Canonical symplectic structure and structurepreserving geometric algorithms for Schrödinger–Maxwell systems
An infinite dimensional canonical symplectic structure and structurepreserving 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 timesteps. Here, this new numerical capability enables us to carry out firstprinciple based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with longterm accuracy and fidelity.
 Authors:

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 Univ. of Science and Technology of China, Anhui (China); Luoyang Electronic Equipment Testing Center, Luoyang (China)
 Univ. of Science and Technology of China, Anhui (China); Princeton Univ., Princeton, NJ (United States). Princeton Plasma Physics Lab.
 Univ. of Science and Technology of China, Anhui (China)
 Univ. of Science and Technology Beijing, Beijing (China)
 Publication Date:
 Grant/Contract Number:
 51477182; 11575185; 11575186; 2015GB111003; QYZDBSSWSYS004
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 349; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Research Org:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Sponsoring Org:
 USDOE
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Schrödinger–Maxwell equations; Symplectic structure; Discrete Poisson bracket; Geometric algorithms; Firstprinciple simulation
 OSTI Identifier:
 1420776
Chen, Qiang, Qin, Hong, Liu, Jian, Xiao, Jianyuan, Zhang, Ruili, He, Yang, and Wang, Yulei. Canonical symplectic structure and structurepreserving geometric algorithms for Schrödinger–Maxwell systems. United States: N. p.,
Web. doi:10.1016/j.jcp.2017.08.033.
Chen, Qiang, Qin, Hong, Liu, Jian, Xiao, Jianyuan, Zhang, Ruili, He, Yang, & Wang, Yulei. Canonical symplectic structure and structurepreserving geometric algorithms for Schrödinger–Maxwell systems. United States. doi:10.1016/j.jcp.2017.08.033.
Chen, Qiang, Qin, Hong, Liu, Jian, Xiao, Jianyuan, Zhang, Ruili, He, Yang, and Wang, Yulei. 2017.
"Canonical symplectic structure and structurepreserving geometric algorithms for Schrödinger–Maxwell systems". United States.
doi:10.1016/j.jcp.2017.08.033. https://www.osti.gov/servlets/purl/1420776.
@article{osti_1420776,
title = {Canonical symplectic structure and structurepreserving geometric algorithms for Schrödinger–Maxwell systems},
author = {Chen, Qiang and Qin, Hong and Liu, Jian and Xiao, Jianyuan and Zhang, Ruili and He, Yang and Wang, Yulei},
abstractNote = {An infinite dimensional canonical symplectic structure and structurepreserving 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 timesteps. Here, this new numerical capability enables us to carry out firstprinciple based simulation study of important photon–matter interactions, such as the high harmonic generation and stabilization of ionization, with longterm accuracy and fidelity.},
doi = {10.1016/j.jcp.2017.08.033},
journal = {Journal of Computational Physics},
number = C,
volume = 349,
place = {United States},
year = {2017},
month = {8}
}