Research Centre: Department of Mathematics
Speaker: Ali Mostafazadeh (Koc)
Potential scattering admits a dynamical formulation in which the scattering amplitude for a given real or complex scattering potential can be obtained from the evolution operator for an effective non-unitary quantum system. This formulation is particularly effective in dealing with point scatterers, for it avoids the divergences of the standard Lipmann-Schwinger/Green’s function approach in two and higher dimensions; it seems to have a built-in renormalization property. It also provides a convenient route for achieving broadband invisibility in two and three dimensions. In this talk I will present a general introduction to this formulation of scattering theory and survey some of its applications. In particular, I will use it to address some basic open problems of scattering theory such as inquiring into potentials with identical scattering properties below a prescribed critical energy and potentials for which the first Born approximation is exact. The latter leads to a curious notion of quasi-exact solvability for scattering problems and provides means for achieving broadband unidirectional invisibility in two dimensions. If time permits, I will also comment on a recent extension of this approach to the scattering of electromagnetic waves. A notable outcome of this extension is the discovery of a large class of isotropic material that display perfect broadband invisibility for arbitrary time-harmonic electromagnetic waves.
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When & where
3.00pm - 4.00pmTuesday 12th March 2019