标题： 时域约束对于正实函数：被动材料的介电响应应用 显示英文标题

标题： Time-domain constraints for Positive Real functions: Applications to the dielectric response of a passive material

摘要： 本文提出了一种系统的方法，直接在时域（TD）中推导正实（PR）函数的物理界限。该理论基于任意PR函数的Cauer表示以及相关的求和规则（测度的矩），并利用单边拉普拉斯变换来推导被动系统的时域响应的严格界限。有用的求和规则及相关物理界限的存在很大程度上依赖于关于PR函数在高频或低频处至少具有奇数阶渐近展开的假设。作为典型例子，我们研究了被动材料的时域介电阶跃响应，无论是否存在给定的脉冲上升时间。作为一个具体的数值例子，我们考虑了金（Au）的电极化率，它通常由已建立的Drude或Brendel Bormann模型进行建模。然后，以时间的二次函数形式给出了材料早期时间阶跃响应的显式物理界限，该二次函数完全由金属的等离子体频率确定。 显示英文摘要

摘要： This paper presents a systematic approach to derive physical bounds for Positive Real (PR) functions directly in the Time-Domain (TD). The theory is based on Cauer's representation of an arbitrary PR function together with associated sum rules (moments of the measure) and exploits the unilateral Laplace transform to derive rigorous bounds on the TD response of a passive system. The existence of useful sum rules and related physical bounds relies heavily on an assumption about the PR function having a low- or high-frequency asymptotic expansion at least of odd order 1. As a canonical example, we explore the time-domain dielectric step response of a passive material, either with or without a given pulse raise time. As a particular numerical example, we consider here the electric susceptibility of gold (Au) which is commonly modeled by well established Drude or Brendel Bormann models. An explicit physical bound on the early-time step response of the material is then given in terms of a quadratic function in time which is completely determined by the plasma frequency of the metal.