Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems, non-perturbative of various large-N field theories, and closely related solitonic the Bogoliubov-de Gennes equations theory superconductivity. These rely on inverse scattering method, which reduces these seemingly unrelated problems identifying reflectionless auxiliary one-dimensiona...

Modified group projector technique for induced representations is a powerful tool for calculation and symmetry quantum numbers assignation of a tight binding Hamiltonian energy bands of crystals. Namely, the induced type structure of such a Hamiltonian enables efficient application of the procedure: only the interior representations of the orbit stabilizers are to be considered. Then the genera...

A general tight-binding analysis is described which differs from traditional methods in that 1) analytical forms are derived and utilized for obtaining the coupling parameters, and 2) the calculation of electronic-state energies is simplified sufficiently that they also can be obtained analytically. With these two features it becomes possible to write formulae for a wide range of bonding, diele...

A tight-binding model Hamiltonian is newly parametrized for silicon carbide based on fits to a database of energy points calculated within the density functional theory approach of the electronic energy surfaces of nanoclusters and the total energy of bulk 3C and 2H polytypes at different densities. This TB model includes s and p angular momentum symmetries with nonorthogonal atomic basis funct...

The existence of an energy gap of graphene is vital as far as nano-electronic applications such as nano-transistors are concerned. In this paper, we present a method for introducing arbitrary energy gaps through breaking the symmetry point group of graphene. We investigate the tight-binding approximation for the dispersion of π and π∗ electronic bands in patterned graphene including up to five ...