Size of quantum networks

Abstract

The metric structure of bosonic scale-free networks and fermionic Cayley-tree networks is analyzed focousing on the directed distance of nodes from the origin. The topology of the netwoks strongly depends on the dynamical parameter $T$, called temperature. At $T=\infty$ we show analytically that the two networks have a similar behavior: the distance of a generic node from the origin of the network scales as the logarithm of the number of nodes in the network. At T=0 the two networks have an opposite behavior: the bosonic network remains very clusterized (the distance from the origin remains constant as the network increases the number of nodes) while the fermionic network grows following a single branch of the tree and the distance from the origin grows as a power-law of the number of nodes in the network.

5 pages,8 figures

References in corpus (9)

• Statistical mechanics of complex networks
• Evolution of networks
• Scale-Free Networks are Ultrasmall
• Ising Model on Networks with an Arbitrary Distribution of Connections
• Ferromagnetic ordering in graphs with arbitrary degree distribution
• Ferromagnetic Phase Transition in Barabasi-Albert Networks
• Mean field solution of the Ising model on a Barabasi-Albert network
• Quantum statistics in complex networks
• Growing Cayley trees described by Fermi distribution

Cited by in corpus (3)

• A statistical mechanics approach for scale-free networks and finite-scale networks
• Complex Quantum Networks: a Topical Review
• On the Importance of Hubs in Hopfield Complex Neuronal Networks under Attack