Traffic of indistinguishable particles in complex networks |
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Authors: | Meng Qing-Kuan and Zhu Jian-Yang |
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Institution: | Department of Physics, Beijing Normal University, Beijing
100875, China |
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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. |
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Keywords: | complex networks statistical
mechanics of networks |
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