On bound electron pairs in a quantum wire

TL;DR

This paper investigates bound electron pairs in a quantum wire, analyzing their spectral properties, energy gap, and condensation phenomena, including effects of disorder, to understand pairing mechanisms related to superconductivity.

Contribution

It establishes a connection between the topology of configuration spaces and spectral properties, providing explicit energy gap estimates and demonstrating condensation and its destruction under disorder.

Findings

Derived explicit energy gap estimates.

Proved condensation of non-interacting pairs.

Showed disorder destroys the condensate.

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.