A quadratic-scaling algorithm with guaranteed convergence for quantum coupled-channel calculations

[2601.01159] A quadratic-scaling algorithm with guaranteed convergence for quantum coupled-channel calculations Skip to main content Search Submit Donate Log in Physics > Chemical Physics arXiv:2601.01159 (physics) [Submitted on 3 Jan 2026 ( v1 ), last revised 7 Jul 2026 (this version, v2)] Title: A quadratic-scaling algorithm with guaranteed convergence for quantum coupled-channel calculations Authors: Hubert J. Jóźwiak , Md Muktadir Rahman , Timur V. Tscherbul View PDF HTML (experimental) Abstract: Rigorous quantum dynamics calculations provide essential insights into complex scattering phenomena across atomic and molecular physics, chemical reaction dynamics, and astrochemistry. However, the application of the gold-standard quantum coupled-channel (CC) method has been fundamentally constrained by a steep cubic scaling of computational cost $[{O}(N^3)]$. Here, we develop a general, rigorous, and robust method for solving the time-independent Schrödinger equation for a single column of the scattering S-matrix with quadratic scaling $[{O}(N^2)]$ in the number of channels. The Weinberg-regularized Iterative Series Expansion (WISE) algorithm resolves the divergence issues affecting iterative techniques by applying a regularization procedure to the kernel of the multichannel Lippmann-Schwinger integral equation. The method also explicitly incorporates closed-channel effects, including those responsible for multichannel Feshbach resonances. We demonstrate the power of this approach by performing rigorous calculations on He + CO and CO + N$_2$ collisions, achieving exact quantum results with quadratic scaling guaranteed by a contour-integral construction. Our results establish a highly scalable computational paradigm, enabling state-to-state quantum scattering computations for complex molecular systems. Comments: 44 pages, 9 figures Subjects: Chemical Physics (physics.chem-ph) ; Atomic Physics (physics.atom-ph); Computational Physics (physics.comp-ph) Cite as: arXiv:2601.01159 [physics.chem-ph] (or arXiv:2601.01159v2 [physics.chem-ph] for this version) https://doi.org/10.48550/arXiv.2601.01159 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Science Advances 12, eaef1257 (2026) Related DOI : https://doi.org/10.1126/sciadv.aef1257 Focus to learn more DOI(s) linking to related resources Submission history From: Hubert Jóźwiak [ view email ] [v1] Sat, 3 Jan 2026 11:22:59 UTC (896 KB) [v2] Tue, 7 Jul 2026 21:27:46 UTC (1,954 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: physics.chem-ph < prev | next > new | recent | 2026-01 Change to browse by: physics physics.atom-ph physics.comp-ph References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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