The non-linear transport through a tunnel barrier in a Luttinger system is investigated for repulsive electron-electron interaction of finite range [1]. Depending on whether the electrons are located on different or on the same sides of the barrier, the interaction strengths are assumed to be given by V₁₂ and V₁₁, respectively. The features of the Coulomb blockade are found in the current-voltage characteristics when the range of the interaction potential is non-zero, and if V₁₂ = 0. In this limit, the parameters of the semiclassical theory of the Coulomb blockade, namely the tunneling resistance, the capacitance, and the impedance of the circuit are identified in terms of the microscopic parameters of the quantum mechanical model of the interacting electrons. If V₁₂ = V₁₁ the current is still suppressed at small bias voltage but the charging energy vanishes. We demonstrate that the latter is a consequence of an exact sum rule. The results are discussed in the light of experimental findings.

[1] M. Sassetti, G. Cuniberti, B. Kramer, in press