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A statistical theory of electronic degrees of freedom in wave packet molecular dynamics

Daniel Plummer, Pontus Svensson, Wiktor Jasniak, Patrick Hollebon, Sam M. Vinko, Gianluca Gregori

TL;DR

The paper develops a statistical framework for electronic widths in wave packet molecular dynamics under warm dense matter conditions, deriving analytic width distributions for both anisotropic and isotropic Gaussian wavepackets from the underlying WP Hamiltonian. By comparing non-interacting theory to fully interacting molecular dynamics data, it shows remarkable agreement and reveals a shoulder in the width distributions caused by eigenvalue repulsion, which governs effective Coulomb interactions. A crucial finding is the necessity of a confining potential to prevent unphysical width divergence, linking width statistics to practical constraints in WPMD simulations. The work provides a pathway to predict confinement strength a priori and clarifies how different wavepacket Ansätze affect electronic structure and transport properties in dense plasmas.

Abstract

We derive statistical distributions for the degrees of freedom in wave packet molecular dynamics models. Specifically, a theory is developed for the width distributions of Gaussian wavepackets in both isotropic and anisotropic formulations. The resulting distribution functions show good agreement with molecular dynamics data under warm dense matter conditions, providing practical guidance for constraining the confining potential, an empirical parameter in the model. We also discuss how these distributions influence the resulting effective Coulomb interactions.

A statistical theory of electronic degrees of freedom in wave packet molecular dynamics

TL;DR

The paper develops a statistical framework for electronic widths in wave packet molecular dynamics under warm dense matter conditions, deriving analytic width distributions for both anisotropic and isotropic Gaussian wavepackets from the underlying WP Hamiltonian. By comparing non-interacting theory to fully interacting molecular dynamics data, it shows remarkable agreement and reveals a shoulder in the width distributions caused by eigenvalue repulsion, which governs effective Coulomb interactions. A crucial finding is the necessity of a confining potential to prevent unphysical width divergence, linking width statistics to practical constraints in WPMD simulations. The work provides a pathway to predict confinement strength a priori and clarifies how different wavepacket Ansätze affect electronic structure and transport properties in dense plasmas.

Abstract

We derive statistical distributions for the degrees of freedom in wave packet molecular dynamics models. Specifically, a theory is developed for the width distributions of Gaussian wavepackets in both isotropic and anisotropic formulations. The resulting distribution functions show good agreement with molecular dynamics data under warm dense matter conditions, providing practical guidance for constraining the confining potential, an empirical parameter in the model. We also discuss how these distributions influence the resulting effective Coulomb interactions.
Paper Structure (12 sections, 33 equations, 3 figures)

This paper contains 12 sections, 33 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Gaussian wavepacket Ansätze
  3. Additional potentials
  4. Statistical theory for the width distribution
  5. Anisotropic case
  6. Isotropic case
  7. Comparison against interacting molecular dynamics data
  8. Numerical Details
  9. Molecular dynamics
  10. Markov Chain Monte Carlo
  11. Model comparison
  12. Discussion

Figures (3)

  • Figure 1: Marginal width distribution functions for an anisotropic plasma at $r_s=2$ and $\theta=1$ for different confining potentials. Excluding the $A=4.00 \, \text{Ha}/\text{a}_0^2$ case, each curve is shifted by $1 \, a_0$ relative to the curve to its left for clarity. The histograms correspond to molecular dynamics (MD) results in the microcanonical ensemble, while the dashed lines correspond to Markov Chain Monte Carlo (MCMC) sampling of Eq. \ref{['eq:ani_lambda_dist']}. Arrows indicate the shoulder feature discussed in the main text. The simulations are performed within a cubic box of side length $L=52.5 \, a_0$. Hartree atomic units are used in the legend.
  • Figure 2: Effective interparticle Coulomb interactions based on the mean width of the distributions plotted in Fig. \ref{['fig:ani_width_dists']}.
  • Figure 3: Comparison between isotropic and anisotropic width distribution functions at $r_s=2, \theta=1$ for a confining potential of $A=0.17 \, \text{Ha}/\text{a}_0^2$. (a) Average width distribution functions for the isotropic and anisotropic models. (b) Distribution of individual width variables in the anisotropic model. The grey dashed line indicates the modal width of the isotropic model given by Eq. \ref{['eq:iso_mode']}. The mean values of each distribution are also plotted, with the isotropic case given by Eq. \ref{['eq:iso_mean']}, and the anisotropic case calculated numerically.