Traffic of indistinguishable particles in complex networks  

作　　者：孟庆宽 朱建阳 

机构地区：[1]Department of Physics,Beijing Normal University

出　　处：《Chinese Physics B》2009年第9期3632-3638,共7页中国物理B（英文版）

基　　金：supported by the National Natural Science Foundation of China (Grant No 10875012);the High Performance Science Computing Center of Beijing Normal University of China

摘　　要：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.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.

关 键 词：complex networks statistical mechanics of networks 

分 类 号：O414.2[理学—理论物理] TP391.41[理学—物理]