Discipline: 
Mathematics
Status: 
Available
Level: 
PhD Project

Conventional superconductivity is described by the classic theory of Bardeen,  Cooper and Schrieffer (BCS), based on the notion of pairing between fermions. The traditional approach has been to study such models in the framework of mean-field theory. However in recent years it has emerged that in some instances (e.g. s-wave pairing, p+ip-wave pairing) these models can be solved exactly, and analysis of the exact solution goes beyond the capability of mean-field approaches to provide rich insights. The explicit construction of these exact solutions is conducted using a method known as the Bethe ansatz. In this project the scope of the Bethe ansatz approach will be extended to obtain new classes of superconductivity models which can be solved exactly. Once this is achieved, detailed analysis of the exact solutions will be undertaken to extract their physical characteristics. This project is suitable for a student with strong skills in algebraic methods and a good working knowledge of complex analysis techniques.