Problems in semiclassical analysis with an emphasis on quantum chaos
The skills to be developed include, but are not limited to, the following: distribution theory, basic Fourier analysis on $\R^n$, calculus on smooth manifolds, spectral theory of self-adjoint and non-self adjoint operators, basic harmonic analysis on $\R^n$, elements of dynamical systems, elements of geometric measure theory, and some analytic number theory.
Participants in this PhD project will gain exposure to a variety of ideas from microlocal analysis and how they are used in problems initiated with the field of quantum mechanics, more specifically quantum chaos. The goal is to combine microlocal techniques along with those from a variety of other disciplines (as listed above) to give a novel approach to problems which are somewhat out of reach by using solely microlocal methods.
A component of the program will be focused on obtaining numerics for semiclassical asymptotics in certain models, such as compact hyperbolic surfaces. Quantized toral automorphisms can be considered as well.
We are interested in pursuing this project and welcome applications if you are self-funded or have funding from other sources, including government sponsorships or your employer.
Please contact the supervisor when you want to pursue this project, citing the project title in your email, or find out more about our PhD programme in Mathematics.