Transport properties of one dimensional correlated electrons have been studied via the Luttinger liquid model [1,2]. Some of the results found are presented here. For a pure Luttinger liquid (no barriers) the non-local conductivity is determined. The frequency dependent conductance is calculated in the presence of a longitudinal monochromatic electric field, applied to a finite interval of the system. We treat several forms of the interaction potential with finite range. The conductance, as a function of the frequency, shows features that are a signature of elementary excitations. They can be interpreted in terms of a quantum capacitance and inductance. The influence of a finite range of the interactions is also studied for a tunnel barrier in a Luttinger liquid. The non linear DC conductance shows a charging energy associated to the tunnel barrier. This provides a microscopic understanding of earlier phenomenological approaches. The dependence of the charging energy on the strength and the range of the interactions is quantitatively discussed.

[1] G. Cuniberti, M. Sassetti, and B. Kramer, J. Phys. Cond. Mat., 8, L21 (1996)
[2] G. Cuniberti, M. Sassetti, and B. Kramer, Physica B., in press.