Cage correlation and diffusion in strongly coupled three-dimensional Yukawa systems in magnetic fields

The influence of an external homogeneous magnetic field on the quasilocalization of the particles—characterized quantitatively by cage correlation functions—in strongly coupled three-dimensional Yukawa systems is investigated via molecular dynamics computer simulations over a wide domain of the system parameters (coupling and screening strengths, and magnetic field). The caging time is found to be enhanced by the magnetic field $\mathbf{B}$. The anisotropic migration of the particles in the presence of magnetic field is quantified via computing directional correlation functions, which indicate a more significant increase of localization in the direction perpendicular to $\mathbf{B}$, while a moderate increase is also found along the $\mathbf{B}$ field lines. Associating the particles' escapes from the cages with jumps of a characteristic length, a connection is found with the diffusion process: the diffusion coefficients derived from the decay time of the directional correlation functions in both the directions perpendicular to and parallel with $\mathbf{B}$ are in very good agreement with respective diffusion coefficients values obtained from their usual computation based on the mean-squared displacement of the particles.

Figure 1

Cage correlation functions $C^{\left(7\right)}\left(t\right)$ (a, c) and their derivative with respect to time (b, d) obtained for different values of $\beta$ at $\mathrm{\Gamma }=10,\kappa =1$ (a, b)and $\kappa =2$ (c, d). Panels (a) and (c) also indicate a line $C^{\left(7\right)}$ = 0.1 that defines the caging time. In panels (b) and (d), the different curves are shifted vertically for clarity.

Figure 2

Cage correlation functions $C^{\left(7\right)}\left(t\right)$ (a, c) and their derivative with respect to time (b, d), obtained for different values of $\mathrm{\Gamma }$ at $\beta =2,\kappa =1$ (a, b) and $\kappa =2$ (c, d). Panels (a) and (c) also indicate a line $C^{\left(7\right)}$ = 0.1 that defines the caging time. In panels (b, d), the different curves are shifted vertically for clarity.

Figure 3

Dependence of caging time on the strength of magnetic field $\beta$ (a) and on the coupling parameter $\mathrm{\Gamma }$ (b), at $\kappa =1$.

Figure 4

Directional correlation functions obtained for different values of the magnetic field strength: (a) $\beta$ = 0.001, (b) $\beta$ = 0.5, and (c) $\beta$ = 2, at $\mathrm{\Gamma }=10$ and $\kappa =1$.

Figure 5

Normalized “directional” diffusion coefficients, $D^{*}=D/{\omega }_p{a}^2$, as obtained from mean-squared displacements of the particles (lines) and from the directional correlation functions (symbols). (a) $\kappa =1,\beta =0$, (b) $\kappa =1,\beta =0.5$, (c) $\kappa =1,\beta =1$, and (d) $\kappa =2,\beta =0.5$. $\times D_x^{*},\circ D_y^{*},▵D_z^{*}$; $----D_x^{*},---D_y^{*},\cdots D_z^{*}$.