Critical quantum fluctuations in the degenerate parametric oscillator

The problem of the critical fluctuations at threshold, where the previous perturbation theory, as well as diagrammatic techniques which give divergent results are discussed. It is found that the use of an appropriately rescaled asymptotic perturbation method, using the fundamental cubic stochastic process as the zeroth-order term, gives a well-behaved analytic theory. As such, the results are said to be in complete agreement with numerical simulations in the positive-P representation.