Dimensionality effects on the emergence of superdiffusion in Yukawa liquids

A three-dimensional Yukawa liquid exhibits normal self-diffusion which is characterized by Fick's law and a time-independent diffusion coefficient D [1]. This quantity can be evaluated from the Einstein relation, $D=\langle r(t)^2\rangle/6t$. If however the mean-squared displacement $\langle r(t)^2\rangle$ grows faster than linearly with time, the diffusion coefficient is not well defined and the systems exhibits superdiffusive behaviour. Recently, superdiffusion has been observed in two-dimensional Yukawa liquids [2]. In this contribution we enter into the question about the occurrence of superdiffusion in the transiton-region from a purely three-dimensional to a quasi 2D system where one dimension is confined [3,4]. \\[0pt] [1] H. Ohta and S. Hamaguchi, Phys. Plasmas \textbf{7}, 4506 (2000) \\[0pt] [2] B. Liu and J. Goree, Phys. Rev. E \textbf{75}, 016405 (2007) \\[0pt] [3] Z. Donk\'o, P. Hartmann and G. J. Kalman, Phys. Rev. E \textbf{69}, 065401 (2004) \\[0pt] [4] T. Ott, Z. Donk\'o, P. Hartmann and M. Bonitz, Submitted to Phys. Rev. E.