Quantum and classical diffusion on smallworld networks
Abstract
We study numerically quantum diffusion of a particle on smallworld networks by integrating the timedependent 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 smallworld transition is also the fastworld transition from a dynamic point of view. The classical diffusion behavior is also studied and compared with the quantum behavior.
 Publication:

Physical Review B
 Pub Date:
 July 2003
 DOI:
 10.1103/PhysRevB.68.014304
 arXiv:
 arXiv:condmat/0306234
 Bibcode:
 2003PhRvB..68a4304K
 Keywords:

 89.75.Hc;
 03.65.Ge;
 05.60.k;
 73.20.Jc;
 Networks and genealogical trees;
 Solutions of wave equations: bound states;
 Transport processes;
 Delocalization processes;
 Condensed Matter  Disordered Systems and Neural Networks
 EPrint:
 5 pages, to appear in PRB