  We study the quantum electron transport in a one-dimensional interacting
electron system, called Schmid model, reformulating the model in terms of the
bosonic string theory on a disk. The particle-kink duality of the model is
discussed in the absence of the external electric field and further extended to
the model with a weak electric field. Using the linear response theory, we
evaluate the electric conductance both for both weak and strong periodic
potentials in the zero temperature limit. The electric conductance is invariant
under the particle-kink duality.
