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arXiv · 1611.08955

Canonical symplectic structure and structure-preserving geometric algorithms for Schr\"odinger-Maxwell systems

Qiang Chen·Hong Qin·Jian Liu·Jianyuan Xiao·Ruili Zhang·Yang He·Yulei Wang
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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.

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Qiang Chen, Hong Qin, Jian Liu, Jianyuan Xiao, Ruili Zhang, Yang He, Yulei Wang. 2016-11-28. Canonical symplectic structure and structure-preserving geometric algorithms for Schr\"odinger-Maxwell systems. https://doi.org/10.1016/j.jcp.2017.08.033

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