On pairs of interacting electrons in a quantum wire

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.

References in corpus (6)

• On a two-particle bound system on the half-line
• Exactly solvable interacting two-particle quantum graphs
• Two particles on a star graph I
• Two interacting particles on the half-line
• On bound electron pairs in a quantum wire
• Two particles on a star graph II

Cited by in corpus (5)

• On bound electron pairs in a quantum wire
• Bound states of a pair of particles on the half-line with a general interaction potential
• Many-particle quantum graphs: A review
• On the number of isolated eigenvalues of a pair of particles in a quantum wire
• On the impact of surface defects on a condensate of electron pairs in a quantum wire