Numerical Methods and Analysis of Computing Quasiperiodic Systems Article Swipe
Kai Jiang
,
ShiFeng Li
,
Pingwen Zhang
·
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2210.04384
YOU?
·
· 2022
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2210.04384
Quasiperiodic systems are important space-filling ordered structures, without decay and translational invariance. How to solve quasiperiodic systems accurately and efficiently is of great challenge. A useful approach, the projection method (PM) [J. Comput. Phys., 256: 428, 2014], has been proposed to compute quasiperiodic systems. Various studies have demonstrated that the PM is an accurate and efficient method to solve quasiperiodic systems. However, there is a lack of theoretical analysis of PM. In this paper, we present a rigorous convergence analysis of the PM by establishing a mathematical framework of quasiperiodic functions and their high-dimensional periodic functions. We also give a theoretical analysis of quasiperiodic spectral method (QSM) based on this framework. Results demonstrate that PM and QSM both have exponential decay, and the QSM (PM) is a generalization of the periodic Fourier spectral (pseudo-spectral) method. Then we analyze the computational complexity of PM and QSM in calculating quasiperiodic systems. The PM can use fast Fourier transform, while the QSM cannot. Moreover, we investigate the accuracy and efficiency of PM, QSM and periodic approximation method in solving the linear time-dependent quasiperiodic Schrödinger equation.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2210.04384
- https://arxiv.org/pdf/2210.04384
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4304730695
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- DOI
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https://doi.org/10.48550/arxiv.2210.04384Digital Object Identifier
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Numerical Methods and Analysis of Computing Quasiperiodic SystemsWork title
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2022Year of publication
- Publication date
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2022-10-10Full publication date if available
- Authors
-
Kai Jiang, ShiFeng Li, Pingwen ZhangList of authors in order
- Landing page
-
https://arxiv.org/abs/2210.04384Publisher landing page
- PDF URL
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https://arxiv.org/pdf/2210.04384Direct link to full text PDF
- Open access
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YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2210.04384Direct OA link when available
- Concepts
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Quasiperiodic function, Fourier analysis, Fourier transform, Mathematics, Spectral analysis, Spectral method, Mathematical analysis, Applied mathematics, Statistical physics, Physics, Quantum mechanics, SpectroscopyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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