Two interacting electrons in one-dimensional deterministic aperiodic systems : Fibonacci and Thue-Morse lattices

We investigate the influence of the interaction on propagating properties of two electrons with opposite spins in one-dimensional deterministic aperiodic systems, namely the Fibonacci and Thue-Morse lattices, where the interaction was assumed along the Hubbard model. We solve the time dependent Schr\"odinger equation for different values of the interaction strength and degrees of disorder and we vary the initial conditions. We follow the time evolution of the particles and give the mean-square displacement as well as determine the trajectories of the center of the wave packets associated with each of the particles. The interplay between the degree of disorder and the strength of the interaction is analyzed. Both structures present superdiffusive propagation enhanced by the strength of the interaction. We obtained the time exponent for the mean-square displacement. Finally, the action of a dc electric field was included, giving a place to the phenomenon of dynamical localization.