Richard Pincak

By Jan Smotlacha and Richard Pincak

The carbon nanostructures are perspective materials for the future applications. This has two reasons: first, the hexagonal atomic structure, which enables a high molecular variability by placing different kinds of the defects, and second, good electronic properties that can be modified for the purpose of the concrete applications with the help of the defects and of the chemical ingredients. Many kinds of the nanostructures are investigated. Here, the properties of less common forms are examined—the graphitic nanocone and graphitic wormhole.

Part of the book: Recent Advances in Graphene Research

By Richard Pinčák and Erik Bartoš

An important measurable quantity in the carbon nanostructures, including the nanotubular part of the graphitic wormhole, is the spin-orbit coupling. We will present in this chapter spin-orbit coupling for the fermions located in exotic graphene structures as is graphene wormhole and also in biological systems. Considering this influence, the two-component Dirac equation is changed into the usual four-component form. As a consequence, the chiral fermions should be detected close to the wormhole bridge. We will show that the smaller is the radius of the wormhole bridge, the stronger this effect should be. Finally, we will describe the role of spinor fields in the time series of genetic code. The reversed transcription process of the gene expression could be defined by a moduli state space model of a coupling spinor field between the gene of a viral particle and the host cell. As a general result, all states of codon can be computed by the Chern-Simons 3-forms.

Part of the book: Metastable, Spintronics Materials and Mechanics of Deformable Bodies