论文标题
量子统计和网络通过节点的不对称优先附着 - 在玻色子和费米子之间
Quantum statistics and networks by asymmetric preferential attachment of nodes -- between bosons and fermions
论文作者
论文摘要
在本文中，我们讨论了从统一观点点的Barabási-Albert（BA）模型（BA）模型和晶格网络，其参数$ω$分别为$ 1,0，-1 $，分别表征这些网络。该参数与网络中的节点的优先附件有关，并且在传入和传出链接中具有不同的权重。此外，我们讨论了量子统计与网络之间的对应关系。正和负$ω$分别对应于Bose和Fermi样统计数据，我们获得了连接两者的分布。当$ω$是正的时，它与Bose-Einstein凝结的阈值有关（BEC）。随着$ω$的减小，BEC相位的面积被缩小，并在极限$ω= 0 $中消失。当$ω$为负时，节点在新添加的节点（传出链接）的附件数量中有限制，该节点（传出链接）对应于Fermi统计信息。我们还观察到网络的费米退化。当$ω= -1 $时，会观察到标准的类似费米的网络。费米恩网络在加密货币网络“纠缠”中实现。
In this article, we discuss the random graph, Barabási-Albert (BA) model, and lattice networks from a unified view point, with the parameter $ω$ with values $1,0,-1$ characterizing these networks, respectively. The parameter is related to the preferential attachment of nodes in the networks and has different weights for the incoming and outgoing links. In addition, we discuss the correspondence between quantum statistics and the networks. Positive and negative $ω$ correspond to Bose and Fermi-like statistics, respectively, and we obtain the distribution that connects the two. When $ω$ is positive, it is related to the threshold of Bose-Einstein condensation (BEC). As $ω$ decreases, the area of the BEC phase is narrowed, and disappears in the limit $ω=0$. When $ω$ is negative, nodes have limits in the number of attachments for newly added nodes (outgoing links), which corresponds to Fermi statistics. We also observe the Fermi degeneracy of the network. When $ω=-1$, a standard Fermion-like network is observed. Fermion networks are realized in the cryptocurrency network "Tangle."
