Transverse current fluctuations in the Yukawa one-component plasma

Using numerical simulations, we investigate the wave number and frequency dependent transverse current correlation function $C_T(k,\omega )$ of a single-component fluid with Yukawa interaction potential, also known as the Yukawa one-component plasma. The transverse current correlation function is an important quantity because it contains the microscopic details of the viscoelastic behavior of the fluid. We show that, in the region of densities and temperatures in which shear waves do not propagate, the dynamics of the system are in striking agreement with a simple model of generalized hydrodynamics. As either the density is increased or the temperature decreased, the transverse current correlation function shows additional structure that the simple models fail to capture.

Figure 1

Memory function in the time domain for Gaussian (solid line) and exponential (dashed line) models, for ${\tau }_k{\omega }_p=1$.

Figure 2

Comparison between the Gaussian model when only the parameter ${\tau }_k$ is fitted to the MD spectrum (dashed line) and when both ${\tau }_k$ and ${\omega }_T^2\left(k\right)$ are fitted (solid line) for four separate cases. The MD results are given by the dots.

Figure 3

Comparison between ${\omega }_T^2\left(k\right)$ as computed from MD using the formula in the Appendix (dashed line, with $10\%$ error band) and the values obtained from the two-parameter fit of the Gaussian memory function model (triangles) and the exponential model (squares) for three different ($\Gamma ,\kappa$) pairs: (a) $\Gamma =5$, $\kappa =0.1$; (b) $\Gamma =10$, $\kappa =1$; and (c) $\Gamma =1$, $\kappa =2$.

Figure 4

Comparison between the MD data for $C_T(k,\omega )$ (dots) and the Gaussian memory function model with two fitting parameters (solid line) for the smallest $ka$ value accessible to our simulations.

Figure 5

Comparison between the MD data for $C_T(k,\omega )$ (dots) and the Gaussian memory function model with two fitting parameters (solid line) for intermediate $ka$ values.

Figure 6

Comparison between the MD data for $C_T(k,\omega )$ (dots) and the Gaussian memory function model with two fitting parameters (solid line) for large $ka$ values.

Figure 7

Position of shear wave peak $\omega \left(k\right)$ for (a) $\kappa =0.1$ and 1 at a fixed coupling parameter $\Gamma =175$, (b) $\kappa =1$ and 2 at a fixed coupling parameter $\Gamma =200$, and (c) $\Gamma =200,300,350,400$ at fixed screening parameter $\kappa =2$.

Figure 8

Comparison between the MD data for $C_T(k,\omega )$ (dots) and the Gaussian memory function model with two fitting parameters (solid line) in the region of shear wave propagation. Also shown is the exponential memory function model (dashed line).

Figure 9

Comparison between the MD data for $C_T(k,\omega )$ (dots) and the Gaussian memory function model with two fitting parameters (solid line). Also shown is the exponential memory function model (dashed line).