Improving the accuracy of the Lorentz Integral Transform method using complex kernels
Abstract
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.
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BibTeX
@misc{parnes2026improving,
title = {{Improving the accuracy of the Lorentz Integral Transform method using complex kernels}},
author = {Elad Parnes and Nir Barnea},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.05887},
eprint = {2609.05887},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.05887},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Improving the accuracy of the Lorentz Integral Transform method using complex kernels
AU - Elad Parnes
AU - Nir Barnea
PY - 2026
DA - 2026/09/05
PB - arXiv
DO - 10.48550/arxiv.2609.05887
UR - https://arxiv.org/abs/2609.05887
AB - 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.
ER -