Four-wave mixing in degenerate atomic gases

We study the process of four-wave mixing (4WM) in ultracold degenerate atomic gases. In particular we address the problem of 4WM in boson-fermion mixtures. We develop an approximate description of such processes using asymptotic analysis of high order perturbation theory taking into account quantum statistics. We perform also numerical simulations of 4WM in boson-fermion mixtures and obtain an analytic and numerical estimate of the efficiency of the process.