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

Abstract

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.

Authors:
ORCiD logo [1];  [2];  [3];  [3];  [3];  [4];  [3]
  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)
Publication Date:
Research Org.:
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1420776
Grant/Contract Number:  
51477182; 11575185; 11575186; 2015GB111003; QYZDB-SSW-SYS004
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 349; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Schrödinger–Maxwell equations; Symplectic structure; Discrete Poisson bracket; Geometric algorithms; First-principle simulation

Citation Formats

Chen, Qiang, Qin, Hong, Liu, Jian, Xiao, Jianyuan, Zhang, Ruili, He, Yang, and Wang, Yulei. Canonical symplectic structure and structure-preserving geometric algorithms for Schrödinger–Maxwell systems. United States: N. p., 2017. 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 structure-preserving 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. Thu . "Canonical symplectic structure and structure-preserving 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 structure-preserving 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 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.},
doi = {10.1016/j.jcp.2017.08.033},
journal = {Journal of Computational Physics},
number = C,
volume = 349,
place = {United States},
year = {2017},
month = {8}
}

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