Spectral Approximation for Maxwell's Equations in Conductive Media

Explore the spectral approximation for Maxwell's equations in conductive media in this 29-minute conference talk from the Workshop on "Spectral Theory of Differential Operators in Quantum Theory" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the electromagnetic properties of conductive, anisotropic materials described by Maxwell's equations with non-trivial conductivity. Examine the challenges of spectral approximations in the time-harmonic formulation due to the non-selfadjoint nature of the underlying operator. Discover a new non-convex enclosure for the spectrum of the Maxwell system in possibly unbounded three-dimensional Euclidean space, with minimal assumptions on geometry and coefficients. Investigate the essential spectrum for asymptotically constant coefficients and learn about potential spectral pollution within a subset of the real line. Understand the spectral exactness of the domain truncation method outside a 'singular set'. Gain insights into further developments in the spectral analysis of Maxwell's equations in conductive media with 'anisotropy at infinity'. The talk covers topics such as the classical Maxwell system, operator formulation, essential spectrum, domain truncation, and spectral pollution, based on joint works with S. Bögli, M. Marletta, and C. Tretter.