Related papers: Spectra of Half-Infinite Quantum Graph Tubes
We present numerical studies of quantum walks on \C60 and related graphene structures, to investigate their transport properties. Also known as a \emph{honeycomb lattice}, the lattice formed by carbon atoms in the graphene phase can be…
Carbon nanotubes bridge the molecular and crystalline quantum worlds, and their extraordinary electronic, mechanical and optical properties have attracted enormous attention from a broad scientific community. We review the basic principles…
Newly discovered carbon nanotubes provide an environment in which small atoms move relatively freely. An assembly of such atoms provides a realization of a quasi-one dimensional system which is an ideal testing ground for concepts and…
Carbon is one of the most intriguing elements in the Periodic Table. It forms many allotropes, some being known from ancient times (diamond and graphite) and some discovered ten to twenty years ago (fullerenes, nanotubes). Quite…
The spectrum of a semi-infinite quantum graph tube with square period cells is analyzed. The structure is obtained by rolling up a doubly periodic quantum graph into a tube along a period vector and then retaining only a semi-infinite half…
The formation of graphen-nanotube composites addresses a few basic problems. First, both partners are good donors and acceptors of electrons, which significantly complicates the intermolecular interaction between them leading to a two-well…
Quantum graphity is a background independent model for emergent geometry, in which space is represented as a complete graph. The high-energy pre-geometric starting point of the model is usually considered to be the complete graph, however…
Scanning tunneling images of carbon nanotubes frequently show electron distributions which break the local sixfold symmetry of the graphene sheet. We present a theory of these images which relates these anisotropies to the off diagonal…
The interaction between carbon nanostructures like quantum dots and radiation can generate different effects inside the nanomaterial, with the use of computational methods such effects can be predicted and optimize the material allowing a…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
Fundamentally new families of carbon single walled nanotubes are proposed. These nanotubes, called graphynes, result from the elongation of covalent interconnections of graphite-based nanotubes by the introduction of yne groups. Similarly…
A new group-theory method to relate a spectrum of carbon nanotubes with that of a graphene monolayer is elaborated. The spectrum reconstruction is performed using a virtual intermediate planar periodic structure. Selected irreducible…
Quantum graphs can be extended to scattering systems when they are connected by leads to infinity. It is shown that for certain extensions, the scattering matrices of isospectral graphs are conjugate to each other and their poles…
The unique topology and exceptional properties of carbon nanoscrolls (CNSs) have inspired unconventional nano-device concepts, yet the fabrication of CNSs remains rather challenging. Using molecular dynamics simulations, we demonstrate the…
A single-walled carbon nanotube presents a seamless cylindrical graphene surface and is thus an ideal adsorption substrate for investigating the physics of atoms and molecules in two dimensions and approaching the one-dimensional limit.…
We study the transmission of a quantum particle along a straight input--output line to which a graph $\Gamma$ is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant…
Quantum graphity is a background independent model for emergent locality, spatial geometry and matter. The states of the system correspond to dynamical graphs on N vertices. At high energy, the graph describing the system is highly…
The electronic structure of finite-length armchair carbon nanotubes has been studied using several ab-initio and semi-empirical quantum computational techniques. The additional confinement of the electrons along the tube axis leads to the…
We use large scale ab-initio calculations to describe electronic structures of graphene, graphene nanoribbons, and carbon nanotubes periodically perforated with nanopores. We disclose common features of these systems and develop a unified…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…