ABSTRACT
An alternative method was developed in the 1960s by Glauber, Haken and others based on the use of the solutions of Fokker-Planck equations (FPE) for quasi-probability distributions. The FPE works well for cases with stable fixed points, but difficulties with some of the quasi-probability distributions became apparent for the critical case. The master equation can be related to the FPE for a quasi-probability distribution by the use of a characteristic function. The characteristic function has the form of a generating function for the quasi-probability distribution. The evolution towards a steady state probability distribution for the Lorenz system provides a fascinating example of the ideas of algorithmic complexity in quantum chaos. Optical bistability has been extensively studied both experimentally and theoretically. Good agreement has been reached between theory and experiment for steady state quantities, but the quantum statistical predictions of the theory are only beginning to be explored in experiment.
