Is Diffusion Anomalous in Two-Dimensional Yukawa Liquids?

There have recently been many predictions of “superdiffusion” in two-dimensional strongly coupled Yukawa systems, both by computer simulations and in dusty plasma experiments, with substantially varying diffusion exponents. Here we show that the results crucially depend on the strength of dissipation and the time instant of the measurement. For sufficiently large friction even subdiffusion is possible. However, there are strong indications that, in the long-time limit, anomalous diffusion vanishes and the system returns to normal diffusion, for dissipative as well as for frictionless systems.

Figure 1

Diffusion exponent $\alpha$ as a function of ${\Gamma }^{\mathrm{rel}}$ for different values of $\kappa$ (1.0, 2.0, 3.0) obtained from a best fit of Eq. (2) in the time window ${\omega }_{p}t\in [100,320]$. The three ticks on the upper $x$ axis indicate the three values of ${\Gamma }^{\mathrm{rel}}$ used in Figs. 2, 3, 4, 5.

Figure 2

(a) $u_r(t)$ for ${\Gamma }^{\mathrm{rel}}=0.16$ and $\nu =0.001$, 0.08, 1.0. (b) Corresponding $\alpha (t)$.

Figure 3

Instantaneous diffusion exponent $\alpha (t)$ as a function of friction coefficient $\nu$ and time ${\omega }_{p}t$ for ${\Gamma }^{\mathrm{rel}}=0.16$. (a) Density representation with contour lines for $\alpha =1.50$, 1.30, 1.10, 1.03, 0.97. (b) Schematic representation with labeled regions of super-, sub-, and normal diffusion.

Figure 4

Instantaneous diffusion exponent $\alpha (t)$ as a function of friction coefficient $\nu$ and time ${\omega }_{p}t$ for ${\Gamma }^{\mathrm{rel}}=0.40$ (top) and ${\Gamma }^{\mathrm{rel}}=0.040$ (bottom).

Figure 5

Instantaneous diffusion exponent $\alpha (t)$ for $\nu =0$. Subsequent curves differ in ${\Gamma }^{\mathrm{rel}}$ by a factor of 1.41.