On pairs of interacting electrons in a quantum wire

TL;DR

This paper rigorously analyzes pairs of interacting electrons in a quantum wire with contact interactions, exploring spectral properties and demonstrating Bose-Einstein condensation under various interaction strengths.

Contribution

It extends previous models by incorporating Lieb-Liniger contact interactions and proves the existence of Bose-Einstein condensation for these pairs.

Findings

Condensation occurs when the Hamiltonian has a non-trivial discrete spectrum.

Condensation is proven for both very weak and very strong contact interactions.

Spectral properties of the Hamiltonian are characterized rigorously.

Abstract

In this paper we consider pairs of interacting electrons moving in a simple quantum wire, namely the half-line. In particular, we extend the results obtained in [arXiv:1708.03753] by allowing for contact interactions of the Lieb-Liniger type between the two electrons constituting the pair. We construct the associated Hamiltonian rigorously and study its spectral properties. We then investigate Bose-Einstein condensation of pairs and prove, as a main result, the existence of condensation whenever the Hamiltonian has a non-trivial discrete spectrum. Most importantly, condensation is proved for very weak and very strong contact interactions.