Establishing analogies between the physics of extra dimensions and carbon nanotubes

Abstract

We point out a conceptual analogy between the physics of extra spatial dimensions and the physics of carbon nanotubes which arises for principle reasons, although the corresponding energy scales are at least ten orders of magnitude apart. For low energies, one can apply the Kaluza-Klein description to both types of systems, leading to two completely different but consistent interpretations of the underlying physics. In particular, we discuss in detail the Kaluza-Klein description of armchair and zig-zag carbon nanotubes. Furthermore, we describe how certain experimental results for carbon nanotubes could be re-interpreted in terms of the Kaluza-Klein description. Finally, we present ideas for new measurements that could allow to probe concepts of models with extra spatial dimensions in table-top experiments, providing further links between condensed matter and particle physics.

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

“…in agreement with present literature [12]. The lattice limit correctly leads to the effective CN mass spectrum [13]. We find that, for ZigZag (ZZ) and ArmChair (AC) CNs of N carbon atoms in the perimeter, the resulting mass spectra turns out to be, respectively,…”

“…In particular, ECCs in a CN with N carbon atoms along the circumference corresponds to ECs of N lattice sites on a circle. We will use the covariant generalisation of this correspondence to derive in a simple way, and in agreement with present literature [12,13], the essential electronic properties of CNs. CNs can be therefore used to test ECs theory (and in turn CA models) and thus foundational aspects of QM.…”

On the Compton clock and the undulatory nature of particle mass in graphene systems

“…The effective bands of a CN can be then derived by considering the periodicity on a lattice. As a homogenous chain of N springs and masses has frequency spectrum f n = N T π sin nπ N , way we find that, for instance, the mass spectrum (rest energy) of a Armchair CN is m n = h T C v 2 F N π sin nπ N , in agreement with [13,14]. Similarly, according to Compton relation, the mass of the fundamental band of a metallic CN is…”

“…The effective mass spectrum follows by considering that the periodicity is on a lattice 4 . For Zigzag (N 1 = N and N 2 = 0) and Armchair (N 1 = N 2 = N ) CNs we have [14] respectively…”

“…The lattice version leads to the effective energy bands of CNs 5 . For instance, in the Zigzag CNs, we find [14]…”