Canonical symplectic structure and structure-preserving geometric   algorithms for Schr\"odinger-Maxwell systems
  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. 
Qiang Chen, Hong Qin, Jian Liu, Jianyuan Xiao, Ruili Zhang, Yang He,   Yulei Wang
quant-ph math.SG physics.atom-ph physics.plasm-ph