Quantum and classical diffusion in small-world networks

Details Quantum and classical diffusion in small-world networks Quantum and classical diffusion in small-world networks

2003-06-10

arxiv.org/abs/cond-mat/0306234v1

Phys. Rev. B 68, 014304 (2003).

Physics

Condensed Matter

Disordered Systems and Neural Networks

5 pages, to appear in PRB

Scientific paper

10.1103/PhysRevB.68.014304

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 $\tau$ 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 $\tau \sim N$, while the behavior $\tau \sim \log N$ 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.

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