Interacting electrons on a half line coupled to impurities

TL;DR

This paper extends bosonization techniques to analyze how electron interactions and impurities, modeled as a quantum dot, influence boundary conditions and charge fluctuations in a quantum wire.

Contribution

It introduces a model coupling a quantum wire to a quantum dot via capacitive interaction, revealing the impact on boundary conditions and charge dynamics.

Findings

Quantum dot induces dynamical boundary conditions in the wire.

Fermion boundary conditions significantly affect the bosonized theory.

Interactions modify charge fluctuation behavior at the boundary.

Abstract

We generalize the bosonization methods for systems in the half line that we discussed elsewhere, to study the effects of interactions on electronic systems coupled to impurities. We introduce a model for a quantum wire coupled with a quantum dot by a purely capacitive interaction. We show that the effect on the quantum wire is a dynamical boundary condition which reflects the charge fluctuations of the quantum dot. Special attention is given to the role of the fermion boundary conditions and their interplay with the electron interactions on the bosonized effective theory.