Numerical convergence of the self-diffusion coefficient and viscosity obtained with Thomas-Fermi-Dirac molecular...

Area of Science:

• Plasma Physics
• Computational Physics
• Condensed Matter Physics

Background:

• Accurate computation of transport coefficients is crucial for understanding warm dense matter.
• Traditional methods for calculating self-diffusion and viscosity can suffer from numerical inaccuracies and extrapolation errors.

Purpose of the Study:

• To compute the self-diffusion coefficient and viscosity in warm dense matter with high numerical precision.
• To evaluate the reliability of different computational approaches, particularly regarding the Green-Kubo relation and extrapolation methods.
• To identify simple analytical laws approximating these transport coefficients across a wide range of conditions.

Main Methods:

• Utilizing the Green-Kubo relation and orbital-free molecular dynamics simulations.
• Employing the Thomas-Fermi-Dirac model for electronic interactions.
• Ensuring numerical convergence by verifying the plateau of the Green-Kubo integral in the long-time limit.
• Comparing direct constant deduction versus extrapolation for transport coefficients.

Main Results:

• Achieved numerically converged values for self-diffusion coefficient and viscosity.
• Demonstrated that extrapolating the Green-Kubo integral can introduce significant, unknown errors, especially for viscosity.
• Established that both self-diffusion and viscosity are well-approximated by simple analytical laws.
• These laws depend on a single effective atomic number derived from the average-atom model.

Conclusions:

• The study provides reliable transport coefficients for warm dense matter through careful numerical convergence.
• Directly deducing transport coefficients from the plateau of the Green-Kubo integral is preferred over extrapolation.
• Simple analytical laws offer a robust approximation for self-diffusion and viscosity in warm dense matter over a broad parameter range.