Testing cellular automata interpretation of quantum mechanics in carbon nanotubes and superconductivity

Donatello Dolce,Andrea Perali

doi:10.1088/1742-6596/626/1/012062

Donatello Dolce, Andrea Perali

Open Access

https://doi.org/10.1088/1742-6596/626/1/012062

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Abstract

Cellular Automata (CA) are represented at an effective level as intrinsic periodic phenomena, classical in the essence, reproducing the complete coherence (perfect recurrences) associated to pure quantum behaviours in condensed matter systems. By means of this approach it is possible to obtain a consistent, novel derivation of SuperConductivity (SC) essential phenomenology and of the peculiar quantum behaviour of electrons in graphene physics and Carbon Nanotubes (CNs), in which electrons cyclic dynamics simulate CA. In this way we will derive, from classical arguments, the essential electronic properties of these — or similar — graphene systems, such as energy bands and density of states. Similarly, in the second part of the paper, we will derive the fundamental phenomenology of SC by means of fundamental quantum dynamics and geometrical considerations, directly derived from the CA evolution law, rather than on empirical microscopical characteristics of the materials as in the standard approaches. This allows for a novel heuristic interpretation of the related gauge symmetry breaking and of the occurrence of high temperature superconductivity by means of simple considerations on the competition of quantum recurrence and thermal noise.

Highlights

As proven by G. ’t Hoof in recent works, particular Cellular Automata (CA) models have much in common with Quantum Mechanics (QM)
We find that the effective mass scale of the electron in the Carbon Nanotubes (CNs) is determined by the CN circumference according to
For ZigZag (ZZ) and ArmChair (AC) CNs of N carbon atoms in the perimeter, the resulting energy spectra turns out to be, respectively, N πn ZZ) mn = m∗ π sin( N ) ; N

Summary

Introduction

As proven by G. ’t Hoof in recent works, particular CA models have much in common with Quantum Mechanics (QM). For the continuous limit, ’t Hooft has proven that “there is a close relationship between a particle moving on a circle with period T and the Quantum Harmonic Oscillator (QHO) with the same period ” [1] This is a fundamental result as the QHO is the essential ingredient of a second quantised field, and in turn of the whole Quantum Field Theory (QFT). The dynamics described by this CA model, to the EC model, correspond to those of the time evolution of a Quantum Harmonic Oscillator (QHO) of period T , except for the fact that the quantum number can assume negative values, n ∈ Z (positive and negative frequencies) This seems to imply a non positively defined Hamiltonian operator for CA. The electron in the atomic orbitals can be regarded as being locally in a superconducting regime

Testing CA theory by means of Carbon Nanotubes

Conclusions