Universal Dependence of the Mean Square Displacement in Equilibrium Point Vortex Systems without Boundary Conditions

Abstract

The diffusion processes of point vortex systems with no boundary are studied numerically and analytically. The mean square displacements in the radial direction are observed in equilibrium states corresponding to several parameters. It is shown that point vortex systems display an anomalous diffusion and that the mean square displacements exhibit a universal time dependence. The exponent of this time dependence corresponds to the results with circular boundary conditions reported by Kawahara and Nakanishi. On the other hand, the mean square displacement is dependent on system energy exponentially. The energy dependence of the mean square displacement is explained by the rough scaling theory. The probability distribution functions of the velocity field are also investigated numerically, and the results reinforce the theory of the dependence on system energy.