Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases

摘要

We study the structure of Fermionic networks, i.e., a model of networks basedon the behavior of fermionic gases, and we analyze dynamical processes overthem. In this model, particle dynamics have been mapped to the domain ofnetworks, hence a parameter representing the temperature controls the evolutionof the system. In doing so, it is possible to generate adaptive networks, i.e.,networks whose structure varies over time. As shown in previous works, networksgenerated by quantum statistics can undergo critical phenomena as phasetransitions and, moreover, they can be considered as thermodynamic systems. Inthis study, we analyze Fermionic networks and opinion dynamics processes overthem, framing this network model as a computational model useful to representcomplex and adaptive systems. Results highlight that a strong relation holdsbetween the gas temperature and the structure of the achieved networks.Notably, both the degree distribution and the assortativity vary as thetemperature varies, hence we can state that fermionic networks behave asadaptive networks. On the other hand, it is worth to highlight that we did notfind relation between outcomes of opinion dynamics processes and the gastemperature. Therefore, although the latter plays a fundamental role in gasdynamics, on the network domain its importance is related only to structuralproperties of fermionic networks.