Statistical mechanics of dense ionized matter. III. Dynamical properties of the classical one-component plasma

TLDR

The study aims to compute time‑dependent correlation functions of the classical one‑component plasma across a wide range of Γ values using molecular‑dynamics simulations. The authors perform extensive MD simulations to evaluate these correlation functions over a broad spectrum of thermodynamic states defined by Γ= e²/(a k_B T). The simulations show that for Γ ≳ 10 the velocity autocorrelation oscillates at the plasma frequency, the dynamical structure factor has sharp peaks up to k≈1/a, negative dispersion appears for Γ ≳ 3, shear modes emerge at Γ = 152.4, a second high‑frequency transverse mode appears at large k, and the extracted diffusion constant and shear viscosity are unusually large near crystallization.

Abstract

We present extensive molecular-dynamics (MD) computations of the time-dependent correlation functions of the classical one-component plasma over a wide range of thermodynamic states characterized by the dimensionless parameter $\ensuremath{\Gamma}=\frac{{e}^{2}}{a{k}_{B}T}$, where $a$ is the ion-sphere radius. The computed velocity autocorrelation functions exhibit marked oscillations for $\ensuremath{\Gamma}\ensuremath{\gtrsim}10$ at a frequency close to the plasma frequency, showing the existence of strong coupling between single-particle and collective modes; this is confirmed by a standard memory-function analysis. The dynamical structure factor consists of very sharp peaks near the plasma frequency, up to wave vectors of order $\frac{1}{a}$. The resulting dispersion curve exhibits negative dispersion for $\ensuremath{\Gamma}\ensuremath{\gtrsim}3$. A simple memory-function analysis reproduces the MD data very well. At $\ensuremath{\Gamma}=152.4$ our computations also provide evidence of well-defined shear modes. For large wave vectors a second, high-frequency transverse mode appears. From the correlation functions we have finally extracted estimates of the diffusion constant and the coefficient of shear viscosity. Near crystallization the shear viscosity has a value which is unusually large compared with that of simple liquids near the triple point.