New constructions of superintegrable systems and the connection with Painleve transcendents

Abstract:: Superintegrable systems possess unique mathematical properties which lead to novel applications in nuclear physics, condensed matter physics, and quantum chemistry. However the list of known examples of these systems is limited, and the search for new examples is a challenging mathematical problem. By exploiting several deep connections between superintegrability, ladder operators and supersymmetric quantum mechanics, this project will develop methods to identify and classify superintegrable systems and their symmetry algebras. It will also obtain new results concerning Painlev¿¿ transcendents in the context of superintegrability. The project will certainly have an impact on the field of superintegrability, with wider outcomes also expected.
Grant type:: ARC Discovery Early Career Researcher Award
Funded by:: Australian Research Council

The University of Queensland