Marco Marletta (Cardiff University)

Essential spectra and spectral pollution for inhomogeneous, anisotropic dissipative Maxwell and Drude-Lorentz systems

Abstract:

Abstract: The methods required to study spectral pollution for dissipative Maxwell (and related) systems turn out to be closely connected to the methods required to study the essential spectrum for such systems. These are very different from the methods used for Schrödinger equations: in particular, the presence of dissipation - e.g. in the form of conductivity - means that the essential spectrum can be changed by changing the coefficients in the system on any arbitrarily small, non-empty open set. Our methods use instead a reduction of the system to a triangular block operator matrix, together with the concept of limiting essential spectrum developed by Sabine Boegli in 2015. We are able to show that any spectral pollution is confined either to the real axis or to a segment of the imaginary axis: any computed eigenvalue whose real and imaginary parts are both non-zero is genuine.