Higher order rate equations

Abstract

In the preceding chapter electron rate equations of bimolecular form were derived. In this chapter these equations are generalized to include higher order non-linear terms. Such terms occur in rate equations for electrons, phonons, photons, etc., either if many-particle interaction operators are taken into account, or (and) if powers of oneparticle interaction operators are included. The latter case takes place if the transition probabilities (1.5.15) with respect to one-particle interaction operators are evaluated in higher orders. An estimate of the physical consequences of such transitions is, at present, not possible, since for higher order transitions the derivation of rate equations becomes more and more complicated. Hence a rigorous mathematical justification of higher order effects in rate equations starting from first principles seems at present to be extraordinarily hard and has not yet been undertaken. Thus in the following we consider only such interactions which already lead to higher order non-linear terms in the rate equations for first order (resonance) transition probabilities. In particular we concentrate on the electronic many-particle interactions. We will use the same model as in Chapter 3 and in principle the calculations will run along the same lines as in the previous chapter, but the calculation effort will become much greater.