QUANTUM DESCRIPTION OF NONLINEARLY INTERACTING OSCILLATORS VIA CLASSICAL TRAJECTORIES

We investigate systems of few harmonic oscillators with mutual nonline ar coupling. Using classical trajectories-the solutions of Hamiltonian equations of motion for a given nonlinear system-we construct the app roximate quasiprobability distribution function in phase space that en ables a quantum description. The nonclassical effects (quantum noise r eduction) and their scaling laws can be so studied for high excitation numbers. In particular, the harmonic oscillators represent modes of t he electromagnetic field and the Hamiltonians under consideration desc ribe representative nonlinear optical processes (multiwave mixings). T he range of the validity of the approximation for Wigner and Husimi fu nctions evolved within the classical Liouville equation is discussed f or a diverse class of initial conditions, including those without clas sical counterparts, e.g., Fock states.