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. 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.

17 pages, 7 figures

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• Simulating Maxwell-Schrödinger Equations by High-Order Symplectic FDTD Algorithm
• Gauge invariant canonical symplectic algorithms for real-time lattice strong-field quantum electrodynamics
• Variational Schemes and Geometric Simulations for a Hydrodynamic-Electrodynamic Model of Surface Plasmon Polaritons
• Variational formulation of classical and quantum models for intense laser pulse propagation
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• Symmetries and Local Conservation Laws of Variational Schemes for the Surface Plasmon Polaritons