Aarhus University Seal / Aarhus Universitets segl

Magnetic edge and semiclassical eigenvalue asymptotics

Ayman Kachmar (Lebanese University)
Mathematics Seminar
Monday, 2 May, 2022 | 16:15– | Zoom

In a typical setting, the energy levels of an electron moving in a magnetic field are eigenvalues of a special magnetic Laplace operator involving the semiclassical parameter (a very small parameter compared to the sample’s scale). Searching for asymptotic expansions of these eigenvalues, in the singular limit of vanishing semiclassical parameter, is a rich topic that will be partially reviewed, in the present talk. I’ll discuss recent results involving magnetic fields varying on very short scales (modeled by piecewise constant functions with discontinuity along curves), for which some asymptotics are derived via a purely variational proof not involving pseudo-differential calculus.

To get an invitation to the zoom-meeting, please contact one of the organisers.

Organised by: SQM