Eigenvalues of Two-State Quantum Walks Induced by the Hadamard Walk

Existence of the eigenvalues of the discrete-time quantum walks is deeply related to localization of the walks. We revealed, for the first time, the distributions of the eigenvalues given by the splitted generating function method (the SGF method) of the space-inhomogeneous quantum walks in one dimension we had treated in our previous studies. Especially, we clarified the characteristic parameter dependence for the distributions of the eigenvalues with the aid of numerical simulation.

Impurity position effect on the diamagnetic susceptibility of a magneto-donor in GaAs inhomogeneous quantum dots

Inhomogeneous Quantum Dot (IQD) semiconductor represents a newest trend in condensed matter, due to their important quantum levels and the outstanding properties. In this work, the impurity position effect on the diamagnetic susceptibility of a shallow magneto-donor, confined to move in (IQD) made out of Ga1-xAlxAs / GaAs/ Ga1-xAlxAs is reported theoretically. With the increase of the magnetic field, the diamagnetic susceptibility increases. The results using variational method reveal that diamagnetic susceptibility depends on many parameters including the impurity position, the external magnetic field and the nanostructure size. The magnetic field effect is more pronounced when the donor is placed near the extremities of the spherical layer (off-center). In addition, a maximum of diamagnetic susceptibility is observed, corresponding to a critical position value, for strong confinement regime and when the impurity is located in the spherical layer center.