Quantum and classical diffusion in small-world networks

Abstract

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 $\tau$ 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.

5 pages, to appear in PRB

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• Localizations on Complex Networks
• Quantum transport with coupled cavities on the Apollonian network
• Coherent exciton transport and trapping on long-range interacting cycles
• Diffusion on a heptagonal lattice
• Scaling of disordered recursive networks
• Mixing and Decoherence in Continuous-time quantum walks on long-range interacting cycles
• Electron in a tangled chain: multifractality at the small-world critical point
• Multifractal analysis of eigenvectors of smallworld networks
• Quantum transport efficiency in noisy random-removal and small-world networks
• Fluctuations and Persistence in Quantum Diffusion on Regular Lattices
• Small-World Disordered Lattices: Spectral Gaps and Diffusive Transport
• Time Reversibility of Quantum Diffusion in Small-world Networks