抄録
The dielectric function in a disordered system is discussed in the RPA and using the Klauder-Yonezawa model. It is shown that the “vertex correction” is essential for satisfying general requirements of the dielectric function. The high frequency tail of the optical absorption spectrum is shown to be proportional to ω−3⁄2, contrary to the simple Drude theory ω−2, by virtue of allowance of direct transitions. This conclusion seems to be a natural result for the case that impurity band splits from the conduction band. It should be noted, however, that it is also true for the case that impurity potential is weak and it has no bound state, where the perturbational approach can be thought of as good. Several exact properties of the dielectric function are also investigated and it is shown that the static screening constant is given by the same formula as that of uniform electron gas, which is also true for the case that the Fermi level lies in the impurity band.
