2022/06/15 by Francesco Ferraresso, Marco Marletta, Ferraresso, Francesco +1 · 1 citation
Computer Science · Mathematics · #35P99 #35Q61 #47A56 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2206.07644
openalex publication_date 2022/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We establish spectral enclosures and spectral approximation results for the inhomogeneous lossy Drude-Lorentz system with purely imaginary poles, in a possibly unbounded Lipschitz domain of ℝ3. Under the assumption that the coefficients θe, θm of the material are asymptotically constant at infinity, we prove that: 1) the essential spectrum can be decomposed as the union of the spectrum of a bounded operator pencil in the form - div p(ω) ∇ and of a second order curl curl0 - Ve,∞(ω) pencil with constant coefficients; 2) spectral pollution due to domain truncation can lie only in the essential numerical range of a curl curl0 - f(ω) pencil. As an application, we consider a conducting metamaterial at the interface with the vacuum; we prove that the complex eigenvalues with non-trivial real part lie outside the set of spectral pollution. We believe this is the first result of enclosure of spectral pollution for the Drude-Lorentz model without assumptions of compactness on the resolvent of the underlying Maxwell operator.