时间色散和耗散系统的谱理论
Spectral Theory of Time Dispersive and Dissipative Systems
摘要：
我们研究线性时间色散和耗散系统。通常这样的系统是不保守的，标准的谱理论不能应用。我们开发了一个数学上一致的框架，允许（i）建设性地确定，如果一个给定的时间色散系统可以扩展到一个保守的;（ii）构建非常保守的系统-这是我们所展示的本质上是唯一的。我们将其应用于时间色散振荡器和阻尼振动器的频谱分析，说明了该方法。特别地，我们得到了色散和有耗介质中的麦克斯韦方程组的一个保守扩展，它等价于原来的麦克斯韦方程组。
英文摘要：
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively determine if a given time dispersive system can be extended to a conservative one; (ii) to construct that very conservative system -- which we show is essentially unique. We illustrate the method by applying it to the spectral analysis of time dispersive dielectrics and the damped oscillator with retarded friction. In particular, we obtain a conservative extension of the Maxwell equations which is equivalent to the original Maxwell equations for a dispersive and lossy dielectric medium.
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