In quantum systems one normally deals with Hermitian operators since these are guaranteed to have a real spectrum and thus expected to correspond with real observables. While Hermitian operators necessarily imply a real spectrum, a real spectrum does not necessarily need to come from a Hermitian operator. A particular class that have been receiving focus are PT (parity-time) symmetric operators, advocated by Carl Bender and collaborators as a generalisation of Hermitian operators in quantum mechanics, which has also found applications in classical physics. For this project, the goal is primarily to explore the role of PT symmetry and spontaneous PT symmetry breaking in fluid problems, particularly in relation to the propagation of waves, mode merging, and fluid instabilities.

The applicant should be comfortable in mathematical techniques particularly in relation to calculus, but an in-depth understanding of fluids and/or quantum mechanics is not required, although it might be helpful. The main goal is to review the literature and explore some of the established technicalities within this field, but with some room to do some new research. The project can stay classical (focusing on fluid mechanics), go more towards quantum mechanics (with possible forays into quantum chaos), and more theoretical (operator and spectral theory), depending on interest and expertise of application.