论文标题
不均匀的drude-lorentz模型的光谱特性
Spectral properties of the inhomogeneous Drude-Lorentz model with dissipation
论文作者
论文摘要
我们在可能无限的lipschitz域中建立了具有纯粹想象的杆的不均匀损失的drude-lorentz系统的光谱外壳和光谱近似结果。在假设$θ_e$，$θ_m$的材料的假设上是渐近的，我们证明：1）可以将基本频谱分解为有界操作员频谱的结合，形式为$ - \ perpotatornAme {div} p（div} p（div} p（ω） \ operatatorName {curl} _0 -v_ {e，\ infty}（ω）$ pencil具有常数系数； 2）由于域截断而引起的光谱污染只能位于$ \ operatatorName {curl} \ operatatorName {curl} _0 -f（ω）$ pencil的基本数值范围内。作为应用程序，我们考虑在与真空的接口处进行超材料。我们证明，具有非平凡实际部分的复杂特征值在光谱污染的集合之外。我们认为，这是DRUDE-LORENTZ模型的光谱污染围栏的第一个结果，而没有对基础麦克斯韦操作员的分解的假设。
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 $\mathbb{R}^3$. Under the assumption that the coefficients $θ_e$, $θ_m$ 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 $- \operatorname{div} p(ω) \nabla$ and of a second order $\operatorname{curl} \operatorname{curl}_0 - V_{e,\infty}(ω)$ pencil with constant coefficients; 2) spectral pollution due to domain truncation can lie only in the essential numerical range of a $\operatorname{curl} \operatorname{curl}_0 - f(ω)$ 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.
