Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	Dr. Qiang Chen, Luoyang Electronic Equipment Testing Center
Inviter:
Title:	Structure-preserving geometric simulations for quantum electrodynamics
Time & Venue:	2019.09.13 11:35-12:20 N204
Abstract:	Quantum electrodynamics (QED) at extreme conditions is becoming more and more important, as the relativistic quantum effects are becoming dominant mechanism in many branches of modern physics. The chirped pulse amplification (CPA) based high power laser technologies bring a 1022 W·cm 2 power density, which is stronger than the direct ionization threshold. Such a strong field brings many new physics, e.g., multiphoton ionization, above threshold ionization (ATI), high harmonic generation (HHG) and stabilization, which play a major role in modern high energy density physics, experimental astrophysics, attosecond physics, strong field QED (SFQED) and controlled fusion. Effective and accurate non-perturbative methods are needed in understanding these QED phenomena. In non-relativistic regime, an infinite dimensional canonical symplectic structure and structure-preserving geometric algorithms are developed for the photon-matter interactions described by the Schrodinger-Maxwell equations. Discrete exterior calculus (DEC), discrete canonical Poisson bracket (DCPB), Hamiltonian splitting method, and symmetric composition technique are introduced to construct the geometric algorithms. The algorithms preserve the symplectic structure of the system and the unitary nature of the wave functions, and bound the energy error of the simulation for all time steps. In relativistic regime, a class of high-order canonical symplectic structure-preserving geometric algorithms are developed for high-quality simulations of the Dirac-Maxwell theory based SFQED and relativistic quantum plasmas (RQP) phenomena. The Lagrangian density of an interacting bispionr-gauge fields theory is constructed in a conjugate real fields form, and the canonical symplectic structure is obtained directly. In the unified DEC framework, we treat the bispinor components as different differential forms on the space-like submanifold. As a result, the lattice Brillouin zone (BZ) is modified and the pseudo-fermion modes in naive discretization can be effectively suppressed. With Wilson lines, the discrete action is gauge invariant. A well-defined DCPB generates a semi-discrete lattice canonical field theory, which admits canonical symplectic form, unitary property, gauge symmetry and Poincaré invariance. Then a class of structure-preserving geometric algorithms are constructed for the lattice field theory. These schemes are fermion doubling free and locally unconditional stable. Equipped with well-defined vacuum models, the schemes are expected to have good performance in secular simulations of SFQED and RQP phenomena. In summary, the canonical symplectic structure-preserving geometric algorithms constructed for QED can preserve the symmetries and geometric structures of the semi-discrete fields theory. This new numerical capability enables us to carry out first-principle based simulation study of important photon-matter interactions with long-term accuracy and fidelity.