本构关系的细观计算
Microscopic Calculation of the Constitutive Relations
摘要：
利用均匀化理论，从周期介质的量子微观介电函数计算宏观介电常数。该方法可用于计算任何宏观本构关系，但它是在这里说明的情况下，电动力学的物质。解决了均匀化理论中的所谓胞腔问题，并给出了宏观介电常数的一个类似于克劳修斯-莫索蒂或洛伦兹-洛伦兹关系的显式表达式。通过表明宏观介电常数是因果关系并且具有预期的对称性，并且微观能量密度的平均值是宏观介电常数，来检查该表达式的有效性。最后，将一般表达式应用于Bloch本征态.最后对相应的多体问题作了简要的讨论。
英文摘要：
Homogenization theory is used to calculate the macroscopic dielectric constant from the quantum microscopic dielectric function in a periodic medium. The method can be used to calculate any macroscopic constitutive relation, but it is illustrated here for the case of electrodynamics of matter. The so-called cell problem of homogenization theory is solved and an explicit expression is given for the macroscopic dielectric constant in a form akin to the Clausius-Mossotti or Lorentz-Lorenz relation. The validity of this expression is checked by showing that the macroscopic dielectric constant is causal and has the expected symmetry properties, and that the average of the microscopic energy density is the macroscopic one. Finally, the general expression is applied to Bloch eigenstates. Finally, the corresponding many-body problem is briefly discussed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
