Moment hierarchies and cumulants in quantum optics
Rüdiger Schack, Axel Schenzle · Physical Review A · 1990
Nonlinear problems in quantum optics can be described by an infinite hierarchy of ordinary differential equations for the moments. We discuss different truncation schemes involving cumulants. For illustration the method is applied to second-harmonic generation. We prove that all but second-order cumulants are equal for any quasiprobability distribution ${\mathit{P}}_{\mathit{s}}$, especially for the P, Q, and W functions.