Table of contents

The theory or percolation models is developed following general ideas in the area of critical phenomena. The review is an exposition of current phase transition theory in a geometrical context. As such, it includes a discussion of scaling relations between critical exponents and their calculation using series expansion methods. Renormalisation group techniques are also considered. The major difference between percolation and other phase transition models is the absence of a Hamiltonian. Instead, the theory is based entirely on probabilistic arguments. A discussion of the connections with classical probability theory is also given.

Measurements on non-classical effects fall into two categories depending on whether the two intensities or photon counts to be correlated refer to a single light beam or to two different beams. The main experimental work in the single-beam case is on resonance fluorescence; the relevant theory is reviewed in some detail, with particular emphasis on the simpler aspects of the calculations. Alternative proposals for generating non-classical single beams by non-linear optical experiments are reviewed more briefly. A similar coverage of double-beam experiments is given, with a detailed account of the theory of non-classical correlations between the light beams generated in two-photon cascade emission, and a briefer survey of corresponding non-linear optical experiments.