On bound electron pairs in a quantum wire

Abstract

Based on the quantum two-body problem introduced in [arXiv:1604.06693] we consider bound pairs of electrons moving on the positive half-line. The analysis is motivated by the ground-breaking work of Cooper who identified the pairing of electrons as a possible explanation for superconducting behaviour in metals. In this paper we are interested in the connection between the topologies of the underlying one- and two-particle configuration spaces and spectral properties of the Hamiltonian linked to a condensation of pairs. We derive explicit estimates for the energy gap and prove condensation for a gas of non-interacting pairs. Finally, we add some disorder to the system and prove destruction of the condensate.

Improved proofs

References in corpus (3)

• On a two-particle bound system on the half-line
• Two interacting particles on the half-line
• On pairs of interacting electrons in a quantum wire

Cited by in corpus (5)

• On pairs of interacting electrons 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