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Peierls gap is analized in case of a two-dimensional lattice under the influence of a magnetic field, in a tight-binding approximation. By using a non-analytic class of potentials, such as the Kohmoto potential in the Harper model, splitting effect occurs in the energy bands. In the metalinsulator transition point, the charge carriers become separated due to their energy, releasing and expanding the Peierls gap. As a result, the energy bands around

Proofs are given that the quantum-mechanical description of the LC -circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schrodinger-equation established before via F(n)=n, as well

Electrons on infinite coupled chains with nearest neighbour couplings under uniform electric and magnetic fields can be expressed as conditionally solvable systems, which concerns both discrete coordinate and wavenumber representations. We then have to account for multiparameter extra-conditions relying on the single chain phase of the system, which amounts to perform a suitable selection of parameters. The implicit plots provided by such conditions

The movement of the electrons under the simultaneous influence of a scalar periodic potential and of a uniform transversal magnetic field is described by the well-known second order discrete Harper equation. This equation originates from a two-dimensional energy dispersion law under the minimal substitution. Here one deals with the Harper model under the additional influence of the discretized spin orbit interaction. Converting the spin-orbit interaction

Coupled chains in longitudinal electric and transversal magnetic fields are able to be formulated as a conditionally solvable problem. This opens the way to the onset of Wannier-Stark resonances, such as discussed before [E. Papp et al, Physica B. 403, (2008) 3289]. However, such resonances proceed under well defined relationships concerning the energy quantum number, the inter- and intra- chain hopping, as well as the magnitudes of the external

Peierls gap is analyzed in case of a two-dimensional lattice under the influence of a magnetic field, in a tight-binding approximation. By using a non-analytic class of potentials, such as the Kohmoto potential in the Harper model, splitting effect occurs in the energy bands. In the metalinsulator transition point, the charge carriers become separated due to their energy, releasing and expanding the Peierls gap. As a result, the energy bands around

The movement of the electrons under the simultaneous influence of a scalar periodic potential and of a uniform transversal magnetic field is described by the well-known second order discrete Harper equation. This equation originates from a two-dimensional energy dispersion law under the minimal substitution. Here one deals with the Harper model under the additional influence of the discretized spin orbit interaction. Converting the spin-orbit interaction

Proofs are given that the quantum-mechanical description of the LC-circuit with a time dependent external source can be readily established by starting from a more general discretization rule of the electric charge. For this purpose one resorts to an arbitrary but integer-dependent real function F(n) instead of n. This results in a nontrivial generalization of the discrete time dependent Schr¨odingerequation established before via F(n) = n, as well