Testing Elementary Cycles Formulation of Quantum Mechanics in Carbon Nanotubes and Superconductivity

Elementary Cycles are intrinsic periodic phenomena, classical in the essence, whose classical relativistic dynamics reproduce the complete coherence (perfect recurrences) typically associated to the pure quantum behaviours of elementary particles. They can be regarded as effective representations of 't Hooft Cellular Automata. By means of Elementary Cycles physics we obtain a consistent, intuitive, novel derivation of the peculiar quantum dynamics of electrons in Carbon Nanotubes, as well as of Superconductivity fundamental phenomenology. In particular we derive, from classical arguments, the essential electronic properties of graphene systems, such as energy bands and density of states. Similarly, in the second part of the paper, we derive the Superconductivity fundamental phenomenology in terms of simple geometrical considerations, directly from the Elementary Cycles dynamics rather than from empirical aspects and effective quantities connected to the microscopical characteristics of materials as in the standard approaches to Superconductivity. With this approach simple geometrical considerations about the competition between the quantum recurrence and the thermal noise allow for a novel interpretation of the occurrence of high temperature superconductivity and the related gauge symmetry breaking mechanism.