利用复核改进洛伦兹积分变换方法的精度
Improving the accuracy of the Lorentz Integral Transform method using complex kernels
- The Racah Institute of Physics, The Hebrew University of Jerusalem（耶路撒冷希伯来大学拉卡物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出利用复Stieltjes核和双极点核改进洛伦兹积分变换的反演条件，在氘核光致蜕变基准测试中，将噪声诱导离散度降低2-4倍。
AI中文摘要：
洛伦兹积分变换（LIT）方法是计算量子响应函数的强大工具；然而，它需要不适定的反演。在此我们表明，LIT方程的解也能确定两个额外的积分变换：复Stieltjes变换和双极点变换，且额外计算成本很小。对相关反卷积问题的傅里叶分析表明，在相同宽度参数$\Gamma$下，这两个替代核的条件数均优于洛伦兹核。我们通过向LIT解添加受控噪声，对氘核光致蜕变的反演结果进行了基准测试。相对于标准LIT，替代核产生的响应函数具有更小的噪声诱导离散度：复Stieltjes核降低2-3倍，双极点核降低3-4倍。
英文摘要：
The Lorentz integral transform (LIT) method is a powerful tool for calculating quantum response functions; however, it requires an ill-posed inversion. Here we show that solutions of the LIT equation can also determine two additional integral transforms: a complex Stieltjes transform and a double-pole transform, at little additional computational cost. A Fourier analysis of the associated deconvolution problem shows that both alternative kernels are better conditioned than the Lorentzian kernel at the same width parameter $Γ$. We benchmark the resulting inversions for deuteron photodisintegration by adding controlled noise to the LIT solutions. Relative to the standard LIT, the alternative kernels yield response functions with reduced noise-induced scatter: by a factor of 2-3 for the complex Stieltjes kernel and 3-4 for the double-pole kernel.
