From superintegrability to quasi-exact solvability: theory and application

The project is in the area of integrability and exact solvability. Quantum integrable systems and exact solvable models are of central importance for understanding the correct behaviours of complex quantum problems without approximation. This project aims to develop mathematical frameworks and novel techniques to solve important questions across a variety of models such as superintegrable systems, quantum spin chains and spin-boson systems. Prospective PhD students will work on specific aspects of the project, e.g. (1) the design and exploration of computational experiments to support the theoretical developments of new techniques for solving Rabi type spin-boson models, and (2) the exploration of specific applications of polynomial algebras and orthogonal polynomials, in the context of specific models.