Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems

Journal Article · 24 August 2017 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2017.08.033 · OSTI ID:1420776

Chen, Qiang  ^[1]; Qin, Hong ^[2]; Liu, Jian ^[3]; Xiao, Jianyuan ^[3]; Zhang, Ruili ^[3]; He, Yang ^[4]; Wang, Yulei ^[3]

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1. Univ. of Science and Technology of China, Anhui (China); Luoyang Electronic Equipment Testing Center, Luoyang (China)
2. Univ. of Science and Technology of China, Anhui (China); Princeton Univ., Princeton, NJ (United States). Princeton Plasma Physics Lab.
3. Univ. of Science and Technology of China, Anhui (China)
4. Univ. of Science and Technology Beijing, Beijing (China)

An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon–matter interactions described by the Schrödinger–Maxwell equations. The algorithms preserve the symplectic structure of the system and the unitary nature of the wavefunctions, and bound the energy error of the simulation for all time-steps. Here, this new numerical capability enables us to carry out first-principle based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with long-term accuracy and fidelity.

• Research Organization: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: 51477182; 11575185; 11575186; 2015GB111003; QYZDB-SSW-SYS004
• OSTI ID: 1420776
• Journal Information: Journal of Computational Physics, Vol. 349, Issue C; ISSN 0021-9991
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English