Spectral analysis of random non-self-adjoint Schroedinger operators

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2016 (funded students) or at any point in the academic year (self-funded students).

Open disordered quantum systems are often described/modelled by non-self-adjoint random operator. The study of spectral properties of such operators was iniated relatively recently by physicists. Unlike in the self-adjoint case, the general theory of such operators is essentially non-existent. This means that it is interesting to look at concrete examples of operators naturally arising in areas ranging from physics of superconductors to biology and try to understand their spectral properties.

During the past 15 years, fascinating features of such operators - unseen in the classical theory - were discovered and studied by mathematicians working in this area. The methods used so are based on the spectral theory, the theory of products of random matrices, and the theory of analytic functions.

This project will be supervised by Professor Ilya Goldsheid.

The application procedure is described on the School website. For further enquiries please contact Prof Ilya Goldsheid ([Email Address Removed]).

This project is eligible for several sources of full funding for the 2016/17 academic year, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process. The best candidates will be eligible to receive a prestigious Ian Macdonald Postgraduate Award of £1000, for which you will be considered alongside your application. The application deadline for full funding is January 31st 2016.

There is also 50% funding scheme available for students who are able to find the matching 50 % of the cost of their studies. Competition for these half-funded slots will be less intensive, and eligible students should mention their willingness to be considered for them in their application. The application deadline for 50 % funding is January 31st 2016.

This project can be also undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.