A quadratic-scaling algorithm with guaranteed convergence for quantum coupled-channel calculations
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 []. Here, we develop a general, rigorous, and robust method for solving the time-independent Schr\"odinger equation for a single column of the scattering S-matrix with quadratic scaling [] 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 collisions, achieving exact quantum results with demonstrably quadratic scaling. Our results establish a new computational paradigm, enabling state-to-state quantum scattering computations for complex molecular systems and providing a novel window onto the intricate multichannel molecular collision dynamics.
Cite
@article{arxiv.2601.01159,
title = {A quadratic-scaling algorithm with guaranteed convergence for quantum coupled-channel calculations},
author = {Hubert J. Jóźwiak and Md Muktadir Rahman and Timur V. Tscherbul},
journal= {arXiv preprint arXiv:2601.01159},
year = {2026}
}
Comments
32 pages, 4 figures