2003/06/10 by Beom Jun Kim, H. Hong, M. Y. Choi
Physics and Astronomy · #cond-mat.dis-nn
paper · pdf · doi:10.1103/physrevb.68.014304
published as Phys. Rev. B 68, 014304 (2003). · 5 pages, to appear in PRB
arxiv created 2003/06/10 · arxiv updated 2009/11/30
We study numerically quantum diffusion of a particle on small-world networks by integrating the time-dependent Schrödinger equation with a localized initial state. The participation ratio, which corresponds to the number of visited sites in the case of classical diffusion, as a function of time is measured and the corresponding diffusion time τ is computed. In a local regular network, i.e., in the network with the rewiring probability p=0, the diffusion time depends on the network size N as τ∼ N, while the behavior τ∼ log N is observed as p becomes finite. Such fast diffusion of a particle on a complex network suggests that the small-world transition is also the fast-world transition from a dynamic point of view. The classical diffusion behavior is also studied and compared with the quantum behavior.