Beschreibung:
<jats:p>The exact Markoffian evolution equation for the electron density operator n (t) averaged over impurity configurations (describing a grand ensemble of non-interacting electrons in the potential fields of impurities fixed in space) is not closed. The interaction term, that is, the integral involving the electron-impurity interaction and the electron-impurity density operator is analyzed with the aid of diagrams after its evolution operator is expanded in perturbation and its initial density operators are expanded in terms of correlation operators. A closed non-Markoffian equation for n (t) is obtained without introducing any approximations. This equation contains infinite sets of collision and initial correlation terms which are most conveniently represented by connected diagrams, and which can be expressed in terms of n (t) and initial correlation operators arbitrarily given. The equation is found to be identical with the closed evolution equation obtained earlier in the fixed-particle-number ensemble theory with the bulk limit.</jats:p>