Quantum Electron Transport and Duality in a One-Dimensional Interacting System

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.