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

TL;DR

This paper investigates quantum electron transport in a one-dimensional interacting system, revealing that electric conductance remains invariant under particle-kink duality, with implications for understanding dualities in quantum transport models.

Contribution

It reformulates the Schmid model using bosonic string theory and extends the particle-kink duality to systems with weak electric fields, analyzing conductance invariance.

Findings

Electric conductance is invariant under particle-kink duality.

Conductance evaluated for weak and strong periodic potentials at zero temperature.

Model reformulated using bosonic string theory on a disk.

Abstract

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.