Comparative merits of the memory function and dynamic local-field correction of the classical one-component plasma

The complementarity of the liquid and plasma descriptions of the classical one-component plasma is explored by studying wave number and frequency dependent dynamical quantities: the dynamical structure factor (DSF) and the dynamic local field correction (LFC). Accurate molecular dynamics (MD) simulations are used to validate and test models of the DSF and LFC. Our simulations, which span the entire fluid regime ($\Gamma =0.1–175$), show that the DSF is very well represented by a simple and well known memory function model of generalized hydrodynamics. On the other hand, the LFC, which we have computed using MD for the first time, is not well described by existing models.

Figure 1

MD results for the DSF at selected $\Gamma$ and $ka$ values (dots) and the result of the Gaussian model when the parameter ${\tau }_k$ is fitted to the MD spectrum (dashed line).

Figure 2

MD results for the DSF at selected $\Gamma$ and $ka$ values (dots) along with the result of the Gaussian model when only the parameter ${\tau }_k$ is fitted to the MD spectrum (dashed line) and the result when $\langle {\omega }_k^2\rangle$, $\langle {\omega }_L^2\left(k\right)\rangle$, and ${\tau }_k$ are all fitted (solid line).

Figure 3

Comparison between $\langle {\omega }_k^2\rangle$ as computed from MD using the formulas in the Appendix (dashed line, with $10\%$ error band) and the values obtained from the three-parameter fit of the Gaussian memory function model (triangles) for three different coupling parameters.

Figure 4

Comparison between ${\omega }_L^2\left(k\right)$ as computed from MD using the formulas in the Appendix (dashed line, with $10\%$ error band) and the values obtained from the three-parameter fit of the Gaussian memory function model (triangles) for three different coupling parameters.

Figure 5

MD results for the DSF at $\Gamma =0.3$, 1, 5, and 10 (dots) and the memory function fits (solid lines).

Figure 6

MD results for the DSF at $\Gamma =50$, 120, 160, and 175 (dots) and the memory function fits (solid lines).

Figure 7

MD data for the DSF at $ka=6.19$ (dots) and the ideal gas limit given by Eq. (9) (solid line).

Figure 8

MD data for the static structure factor $S\left(k\right)$ at different coupling parameters. Also plotted is the Debye (mean field) result $S_D\left(k\right)=k^2/(k^2+k_D^2)$ for $\Gamma =0.3$, which—as expected—agrees well with the MD data in this weakly coupled regime.

Figure 9

The relaxation time ${\tau }_k$ as determined from the fit of the Gaussian model to the MD spectrum of $S(k,\omega )$.

Figure 10

Real and imaginary parts of dynamic LFC $G(k,\omega )$ as computed from MD at $ka=1.02$ (red dots). Also shown is the model of Hong and Kim as given in Eq. (14) (dotted line). For $\Gamma =160$, the model of Tanaka and Ichimaru is shown with both the Gaussian approximation (light gray line) and the Lorentzian approximation (dark gray line) for the relaxation time ${\tau }_M\left(k\right)$. The dashed lines (Re$\left\{G\right\}$ only) show $G(k,\infty )$.

Figure 11

Same as Fig. 10 but for $ka=3.09$.

Figure 12

Same as Fig. 10 but for $ka=6.19$.