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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.17432 |
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| _version_ | 1866911224155865088 |
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| author | Fu, Zhichang Li, Yunhai Zhou, Weiqing Yuan, Shengjun |
| author_facet | Fu, Zhichang Li, Yunhai Zhou, Weiqing Yuan, Shengjun |
| contents | The $O(N)$ stochastic propagation method, which relies on the numerical solution of the time-dependent Schrödinger equation using random initial states, is widely used in large-scale first-principles calculations. In this work, we eliminate the conventional sequential computation of intermediate states by introducing a concurrent strategy that minimizes information redundancy. The new method, in its state-, moment-, and energy-based implementations, not only surpasses the time step constraint of sequential propagation but also maintains precision within the framework of the Nyquist-Shannon sampling theorem. Systematic benchmarking on one billion atoms within the tight-binding model demonstrates that our new concurrent method achieves up to an order-of-magnitude speedup, enabling the rapid computation of a wide range of electronic, optical, and transport properties. This performance breakthrough offers valuable insights for enhancing other time-propagation algorithms, including those employed in large-scale stochastic density functional theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17432 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Large-scale stochastic propagation method beyond the sequential approach Fu, Zhichang Li, Yunhai Zhou, Weiqing Yuan, Shengjun Computational Physics Materials Science The $O(N)$ stochastic propagation method, which relies on the numerical solution of the time-dependent Schrödinger equation using random initial states, is widely used in large-scale first-principles calculations. In this work, we eliminate the conventional sequential computation of intermediate states by introducing a concurrent strategy that minimizes information redundancy. The new method, in its state-, moment-, and energy-based implementations, not only surpasses the time step constraint of sequential propagation but also maintains precision within the framework of the Nyquist-Shannon sampling theorem. Systematic benchmarking on one billion atoms within the tight-binding model demonstrates that our new concurrent method achieves up to an order-of-magnitude speedup, enabling the rapid computation of a wide range of electronic, optical, and transport properties. This performance breakthrough offers valuable insights for enhancing other time-propagation algorithms, including those employed in large-scale stochastic density functional theory. |
| title | Large-scale stochastic propagation method beyond the sequential approach |
| topic | Computational Physics Materials Science |
| url | https://arxiv.org/abs/2510.17432 |