Year: 2003
Type: article
Abstract: We study numerically quantum diffusion of a particle on small-world networks by integrating the time-dependent Schr\"odinger 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, $\ensuremath{\tau}$ 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 $\ensuremath{\tau}\ensuremath{\sim}N,$ while the behavior $\ensuremath{\tau}\ensuremath{\sim}\mathrm{log}N$ 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.
Authors: Beom Jun Kim, H. Hong, M. Y. Choi
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2030825281