实物理系统，即在外部电场和磁场中氧化亚铜中激子的共振谱中定位奇异点。通过考虑晶体的完整价带结构和中心晶胞修正来精确计算奇异点，可以为在该系统中实验观测奇异点奠定基础。
英文摘要：
Resonances in open quantum systems depending on at least two controllable parameters can show the phenomenon of exceptional points (EPs), where not only the eigenvalues but also the eigenvectors of two or more resonances coalesce. Their exact localization in the parameter space is challenging, in particular in systems, where the computation of the quantum spectra and resonances is numerically very expensive. We introduce an efficient machine learning algorithm to find exceptional points based on Gaussian process regression (GPR). The GPR-model is trained with an initial set of eigenvalue pairs belonging to an EP and used for a first estimation of the EP position via a numerically cheap root search. The estimate is then improved iteratively by adding selected exact eigenvalue pairs as training points to the GPR-model. The GPR-based method is developed and tested on a simple low-dimensional matrix model and then applied to a challenging real physical system, viz., the localization of EPs in the resonance spectra of excitons in cuprous oxide in external electric and magnetic fields. The precise computation of EPs, by taking into account the complete valence band structure and central-cell corrections of the crystal, can be the basis for the experimental observation of EPs in this system.
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