Canonical symplectic structure and structure-preserving geometric algorithms for Schr\"odinger-Maxwell systems
Quantum Physics
2017-09-05 v4 Symplectic Geometry
Atomic Physics
Plasma Physics
Abstract
An infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schr\"odinger-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. 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.
Cite
@article{arxiv.1611.08955,
title = {Canonical symplectic structure and structure-preserving geometric algorithms for Schr\"odinger-Maxwell systems},
author = {Qiang Chen and Hong Qin and Jian Liu and Jianyuan Xiao and Ruili Zhang and Yang He and Yulei Wang},
journal= {arXiv preprint arXiv:1611.08955},
year = {2017}
}
Comments
17 pages, 7 figures