Pumping current of a Luttinger liquid with finite length

TL;DR

This paper analyzes how finite length affects the pumping current in a Luttinger liquid with time-dependent impurities, revealing modifications to infinite-length results through analytical and perturbative methods.

Contribution

It provides a detailed analytical study of finite-size effects on backscattering pumping current in a Luttinger liquid with dynamic impurities, extending previous infinite-length models.

Findings

Finite length modifies the backscattering current behavior.

Impurity position influences the pumping current.

Finite size effects alter infinite-length theoretical predictions.

Abstract

We study transport properties in a Tomonaga-Luttinger liquid in the presence of two time-dependent point like weak impurities, taking into account finite-length effects. By employing analytical methods and performing a perturbation theory, we compute the backscattering pumping current (I_bs) in different regimes which can be established in relation to the oscillatory frequency of the impurities and to the frequency related to the length and the renormalized velocity (by the electron-electron interactions) of the charge density modes. We investigate the role played by the spatial position of the impurity potentials. We also show how the previous infinite length results for I_bs are modified by the finite size of the system.