Fermionic Networks: Modeling Adaptive Complex Networks with Fermionic Gases

We study the structure of Fermionic networks, i.e., a model of networks based on the behavior of fermionic gases, and we analyze dynamical processes over them. In this model, particle dynamics have been mapped to the domain of networks, hence a parameter representing the temperature controls the evolution of 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, networks generated by quantum statistics can undergo critical phenomena as phase transitions and, moreover, they can be considered as thermodynamic systems. In this study, we analyze Fermionic networks and opinion dynamics processes over them, framing this network model as a computational model useful to represent complex and adaptive systems. Results highlight that a strong relation holds between the gas temperature and the structure of the achieved networks. Notably, both the degree distribution and the assortativity vary as the temperature varies, hence we can state that fermionic networks behave as adaptive networks. On the other hand, it is worth to highlight that we did not find relation between outcomes of opinion dynamics processes and the gas temperature. Therefore, although the latter plays a fundamental role in gas dynamics, on the network domain its importance is related only to structural properties of fermionic networks.Comment: 19 pages, 5 figure

Statistical mechanics of strings with Y-junctions

We investigate the Hagedorn transitions of string networks with Y-junctions as may occur, for example, with (p,q) cosmic superstrings. In a simplified model with three different types of string, the partition function reduces to three generalised coupled XY models. We calculate the phase diagram and show that, as the system is heated, the lightest strings first undergo the Hagedorn transition despite the junctions. There is then a second, higher, critical temperature above which infinite strings of all tensions, and junctions, exist. Conversely, on cooling to low temperatures, only the lightest strings remain, but they collapse into small loops

The Schwinger Model on the lattice in the Microcanonical Fermionic Average approach

The Microcanonical Fermionic Average method has been used so far in the context of lattice models with phase transitions at finite coupling. To test its applicability to Asymptotically Free theories, we have implemented it in QED$_2$, \it i.e.\rm the Schwinger Model. We exploit the possibility, intrinsic to this method, of studying the whole $\beta, m$ plane at negligible computer cost, to follow constant physics trajectories and measure the $m \to 0$ limit of the chiral condensate. We recover the continuum result within 3 decimal places.Comment: TeX file, 7 pages + 3 figures in Postscrip

Fermi-Bose mixtures and BCS-BEC crossover in high-Tc superconductors

In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC crossover compared with the strong-coupling approach, which can serve as the cornerstones on the way from high-temperature to room-temperature superconductivity in pressurized metallic hydrides. We discuss some key theoretical ideas and mechanisms proposed for unconventional superconductors (cuprates, pnictides, chalcogenides, bismuthates, diborides, heavy-fermions, organics, bilayer graphene, twisted graphene, oxide hetero-structures), superfluids and balanced or imbalanced ultracold Fermi gases in magnetic traps. We build a bridge between unconventional superconductors and recently discovered pressurized hydrides superconductors H3S and LaH10 with the critical temperature close to room temperature. We discuss systems with line of nodal Dirac points close to the Fermi surface, superconducting shape resonances and hyperbolic superconducting networks which are very important for the development of novel topological superconductors, for the energetics, for the applications in nano-electronics and quantum computations.Comment: 19 pages, 7 figure