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

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 $\Gamma =\frac{e^2}{a{k}_{B}T}$, where $a$ is the ion-sphere radius. The computed velocity autocorrelation functions exhibit marked oscillations for $\Gamma \gtrsim 10$ 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 $\Gamma \gtrsim 3$. A simple memory-function analysis reproduces the MD data very well. At $\Gamma =152.4\mathrm{}$ 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.