Scattering of electrons from an interacting region

TL;DR

This paper investigates electron transmission through an interacting quantum dot region, deriving exact two-particle scattering states and analyzing the impact of interactions on current, with extensions to many particles and spin considerations.

Contribution

It provides exact solutions for two-particle scattering states in an interacting lattice model and explores interaction effects on electron transport.

Findings

Exact two-particle scattering states derived

Interaction modifies Landauer current

Perturbative approach for many particles

Abstract

We address the problem of transmission of electrons between two noninteracting leads through a region where they interact (quantum dot). We use a model of spinless electrons hopping on a one-dimensional lattice and with an interaction on a single bond. We show that all the two-particle scattering states can be found exactly. Comparisons are made with numerical results on the time evolution of a two-particle wave packet and several interesting features are found for scattering. For N particles the scattering state is obtained by perturbation theory. For a dot connected to Fermi seas at different chemical potentials, we find an expression for the change in the Landauer current resulting from the interactions on the dot. We end with some comments on the case of spin-1/2 electrons.