Superdiffusion in quasi-two-dimensional Yukawa liquids

The emergence and vanishing of superdiffusion in quasi-two-dimensional Yukawa systems are investigated by molecular dynamics simulations. Using both the asymptotic behavior of the mean-squared displacement of the particles and the long-time tail of the velocity autocorrelation function as indicators of superdiffusion, we confirm the existence of a transition from normal diffusion to superdiffusion in systems changing from a three-dimensional to a two-dimensional character. A connection between superdiffusion and dimensionality is established by the behavior of the projected pair distribution function.

Figure 1

Soft-box potential $\varphi \left(z\right)$ and corresponding particle density $n\left(z\right)$. The trap is impenetrable at $\pm W$ and the particles can typically explore the trap width $w$ (here, $w=2a_{ws}$).

Figure 2

The MSD over time for different trap amplitudes in the harmonic confinement and $\kappa =2.0$. The solid lines have slope 2.0 (ballistic regime) and 1.0 (normal diffusion), respectively. The slope of the MSD in this log-log plot is the diffusion exponent; see Fig. 3.

Figure 3

The diffusion exponent for different trap amplitudes and $\kappa =2.0$ in the harmonic confinement. The straight line is a guide for the eyes. Also shown is the value of the (projected) pair correlation function at the distance $r=a_{ws}$. The top graphs show the density profile in the confined direction from $z=-4a_{ws}$ to $z=4a_{ws}$ at the trap amplitude indicated by the arrows. The $n\left(z\right)$ distributions are normalized here to unit amplitude.

Figure 4

The diffusion exponent for different trap amplitudes and $\kappa =3.0$ in the harmonic confinement. Also shown is the value of the (projected) pair correlation function at the distance $r=a_{ws}$. The top graphs show the density profile from $z=-4a_{ws}$ to $z=4a_{ws}$ in the confined direction at the trap amplitude indicated by the arrows. The $n\left(z\right)$ distributions are normalized here to unit amplitude.

Figure 5

The diffusion exponent $\gamma$ as a function of the projected pair distribution $g^{*}\left(a_{ws}\right)$ for $\kappa =2.0$ and $\kappa =3.0$ in the harmonic confinement.

Figure 6

(a) Double-logarithmic plot of the long-time tail of the VACF $Z\left(t\right)$ $[Z\left(0\right)=1]$ from $f=0.01$ (top) to $f=0.28$ (bottom). (b) The exponent of the algrebraic decay of the velocity autocorrelation function for $\kappa =2.0$ and different trap amplitudes in the harmonic confinement. Error bars denote standard errors from the jackknife estimator. The top graphs show the density profile in the confined direction from $z=-4a_{ws}$ to $z=4a_{ws}$ at the trap amplitude indicated by the arrows. The $n\left(z\right)$ distributions are normalized here to unit amplitude.

Figure 7

The exponent of the algrebraic decay of the velocity autocorrelation function for $\kappa =3.0$ and different trap amplitudes in the harmonic confinement. Error bars denote standard errors from the jackknife estimator. The top graphs show the density profile in the confined direction from $z=-4a_{ws}$ to $z=4a_{ws}$ at the trap amplitude indicated by the arrows. The $n\left(z\right)$ distributions are normalized here to unit amplitude.

Figure 8

(Color online) The diffusion exponent for different box widths and $\kappa =3.0$ in the soft-box confinement. Also shown is the value of the (projected) pair correlation function at the distance $r=a_{ws}$. The top graphs show the density profile in the confined direction from $z=-3a_{ws}$ to $z=3a_{ws}$ at the box width indicated by the arrows. The $n\left(z\right)$ distributions are normalized here to unit amplitude. The background color separates regions of one, two, and three layers.

Figure 9

(Color online) The diffusion exponent for different box widths and $\kappa =2.0$ in the soft-box confinement. The top graphs show the density profile in the confined direction from $z=-3a_{ws}$ to $z=3a_{ws}$ at the box width indicated by the arrows. The $n\left(z\right)$ distributions are normalized here to unit amplitude. The background color separates regions of one, two, and three layers.