The difference equation approach to steady-state fluctuations in semiconductors

In this paper the fluctuations of electron numbers in a general M -level system are discussed. Using a difference equation in the occupation probability, equations are found for the variances of these fluctuating variables, provided they are small. When certain transitions are excluded from consideration these equations reduce to those derived earlier from the Fokker-Planck equation. The present approach lends itself to the derivation of more general expressions for the variances than have so far been obtained. These are given explicitly for a three-level system in terms of the given transition rates. The results are illustrated by some simple examples.