含自由载流子的时间色散介质介电常数的定义
On the definition of dielectric permittivity for media with temporal dispersion in the presence of free charge carriers
摘要：
我们表明，在存在自由载流子的频率依赖的介电常数的定义需要额外的正则化。作为一个例子，Drude模型的介电常数被认为是其依赖于时间的对应推导和分析。相应的电位移不能用标准傅立叶积分表示。正则化程序允许规避这些困难的建议。为了比较的目的，它表明，频率依赖的绝缘体的介电常数满足所有严格的数学准则。这使我们能够得出结论，在自由载流子的存在下，介电常数的概念并不像绝缘体那样定义明确，我们将其与热卡西米尔力理论中广泛讨论的难题联系起来，这些难题可能是由使用这种介电常数引起的。
英文摘要：
We show that in the presence of free charge carriers the definition of the frequency-dependent dielectric permittivity requires additional regularization. As an example, the dielectric permittivity of the Drude model is considered and its time-dependent counterpart is derived and analyzed. The respective electric displacement cannot be represented in terms of the standard Fourier integral. The regularization procedure allowing to circumvent these difficulties is suggested. For purpose of comparison it is shown that the frequency-dependent dielectric permittivity of insulators satisfies all rigorous mathematical criteria. This permits us to conclude that in the presence of free charge carriers the concept of dielectric permittivity is not as well defined as for insulators and we make a link to widely discussed puzzles in the theory of thermal Casimir force which might be caused by the use of such kind permittivities.
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