A simple model for the origin of chaos in semiconductors (Q1105888)

It is shown how a simple model for chaos in semiconductors results from a three-fold argument: (a) One starts with a Chapman-Kolmogorov equation for the generation-recombination processes. These are assumed in the simplest case (considered here) to be uniform in space and to involve only holes. A recurrence relation for the average hole concentration at successive discrete time intervals is derived by averaging the Chapman- Kolmogorov equation. (b) One sets up a generation-recombination rate for a special model. (c) The possibility of chaos then follows by combining (a) and (b) and hence finding a recurrence relation of the type \(x_{k+1}=f(x_ k)\) with quadratic maximum, which is known to produce a period doubling route to chaos.