Extended phase-space symplectic integration for electron dynamics.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Plasma Physics

Background:

• Electron dynamics simulations are crucial in plasma physics and quantum chemistry.
• Traditional methods face challenges with complex systems and high degrees of freedom.
• Symplectic integration offers advantages in conserving energy and phase space volume.

Purpose of the Study:

• To investigate extended phase-space symplectic integration for simulating electron dynamics.
• To adapt and validate high-order symplectic split-operator schemes for systems with finite and infinite degrees of freedom.
• To develop an efficient metric for on-the-fly accuracy estimation in simulations.

Main Methods:

• Extended phase-space symplectic integration was applied to two distinct electron dynamics models.
• The first model involved classical dynamics in plasma physics (1.5 degrees of freedom).
• The second model utilized Kohn-Sham time-dependent density-functional theory from physical chemistry (infinite degrees of freedom).

Main Results:

• The study outlines the extension procedure and stability conditions for numerical integration.
• High-order symplectic split-operator schemes were successfully implemented for both systems.
• A computationally inexpensive metric for on-the-fly accuracy estimation was identified.

Conclusions:

• Extended phase-space symplectic integration is a viable and accurate method for simulating diverse electron dynamics.
• The developed techniques and accuracy metric enable broader applications in classical and quantum Hamiltonian systems.
• This work facilitates more efficient and reliable simulations across computational physics and chemistry domains.