This work pertains to the spin and charge transports in low dimensional electronic systems. The general concept of low dimensional physics is briefly introduced. We studied the spin transport of a spin polarized Luttinger liquid in the presence of a single impurity. We found that, by considering the extended Hubbard interaction, a spin-polarized wire is obtained in response to an external magnetic field. In addition, we studied the charge transport of a confined two-dimensional electron gas in the presence of an insulating region. We considered the two-dimensional electron gas as being...