Abstract In this paper, we apply a simple walk mechanism to the study of the traffic of many indistinguishable particles in complex networks. The network with particles stands for a particle system, and every vertex in the network stands for a quantum state with the corresponding energy determined by the vertex degree. Although the particles are indistinguishable, the quantum states can be distinguished. When the many indistinguishable particles walk randomly in the system for a long enough time and the system reaches dynamic equilibrium, we find that under different restrictive conditions the particle distributions satisfy different forms, including the Bose--Einstein distribution, the Fermi--Dirac distribution and the non-Fermi distribution (as we temporarily call it). As for the Bose--Einstein distribution, we find that only if the particle density is larger than zero, with increasing particle density, do more and more particles condense in the lowest energy level. While the particle density is very low, the particle distribution transforms from the quantum statistical form to the classically statistical form, i.e., transforms from the Bose distribution or the Fermi distribution to the Boltzmann distribution. The numerical results fit well with the analytical predictions.
Received: 26 September 2008
Revised: 16 April 2009
Accepted manuscript online:
Fund: Project
supported by the National Natural Science Foundation of China (Grant
No 10875012), and the High Performance Science Computing Center of
Beijing Normal University of China.
Cite this article:
Meng Qing-Kuan(孟庆宽) and Zhu Jian-Yang(朱建阳) Traffic of indistinguishable particles in complex networks 2009 Chin. Phys. B 18 3632
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