Richardson models for mesoscopic pairing interactions

Abstract

Pairing interactions in quantum mechanics have previously been used to model a wide variety of systems, including nuclear physics and superconductors. A main benefit of such models is that they, unlike many other popular interaction models, are integrable. This enables pairing problems to be solved exactly at a comparatively low computational cost. In this thesis, such models have been employed to study the mesoscopic physics of superconductors and harmonically trapped ultracold atoms. An numerical algorithm was developed to solve the pairing models, and obtain exact solutions for arbitrary excited states and single-particle spectra. This has enabled producing excitation spectra for significantly larger systems of trapped atoms than what was previously possible, and has led to a greater understanding of previous observed experimental data. A prediction for the functional dependence of the minimal first pair excitation energy has been obtained, which future experiments should be able to test.