Effect of the coupling constants between nearest-neighbors in quantum wire coupled to a ring

The electronic transport in an infinite arrays of driven quantum wells coupled to a quantum ring is studied via a single-band tunneling tight-biding Hamiltonian by perturbing and numerical simulations approaches. In the perturbing approach, an analytical relationship in terms of the coupling constants between nearest-neighbors in quantum wire coupled to a ring based on the quantum dynamical algebra is obtained. With a choice of three wells on the quantum ring, the transmission probabilities of electron of the number zero well of an  wire under the effect of a constant field to the first, second and third well of quantum ring has been obtained for different values of the nearest-neighbors coupling constants in  wire and quantum ring of the system. The effect of changes these parameters on the location and height of the first peaks related to the diagrams of transmission probability have been studied.