Theory of measuring the "Luttinger-g" of a one-dimensional quantum dot

We study electron transport through a quantum dot in a Tomonaga-Luttinger liquid with an inhomogeneity induced either by a non-uniform electron interaction or by the presence of tunnel resistances of contacts. The non-analytic temperature behavior of the conductance peaks show crossovers determined by the different energy scales associated with the dot and the inhomogeneity despite the Coulomb blockade remains intact. This suggests an explanation of recent findings in semiconductor quantum wires and carbon nanotubes.