Accurate time propagation method for the coupled Maxwell and Kohn-Sham equations

Area of Science:

• Computational Physics
• Quantum Chemistry
• Electromagnetism

Background:

• Accurate time propagation of coupled Maxwell and time-dependent Kohn-Sham (TDKS) equations is crucial for simulating light-matter interactions.
• Existing methods face challenges in stability, accuracy, and computational efficiency.

Purpose of the Study:

• To present a novel, accurate, and efficient method for the time propagation of the coupled Maxwell and TDKS equations.
• To evaluate the performance of the new method against conventional approaches.

Main Methods:

• A simultaneous fourth-order Runge-Kutta-based propagation scheme for both the vector potential and Kohn-Sham orbitals.
• Comparison with conventional fourth-order Taylor propagation and predictor-corrector methods.

Main Results:

• The new method demonstrates superior computational performance and numerical stability.
• Enhanced accuracy and faster convergence were observed compared to traditional methods.
• The simultaneous propagation approach effectively handles the coupled nature of the equations.

Conclusions:

• The presented Runge-Kutta-based method offers significant advantages for time-dependent simulations involving coupled electromagnetic and electronic dynamics.
• This advancement facilitates more accurate and efficient modeling of complex quantum systems interacting with electromagnetic fields.