PHASE-SPACE APPROACH TO QUANTUM DYNAMICS

We replace the Schrodinger equation for the time propagation of states of a quantized 2D spherical phase space by the dynamics of a system of N particles lying in phase space. This is done through factorization formulae of analytic function theory arising in coherent-state representation, the 'particles' being the zeroes of the quantum state. For linear Hamiltonians, like a spin in a uniform magnetic field, the motion of the particles is classical. However, nonlinear terms induce interactions between the particles. Their time propagation is studied and we show that, contrary to integrable systems, for chaotic maps they tend to fill, as their classical counterpart, the whole phase space in a uniform way.