A general method is proposed to study non-classical scaling behaviors of cooperative systems. This is based on the appearance of a "coherent anomaly" in mean-field-type or classical approximations of cooperative systems. The degree of approximation is analytically continued to construct a parameterized expression of a whole set of approximations, using Kubo's linear response theory. General relations between scaling (or critical) exponents and "coherent-anomaly exponents" are derived using the theory of envelope and are also obtained from a finite-degree-of-approximation scaling, which is inspired by Fisher's finite-size scaling. The present coherent-anomaly method (CAM) is promising for calculating analytically non-classical scaling exponents in cooperative phenomena. A general scheme of CAM in critical phenomena is presented. It is shown that even the combination of the Weiss and Bethe approximations gives rather good estimates of static and dynamic critical exponents.
This paper is devoted to the study of the cooperative two-photon scattering processes between two resonator modes stimulated by an excited atomic beam. It has been proved that these collective scattering phenomena between the Stokes and anti-Stokes resonator modes are taking place due to the energy transfer between these fields. The statistical properties of the Stokes and anti-Stokes photons have been described using the photon correlation functions. The numerical solution of this equation describes the statistical transformation of n-Stokes photons into anti-Stokes photons.