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Condensed Matter > Statistical Mechanics
Title: Quantum statistics and networks: Between bosons and fermions
(Submitted on 29 Nov 2020 (this version), latest version 16 Jun 2021 (v3))
Abstract: In this article, we discuss several types of networks: random graph, Barab\'{a}si-Albert (BA) model, and lattice networks, from the unified view point. The parameter $\omega$ with values $1,0, -1$ corresponds to these networks, respectively. The parameter is related to the preferential attachment of nodes in the networks and has different weights for the incoming and out-going links. In other viewpoints, we discuss the correspondence between quantum statistics and the networks. Positive (negative) $\omega$ corresponds to Bose (Fermi)-like statistics. We can obtain the distribution that connects Boson and Fermion. When $\omega$ is positive, $\omega$ is the threshold of Bose-Einstein condensation (BEC). As $\omega$ decreases, the area of the BEC phase is narrowed and disappears in the limit $\omega=0$. When $\omega$ is negative, there exists the maximum occupied number which corresponds to that the node has the maximum number of links. We can observe the Fermi degeneracy of the network. When $\omega=-1$, a standard Fermion-like network is observed. In fact Fermion network is realized in the criptcurrency network, "Tangle".
Submission history
From: Shintaro Mori Dr. [view email][v1] Sun, 29 Nov 2020 01:14:00 GMT (427kb)
[v2] Wed, 24 Mar 2021 03:53:22 GMT (515kb)
[v3] Wed, 16 Jun 2021 23:24:46 GMT (528kb)
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